Surface-functionalization based authentication elements for authenticating objects and objects and methods using them

Abstract

An authentication element may include molecules where the molecules are arranged to encode at least a portion of an authentication code. The molecules may be polymer chains. The molecules may be polymer chains in a polymer ink. The molecules may be x-ray sensitive. A shape in which the molecules are arranged, for example on a surface to which they are attached, may encode the at least a portion of the authentication code. The molecules may be arranged as a two-dimensional pattern, such as a barcode or QR-code. A method of applying an authentication element includes disposing molecules onto a polymer surface and irradiating at least a portion of the molecules thereby attaching the at least a portion of the molecules to the surface such that the at least a portion of the molecules are arranged in an arrangement corresponding to at least a portion of an authentication code.

Description

Attorney Docket No.: 2019150-0023SURFACE-FUNCTIONALIZATION BASED AUTHENTICATION ELEMENTS FOR AUTHENTICATING OBJECTS AND OBJECTS AND METHODS USING THEMCROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims priority to and benefit of U.S. Provisional Patent Application No. 63 / 703,200 filed October 3, 2024, the disclosure of which is incorporated by reference herein in its entirety.BACKGROUND

[0002] There is an ongoing need to be able to verify the authenticity of objects, especially high-value objects and objects for which there is a desire to track them. For example, it is desirable to be able to verify the authenticity of artworks, antiques, and designer fashion items (e.g., clothing, handbags, and accessories). As another example, it is desirable to be able to verify the authenticity of weapons and ammunition for weapons, in some contexts for valuation purposes (e.g., for collectable weapons) and in some contexts for tracking purposes (e.g., crime solving).

[0003] Current approaches rely on technology, such as Radiofrequency Identification (RFID), that is not suitable for all applications. For example, RFID does not fit on all objects, is usually visible to humans (e.g., such that it can be defeated by removal and / or interferes with aesthetics), can be blocked, and is active (e.g., uses circuitry powered internally or using an internal antenna). Other authentication schemes that are not RFID are often human-visible or require being viewed by a human in order to be used for authentication. Therefore, there is a need for alternative ways to verify authenticity of objects, especially those that are difficult for counterfeiters to circumvent.SUMMARY

[0004] Authentication elements disclosed herein encode at least a portion of an authentication code. Such authentication elements can address one or more problems associated with conventional authentication schemes, like RFID. For example, authentication elements disclosed herein may be invisible to an unaided human viewer, may be readable when covered and / or embedding in an object, may be readable when disposed inside an opaque outer container, may be irremovable from being associated with an object (e.g., irremovable from the object or a label affixed to an object), or a combination thereof. Therefore, it may be harder (or impossible) Page 1 of 21213013588vlAttorney Docket No.: 2019150-0023 to defeat authentication schemes that use one or more authentication elements disclosed herein than it is to defeat conventional security schemes, such as RFID-based schemes. Similarly, authentication elements disclosed herein may be hard to duplicate thereby being less susceptible to counterfeiting. Moreover, some such authentication elements disclosed herein can be read inline, such as during an existing logistics process for shipping, sorting, and / or storing objects. In some embodiments, an authentication element is readable using commercially available equipment, such as an x-ray, CT, or MRI machine with a conveyor belt, thereby facilitating easy integration into existing processes. Examples of such processes include a logistics process, such as a sorting process, a routing process, a shipping process, a warehouse process, and / or a distribution process. Authentication elements disclosed herein may be used to determine whether one or more objects is authentic or inauthentic (e.g., fraudulent and / or counterfeit).

[0005] Authentication elements may be physically associated with objects in order to authenticate the objects. An authentication element encodes at least a portion of an authentication code, for example using one or more encoding portions, such as radiopaque and / or soundattenuating encoding portion(s). In some embodiments, an authentication element is readable using x-rays, radio waves, sound waves, magnetization, or a combination thereof. An authentication code may be known only to a certain individual or organization. An authentication code may be distinct in some manner, for example, may be unique or correspond to a certain individual or organization. In some embodiments, a composite authentication element is used, for example, for a set of objects where each object is physically associated with a distinct portion of the composite authentication element. An authentication element (or composite authentication element) may be a passive element, for example that does not contain any circuitry and / or antenna. Using circuitry and / or antenna as part of an authentication element, such as with RFID, can require using larger sizes and / or more complex manufacturing, leading to increased costs and reduced versatility. In some embodiments, an authentication element may be able to be read to determine an authentication code, for example using only that information which is readable from the authentication element or in combination with other information (e.g., another portion of the authentication code or a key), in order to verify authenticity of an object.

[0006] An object may be physically associated with an authentication element. For example, an object may include an authentication element, for example embedded in the object, integrated with the object, or disposed on an interior or exterior surface of the object. As anotherPage 2 of 21213013588vlAttorney Docket No.: 2019150-0023 example, an authentication element may be included in a label affixed to (e.g., adhered to) an object. An object may be disposed inside of an outer container. In some embodiments, an authentication element physically associated with an object can be read to determine an authentication code, at least a portion of which is encoded by the authentication element. In some embodiments, such reading occurs while the object is inside of an outer container (e.g., packaging), for example secured in the outer container. Accordingly, authentication elements as disclosed herein may be physically associated with objects and used to verify authenticity of the objects.

[0007] Additional security may be provided based on the manner in which an authentication element is physically associated with an object. For example, a tamper-proof mechanism (e.g., seal) may be included an authentication element. In some embodiments, tampering with a tamper-proof mechanism renders an authentication element unable to be read, for example damages or destroys (e.g., tears) the authentication element. Additionally or alternatively, a tamper-proof mechanism, such as a lock or seal, may be used for an outer container inside of which an object is disposed, to prevent unauthorized or surreptitious access to an object or authentication element associated therewith. In some embodiments, a location and / or orientation of one or more authentication elements, relative to the object and / or relative to each other, provides additional security for one or more objects. For example, an authentication element disposed in an incorrect location, disposed an incorrect distance from another authentication element, and / or incorrectly oriented may mean that the authentication element is inauthentic (e.g., fraudulent and / or counterfeit), whether or not an authentication code determined using information read from the authentication element would otherwise verify authenticity or not.

[0008] In some embodiments, the present disclosure is directed to an object that can be authenticated. The object may be physically associated with a passive authentication element that encodes at least a portion of an authentication code, for example encodes an entire authentication code.

[0009] In some embodiments, the present disclosure is directed to a passive authentication element that encodes at least a portion of an authentication code, for example encodes an entire authentication code.

[0010] In some embodiments, the present disclosure is directed to a method of verifying authenticity of an object. The method may include receiving an authentication code for an object that has been obtained, at least in part, by reading a passive authentication element. The passivePage 3 of 21213013588vlAttorney Docket No.: 2019150-0023 authentication element may be physically associated with, for example included in, the object that encodes at least a portion of the authentication code. The method may include verifying authenticity of the object using the authentication code. In some embodiments, the authentication code is an alphanumeric string, passcode, password, or passphrase.

[0011] In some embodiments, the present disclosure is directed to a method of verifying authenticity of an object. The method may include receiving information potentially corresponding to an authentication code for an object. At least a portion of the information may have been obtained by reading a passive authentication element. The passive authentication element may be physically associated with (e.g., in or on) the object. The method may further include determining whether the information sufficiently corresponds to the authentication code. For example, the method may include determining that the information at least approximates (e.g., matches) the authentication code. The method may include determining that the information could not correspond to any other authentication code.

[0012] In some embodiments, the present disclosure is directed to a system of contained authenticatable objects. The system may include an (e.g., enclosed) outer container. The system may include objects removably disposed in (e.g., inside) the outer container. The system may further include a composite authentication element encoding at least a portion of an authentication code. In some embodiments, each of the objects is physically associated with (e.g., includes) a distinct portion of the composite authentication element. In some embodiments, the composite authentication element can be read (e g., to determine the authentication code) through the outer container. The composite authentication element may be able to be read without accessing inside of the outer container.

[0013] In some embodiments, the present disclosure is directed to a system of an authenticatable object. The system may include an (e.g., enclosed) (e g., opaque) outer container. The system may further include an object removably disposed in (e.g., inside) the outer container. An authentication element encoding at least a portion of an authentication code physically associated with the object. In some embodiments, the object includes distinct portions of the authentication element each disposed in or on a different portion of the object. In some embodiments, the authentication element is readable without accessing the outer container based on the object being distorted in a particular manner.Page 4 of 21213013588vlAttorney Docket No.: 2019150-0023

[0014] In some embodiments, the present disclosure is directed to a system for contained authenticatable objects. The system may include an (e.g., enclosed) outer container. The system may further include an object removably disposed in (e.g., inside) the outer container. In some embodiments, the object includes an authentication element encoding at least a portion of an authentication code (e.g., an entire authentication code). In some embodiments, the authentication element can be read (e.g., to determine the authentication code) without accessing inside of the outer container.

[0015] In some embodiments, the present disclosure is directed to a method of authenticating objects. The method may include providing a system. The system may include (i) an outer container (e.g., an opaque outer container), (ii) objects removably disposed in (e.g., inside) the outer container, and (iii) a composite authentication element encoding at least a portion of an authentication code, wherein each of the objects is physically associated with (e.g., includes) a portion (e.g., a distinct portion) of the composite authentication element. The method may further include reading the composite authentication element through the outer container. In some embodiments, the reading happens without accessing inside of the outer container.

[0016] In some embodiments, the present disclosure is directed to a method of authenticating objects. The method may include providing a system that includes (i) an outer container (e.g., an opaque outer container), (ii) one or more objects removably disposed in (e.g., inside of) the outer container, and (iii), for each of the one or more objects, an authentication element physically associated with the object that encodes at least a portion of an authentication code. The method may further include reading the authentication element through the outer container (e.g., without accessing inside of the outer container).

[0017] In some embodiments, the present disclosure is directed to a method for registering a fingerprint of an object. The method may include receiving an object physically associated with an authentication element. The method may further include obtaining a fingerprint of the authentication element. The method may further include registering the fingerprint with the obj ect in a registry.

[0018] In some embodiments, the present disclosure is directed to a method of verifying authenticity of an object. The method may include obtaining a comparative fingerprint for an authentication element physically associated with an object. The method may further include receiving, from a registry, a copy of an authentic fingerprint for the object, wherein the object hasPage 5 of 21213013588vlAttorney Docket No.: 2019150-0023 been registered with the registry. The method may further include verifying authenticity of the object by, at least in part, comparing the comparative fingerprint to the authentic fingerprint.

[0019] In some embodiments, the present disclosure is directed to a passive cipher element. The passive cipher element may encode a cipher key, for example for an encrypted authentication code (e.g., corresponding to an object).

[0020] In some embodiments, the present disclosure is directed to a plurality of cipher elements. The cipher elements may encode a cipher key for an encrypted authentication code (e.g., corresponding to an object). The cipher elements may each encode a different cipher key of a set of cipher keys corresponding to an encrypted authentication code (e.g., for an object).

[0021] In some embodiments, the present disclosure is directed to a method of determining authenticity of an object. The method may include reading a cipher element physically associated with an object to determine a cipher key. The method may further include decrypting an encrypted authentication code for the object using the cipher key. The method may further include determining that the object is authentic based on the decrypted authentication code.

[0022] In some embodiments, the present disclosure is directed to a system that includes an enclosed outer container, objects removably disposed in the outer container, and a composite cipher element encoding a cipher key for an encrypted authentication code corresponding to the objects. Each of the objects may be physically associated with (e.g., includes) a distinct portion of the composite cipher element and the composite cipher element can be read (e.g., to determine the cipher key) through the outer container (e.g., without accessing inside of the outer container).

[0023] In some embodiments, the present disclosure is directed to a system that includes an enclosed outer container, an object removably disposed in the outer container. The object may include a cipher element encoding a cipher key for an encrypted authentication code. The authentication code may correspond to the object. The cipher element may be able to be ready (e.g., to determine the cipher key) without accessing inside of the outer container.

[0024] Any two or more of the features described in this specification, including in this summary section, may be combined to form implementations of the disclosure, whether specifically expressly described as a separate combination in this specification or not.Page 6 of 21213013588vlAttorney Docket No.: 2019150-0023BRIEF DESCRIPTION OF THE DRAWINGS

[0025] The patent or application file contains at least one drawing executed in color. Copies of this patent or patent application publication with color drawing(s) will be provided by the Office upon request and payment of the necessary fee.

[0026] The present teachings described herein will be more fully understood from the following description of various illustrative embodiments, when read together with the accompanying drawings. It should be understood that the drawing described below is for illustration purposes only and is not intended to limit the scope of the present teachings in any way. The foregoing and other objects, aspects, features, and advantages of the disclosure will become more apparent and may be better understood by referring to the following description taken in conjunction with the accompanying drawings, in which:

[0027] Fig. 1 illustrates an example of an authentication element, according to illustrative embodiments of the present disclosure;

[0028] Fig. 2A illustrates an example of an authentication element, according to illustrative embodiments of the present disclosure;

[0029] Fig. 2B illustrates an example of an authentication element, according to illustrative embodiments of the present disclosure;

[0030] Fig. 2C illustrates an example of an authentication element, according to illustrative embodiments of the present disclosure;

[0031] Fig. 2D illustrates an example of an authentication element, according to illustrative embodiments of the present disclosure;

[0032] Fig. 3 A illustrates an example of an authentication element, according to illustrative embodiments of the present disclosure;

[0033] Fig. 3B illustrates an example of an authentication element, according to illustrative embodiments of the present disclosure;

[0034] Fig. 3C illustrates an example of an authentication element, according to illustrative embodiments of the present disclosure;

[0035] Fig. 3D illustrates an example of an authentication element, according to illustrative embodiments of the present disclosure;

[0036] Fig. 4A is a brightfield image of an example of an authentication element, according to illustrative embodiments of the present disclosure;Page 7 of 21213013588vlAttorney Docket No.: 2019150-0023

[0037] Fig. 4B is an x-ray image of an authentication element, according to illustrative embodiments of the present disclosure;

[0038] Fig. 5A illustrates an exemplary visibility-enhancing system including an item including at least one visibility-enhancing element, according to illustrative embodiments of the present disclosure;

[0039] Fig. 5B illustrates an exemplary visibility-enhancing system including an item including at least one visibility-enhancing element, according to illustrative embodiments of the present disclosure;

[0040] Figs. 5C-D illustrate views of a purse physically associated with an authentication element, according to illustrative embodiments of the present disclosure;

[0041] Fig. 6 illustrates an exemplary visibility-enhancing system including an item including at least one visibility-enhancing element, according to illustrative embodiments of the present disclosure;

[0042] Fig. 7A illustrates an exemplary visibility-enhancing system including an item including at least one visibility-enhancing element, according to illustrative embodiments of the present disclosure;

[0043] Fig. 7B shows an example of a cross section of the item including the authentication element, according to illustrative embodiments of the present disclosure;

[0044] Fig. 8A shows multiple examples of items including authentication elements, according to illustrative embodiments of the present disclosure;

[0045] Fig. 8B shows x-ray images of the items including authentication elements of Fig. 8A;

[0046] Fig. 9A illustrates an exemplary visibility-enhancing system including at least one item including at least one visibility-enhancing element, according to illustrative embodiments of the present disclosure;

[0047] Fig. 9B illustrates an exemplary visibility -enhancing system including at least one item including at least one visibility-enhancing element, according to illustrative embodiments of the present disclosure;

[0048] Fig. 9C illustrates an exemplary visibility -enhancing system including at least one item including at least one visibility-enhancing element, according to illustrative embodiments of the present disclosure;Page 8 of 21213013588vlAttorney Docket No.: 2019150-0023

[0049] Fig. 10 illustrates an exemplary visibility-enhancing system including an item including at least one visibility-enhancing element, according to illustrative embodiments of the present disclosure;

[0050] Fig. 11 illustrates an exemplary visibility-enhancing system including an item including at least one internal component including at least one visibility-enhancing element, according to illustrative embodiments of the present disclosure;

[0051] Fig. 12 illustrates an exemplary visibility-enhancing system including at least one item including at least one internal component including at least one visibility-enhancing element, according to illustrative embodiments of the present disclosure;

[0052] Fig. 13 shows an example of an authentication system including predefined locations for an authentication element, according to illustrative embodiments of the present disclosure;

[0053] Fig. 14A shows an example of an authentication system including an outer container and an inner object, according to illustrative embodiments of the present disclosure;

[0054] Fig. 14B shows an example of an authentication system including an outer container and multiple inner objects, according to illustrative embodiments of the present disclosure;

[0055] Fig. 14C shows an example of an authentication system including an outer container and multiple inner objects, according to illustrative embodiments of the present disclosure;

[0056] Fig. 14D shows examples of multiple inner objects, according to illustrative embodiments of the present disclosure;

[0057] Fig. 15 shows an example of an authentication system including an outer container and multiple inner objects, according to illustrative embodiments of the present disclosure;

[0058] Fig. 16 shows an exemplary setup to authenticate an object, according to illustrative embodiments of the present disclosure;

[0059] Fig. 17 illustrates a flow diagram of an exemplary method, according to illustrative embodiments of the present disclosure;

[0060] Fig. 18 is a block diagram of an example network environment for use in the methods and systems described herein, according to illustrative embodiments of the present disclosure;Page 9 of 21213013588vlAttorney Docket No.: 2019150-0023

[0061] Fig. 19 is a block diagram of an example computing device and an example mobile computing device, for use in illustrative embodiments of the present disclosure;

[0062] FIG. 20A illustrates an example of an individual polymer chain, according to illustrative embodiments of the present disclosure;

[0063] FIG. 20B illustrates an example of an individual polymer chain, according to illustrative embodiments of the present disclosure;

[0064] FIG. 20C illustrates an example of an individual polymer chain, according to illustrative embodiments of the present disclosure;

[0065] FIG. 21 A illustrates an example of a polymer portion including multiple individual polymer chains, according to illustrative embodiments of the present disclosure;

[0066] FIG. 2 IB illustrates an example of a polymer portion including multiple individual polymer chains, according to illustrative embodiments of the present disclosure;

[0067] FIG. 21C illustrates an example of a polymer portion including multiple individual polymer chains, according to illustrative embodiments of the present disclosure;

[0068] Fig. 22A illustrates an example of a polymer surface coated with a polymer, according to illustrative embodiments of the present disclosure;

[0069] Fig. 22B illustrates an example of a polymer surface coated with a polymer, according to illustrative embodiments of the present disclosure;

[0070] Fig. 23 illustrates an exemplary method of forming a fabric that is coated with a polymer, according to illustrative embodiments of the present disclosure;

[0071] Fig. 24A is a flow chart diagram of a method of manufacturing an authentication element using polymer chains, according to illustrative embodiments of the present disclosure; and

[0072] Fig. 24B is a flow chart diagram of a method of manufacturing an authentication element using polymer chains, according to illustrative embodiments of the present disclosure.DETAILED DESCRIPTION OF CERTAIN EMBODIMENTS

[0073] Disclosed herein are, inter alia, passive authentication elements that are imageable with at least one (non-visible-wavelength) imaging modality, such as one using x-rays, radio waves, sound waves, or more than one of these. Passive authentication elements may be used in authenticating objects. In some embodiments, an authentication element encodes at least a portion of an authentication code. (A portion of an authentication code may itself be an authenticationPage 10 of 21213013588vlAttorney Docket No.: 2019150-0023 code.) In some embodiments, an authentication element encodes an authentication code. In some embodiments, an authentication element encodes an entire authentication code. In some embodiments, an authentication element encodes a complete authentication code. An authentication code may correspond to a particular person or organization (e.g., company). An authentication code may be unique. In some embodiments, an authentication code is only used for one object and never reused. A same authentication code may be used for objects of a same type (e.g., manufacturer and / or model). An authentication element may encode a distinct portion of an authentication code. An authentication element may be a portion of an object.Authentication Elements

[0074] Authentication elements disclosed herein (e.g., that include one or more encoding portions that are radiopaque and / or attenuate sound waves to encode at least a portion of an authentication code) may be located covertly. For example, an authentication element can be covered, embedded in an object, disposed internally to an object, disposed on or in an interior of an object, or disposed on or in an internal component of an object and still be used for authentication purposes. Such authentication elements need not be physically viewable by an unaided human viewer in order for an object to be authenticated.

[0075] Authentication elements disclosed herein may alternatively or additionally be of a size or construction such that they are not visible to an unaided human viewer (e.g., would not be recognized under reasonable scrutiny). For example, they may be too small to be noticeable or may be made of materials that make any encoded information undiscernible without magnification and / or viewed using the appropriate probe waves (e.g., using the appropriate imaging modality or modalities). Moreover, certain manners of encoding information may make an authentication element appear uniform unless viewed in the appropriate manner (e.g., magnification and / or imaging modality). For example, color of an authentication element in the visible spectrum may appear uniform but radiodensity varies. In some embodiments, at least a portion of an authentication code is encoded by an authentication element using one or more optically clear encoding portions, for example that include (e.g., are formed by) optically clear but radiodense ink or dye. Therefore, even if theoretically visible (e.g., because it is disposed on an exposed surface of an object), a viewer (e.g., prospective counterfeiter) may not appreciate that an authentication element is present. One or more non-encoding portions of an authentication element may bePage 11 of 21213013588vlAttorney Docket No.: 2019150-0023 selected to hide that at least a portion of an authentication code is encoded by an authentication element (e.g., selected to have a similar visible color).

[0076] In some embodiments, an authentication element encodes at least a portion of multiple authentication codes (e.g., corresponding to different persons and / or organizations). An authentication element may encode at least a portion of one authentication code or at least a portion of each of multiple authentication codes. Multiple authentication codes in an authentication element may correspond to, for example, different person(s), organization(s), and / or component(s) within an object. An authentication element may encode multiple copies of at least a portion of an authentication code (e.g., multiple copies of an authentication code). For example, an authentication element may encode multiple copies of at least a portion of an authentication code along its length. An authentication element may encode multiple copies of at least a portion of an authentication code periodically (e.g., with or without any spacing between the copies, whether or not a start point and / or end point of each copy is indicated). An authentication element may encode multiple copies of at least a portion of an authentication code with or without any spacing between the copies (e.g., whether or not a start point and / or end point of each copy is indicated). An authentication element may encode at least a portion of an authentication code repeatedly (e.g., along its length). Encoding multiple copies of at least a portion of an authentication code by an authentication element may allow for easy reading of the authentication element, for example reducing sensitivity to position and / or orientation of the authentication element when performing the reading and / or allowing different portions of the authentication element to be read without needing to read a particular portion.

[0077] An authentication element may be physically associated with an object. For example, an authentication element may be embedded in, woven into, incorporated into, embroidered into, stitched into, braided into, integrated with, disposed on or in, and / or printed onto or into an object. As other examples, an authentication element physically associated with an object may be embedded in, woven into, incorporated into, embroidered into, stitched into, braided into, integrated with, disposed on or in, and / or printed onto or into packaging of the object. Such packaging may be tamper-proof. As other examples, an authentication element physically associated with an object may be embedded in, woven into, incorporated into, embroidered into, stitched into, braided into, integrated with, disposed on or in, and / or printed onto or into a labelPage 12 of 21213013588vlAttorney Docket No.: 2019150-0023 that is affixed to (e.g., adhered to) the object or (e.g., tamper-proof) packaging for the object. An authentication element physically associated with an object may be a portion of the object.

[0078] An authentication element may encode at least a portion of an authentication code using one or more encoding portions. An encoding portion may be radiopaque and / or soundattenuating. An encoding portion may be readable using x-rays, radio waves (e.g., in combination with a magnetic field), sound waves, or a combination thereof (more than one of these). An encoding portion may produce signal in response to x-rays, radio waves (e.g., in combination with a magnetic field), sound waves, or a combination thereof. For example, an encoding portion may produce signal by absorption, attenuation, absorption and emission (e.g., down-conversion) (e.g., of a different characteristic particle or signal from an excitation particle or signal, for example fluorescence), reflection, refraction, or a combination thereof. For example, different produced signal may result in different contrast being visible in an image (e.g., a human-readable image). An encoding portion may be readable using an imaging modality, such as, for example, x-ray (e.g., dual-energy x-ray absorptiometry), computed tomography, magnetic resonance imaging, ultrasound, or a combination thereof (more than one of these). An authentication element may be readable using x-rays, radio waves (e.g., in combination with a magnetic field), sound waves, or a combination thereof (more than one of these) such that at least a portion of an authentication code can be determined from the authentication element (e.g., one or more encoding portions thereof). For example, x-ray imaging (e.g., dual-energy x-ray absorptiometry), magnetic resonance imaging (MRI), computed tomography (CT), and / or sonography (e.g., ultrasound) may be used to read an authentication element or one or more encoding portions. An authentication element may be readable only in one or more non-visible imaging modalities (e.g., CT, x-ray, MRI, and / or ultrasound).

[0079] An encoding portion may be radiopaque (e.g., to x-rays and / or radio waves) and / or attenuate sound waves. For example, an encoding portion may be a radiopaque thread, a radiopaque wire, a radiopaque string, a radiopaque cord, a radiopaque fiber, or a radiopaque filament. For example, an encoding portion may be a thread, a wire, a string, a cord, a fiber, or a filament that attenuates sound. An encoding portion may include one or more radiopaque contrasting agents, one or more metallic elements (for example, including gold and / or stainless steel), one or more radiopaque particles, one or more radiopaque dyes, one or more radiopaque inks (e.g., metallic ink(s)), one or more radiopaque pigments, or a combination thereof. AnPage 13 of 21213013588vlAttorney Docket No.: 2019150-0023 encoding portion may include one or more contrasting agents, one or more metallic elements (for example, including gold and / or stainless steel), one or more particles, one or more dyes, one or more inks (e.g., metallic ink(s)), one or more pigments, or a combination thereof that attenuate sound. In some embodiments, an encoding portion is optically clear. In some embodiments, an encoding portion includes one or more optically-clear radiopaque dyes, one or more optically-clear radiopaque inks, one or more optically-clear radiopaque pigments, or a combination thereof. In some embodiments, an encoding portion includes two (e.g., optically clear) radiopaque species (e.g., inks, dyes, pigments, or a combination thereof) of different radiodensities. For example, gadolinium, iodine, an oxide (e.g., iron oxide or titanium dioxide), barium (e.g., as barium sulfate), manganese salt (e.g., manganese chloride), aluminum, bismuth (e.g., elemental bismuth and / or as bismuth oxychloride or bismuth trioxide), titanium, or a combination thereof may be used in an encoding portion. A portion of an authentication element may be radiopaque (e.g., to x-rays and / or radio waves) and / or attenuate sound waves. Radiopaque does not necessarily mean that all incident x-rays and / or radio waves are blocked (e.g., absorbed). A sound-attenuating encoding portion may be discernable in an imaging modality that uses sound waves based on how the encoding portion attenuates sound waves. In some embodiments, an entirety of a fiber or filament (e.g., along its entire length and / or cross sectional area) of an encoding portion is radiopaque and / or sound attenuating. For example, an encoding portion may be a fiber or filament made of gold or stainless steel (e.g., that is braided into an authentication element or used as a core of a thread or fiber of an authentication element). An encoding portion may be discernable (e.g., against background) in CT imaging, MRI imaging, x-ray imaging (e.g., fluoroscopy or two-energy x-ray absorptiometry imaging), or sonography (e.g., ultrasound imaging). An encoding portion may be visible only in one or more non-visible imaging modalities (e.g., CT, x-ray, MRI, and / or ultrasound) (e.g., not visible under any visible wavelength imaging modality).

[0080] An encoding portion may include a radiopaque ink, pigment and / or dye, for example integrated with a filament or fiber. An encoding portion may include particles integrated with, for example embedded in, a filament or fiber. An encoding portion may be incorporated in an authentication element. An encoding portion may be integrated into an authentication element. An encoding portion may be, for example, one or more particles or one or more dyes, inks, and / or pigments (e.g., one or more fluorophores) disposed in or on a thread, string, fiber, cord, wire, or filament. Certain materials, such as ultrahigh molecular weight polyethylene, are hard to coatPage 14 of 21213013588vlAttorney Docket No.: 2019150-0023 and / or impregnate with dye, ink, or pigment, and therefore it may be preferrable to use particles integrated with (e.g., embedded in) such material. Such incorporation may occur through an extrusion, printing, or spinning (e.g., electrospinning) process of forming material (e.g., a polymer fiber or filament). Such incorporation may occur post formation, for example after a polymer fiber or filament has been formed or after a thread or fiber made of more than one fiber and / or more than one filament (e.g., braided together) has been formed. Such incorporation may occur during braiding of fibers and / or threads. An encoding portion may be formed using compounding, for example of particles with a matrix (e.g., polymer), for example thereby resulting in a radiopaque and / or sound attenuating fiber or filament. The use of embedding or weaving or braiding may be preferable for a material because incorporating encoding portion would be difficult or impossible.

[0081] In some embodiments, an authentication element includes one or more encoding portions that are radiopaque such that the one or more encoding portions are discernable against background (e.g., an object and / or label) using x-rays and / or radio waves (e.g., in x-ray and / or MRI, respectively). In some embodiments, an authentication element includes one or more encoding portions that attenuate sound waves such that the one or more encoding portions are discernable against background (e.g., an object and / or label) using sound waves (e.g., in a sonography modality). In some embodiments, an authentication element includes one or more encoding portions that enhance visibility in one or more imaging modalities. In some embodiments, an authentication element includes a first encoding portion that is radiopaque such that it is discernable from a second radiopaque encoding portion included in the authentication element using x-rays and / or radio waves, for example based on wavelength and / or intensity. In some embodiments, an authentication element includes a first encoding portion that attenuates sound waves such that, using sound waves, it is discernable from a second encoding portion included in the authentication element that attenuates sound waves. An encoding portion may have variable radiodensity or constant radiodensity (or variable attenuation or constant attenuation to sound waves). An encoding portion may have variable attenuation of sound waves or constant attenuation of sound waves.

[0082] An authentication element may encode at least a portion of an authentication code using, for example, one or more contrasting agents, one or more particles, one or more metallic elements, one or more dyes, one or more fluorophores, one or more inks (e.g., metallic ink(s)), one or more threads (e.g., one or more monofilament threads, one or more multi-filament threads, or aPage 15 of 21213013588vlAttorney Docket No.: 2019150-0023 combination thereof), one or more fibers (e.g., one or more monofilament fibers, one or more multi-filament fibers, or a combination thereof), one or more filaments, one or more wires, one of more strings, one or more cords, one or more ribbons, or a combination thereof. An encoding portion of an authentication element may be, for example, one or more contrasting agents, one or more particles, one or more metallic elements, one or more dyes, one or more fluorophores, one or more inks (e.g., metallic ink(s)), one or more threads (e.g., one or more mono-filament threads, one or more multi -filament threads, or a combination thereof), one or more fibers (e.g., one or more mono-filament fibers, one or more multi-filament fibers, or a combination thereof), one or more filaments, one or more wires, one or more strings, one or more cords, or one or more ribbons. For example, gadolinium, iodine, an oxide (e.g., iron oxide or titanium dioxide), barium (e.g., as barium sulfate), manganese salt (e.g., manganese chloride), aluminum, bismuth (e.g., elemental bismuth and / or as bismuth oxychloride or bismuth trioxide), titanium, or a combination thereof may be used in an authentication element (e.g., one or more encoding portions thereof). In some embodiments, an authentication element encodes at least a portion of an authentication code using one or more optically-clear radiopaque dyes, one or more optically-clear radiopaque inks, or both. In some embodiments, an authentication element encodes at least a portion of an authentication code using two (e.g., optically clear) radiopaque species (e.g., inks, dyes, or an ink and a dye) of different radiodensities. Such different radiodensity materials may be able to be distinguished during imaging (e.g., x-ray imaging, such as dual -energy x-ray absorptiometry). An authentication element may encode at least a portion of an authentication code using one or more fibers that are braided into a thread (e.g., with or without one or more other fibers). An authentication element, such as a thread, filament, or fiber, may include one or more polymer materials, such as one or more silicones, one or more nylons, one or more polyethylenes (e.g., ultra-high-molecular-weight polyethylene (UHMWPE)), one or more polypropylenes, one or more polyesters, one or more polytetrafluoroethylenes (PTFEs), or a combination thereof. An encoding portion may be a tracer line. An authentication element may encode at least a portion of an authentication code using a single encoding portion, for example a single filament or single fiber.

[0083] An encoding portion may be embedded in an authentication element. An encoding portion may be woven into an authentication element. An encoding portion may be embroidered into an authentication element. An encoding portion may be braided into an authentication element. For example, an authentication element may be or include a single filament that is anPage 16 of 21213013588vlAttorney Docket No.: 2019150-0023 encoding portion that encodes at least a portion of an authentication code that is braided, woven, and / or embroidered into the authentication element. For example, an authentication element may be or include a multifilament fiber where one or more of the filaments in the fiber are encoding portion(s) that encode at least a portion of an authentication code. A multifilament authentication element may include a core (e.g., including one or more filaments) and / or a sheath (e.g., itself including one or more filaments) and, optionally, the core and / or the sheath may (each) include one or more encoding portions. An encoding portion may be or include filament, thread, or fiber that is braided. One or more encoding portions may be included in a braiding pattern of an authentication element, for example a braiding pattern of a sheath, a braiding pattern of a core, or both. For example, one or more encoding portions that is (are) filament(s) may be braided with one or more filament(s) that are not encoding portions, for example as a sheath or core of a fiber or thread. Relative position of one or more encoding portions in a braiding pattern for an authentication element may encode at least a portion of an authentication code.

[0084] For example, an authentication element may be or include a multifilament fiber including a core where the core is an encoding portion that encodes at least a portion of an authentication code. For example, an authentication element may be or include a multifilament fiber where the sheath is encoding portion(s) that encode at least a portion of an authentication code. For example, an authentication element may be or include a multifilament fiber where the core and the sheath are encoding portion(s) that encode at least a portion of an authentication code. An authentication multifilament fiber include an alternating pattern of filaments that are encoding portions and filaments that are non-encoding portions. For example, an authentication element may be or include a multifilament fiber where the core and / or the sheath include an alternating pattern of filaments that are encoding portions and filaments that are non-encoding portions. For example, the core and the sheath may include similar alternating pattern. For example, the core and the sheath may include different alternating patterns. For example, an authentication element may be or include a single fiber thread that is encoding portion(s) that encode at least a portion of an authentication code. For example, an authentication element may be or include a multifiber thread where one or more of the fibers in the thread are encoding portion(s) that encode at least a portion of an authentication code. Such a multifilament or multifiber authentication element may include a core (e.g., including one or more filaments or one or more fibers, respectively) and / or a sheath (e.g., including one or more filaments or one or more fibers, respectively) (e.g., may bePage 17 of 21213013588vlAttorney Docket No.: 2019150-0023 coreless). For example, an authentication element may be or include a multifiber thread where the core is encoding portion(s) that encode at least a portion of an authentication code. For example, an authentication element may be or include a multifiber thread where the sheath is encoding portion(s) that encode at least a portion of an authentication code. For example, an authentication element may be or include a multifiber thread where the core and the sheath are encoding portion(s) that encode at least a portion of an authentication code. An authentication multifiber thread include an alternating pattern of fibers that are encoding portions and fibers that are non-encoding portions. For example, an authentication element may be or include a multifiber thread where the core and / or the sheath include an alternating pattern of fibers that are encoding portions and fibers that are non-encoding portions. The core and the sheath may, for example, include similar alternating pattern. The core and the sheath may, for example, include different alternating patterns.

[0085] An authentication element may encode at least a portion of an authentication code using one or more braided elements (e.g., radiopaque braided element(s)). An encoding portion may be a braided element. An authentication element may encode at least a portion of an authentication code using one or more woven elements (e.g., radiopaque woven element(s)). An encoding portion may be a woven element. In some embodiments, an encoding portion is or is included in a core of an authentication element (e.g., a core of a fiber or thread). In some embodiments, an encoding portion is or is included in a sheath of an authentication element (e.g., a sheath of a fiber or thread) (e.g., whether or not a core is present).

[0086] An encoding portion may have different radiodensity (whether variable or constant) than other material in an authentication element (e.g., other fiber(s) and / or filament(s)) and / or an object. In some embodiments, a radiopaque portion of an authentication element (e.g., an encoding portion) has a radiodensity that is at least l. lx, at least 1.2x, at least 1.3x, at least 1.4x, at least 1.5x, at least 2x, at least 3x, at least 4x, at least 5x, or at least lOx a radiodensity of an object physically associated with the authentication element. In some embodiments, a radiopaque portion of an authentication element (e.g., an encoding portion) has a radiodensity that is at least l.lx, at least 1.2x, at least 1.3x, at least 1.4x, at least 1.5x, at least 2x, at least 3x, at least 4x, at least 5x, or at least lOx a radiodensity of a label that includes the authentication element. In some embodiments, a radiopaque portion of an authentication element (e.g., an encoding portion) has a radiodensity that is at least l.lx, at least 1.2x, at least 1.3x, at least 1.4x, at least 1.5x, at least 2x,Page 18 of 21213013588vlAttorney Docket No.: 2019150-0023 at least 3x, at least 4x, at least 5x, or at least l Ox a radiodensity of a label that includes the authentication element and a radiodensity of an object that the label is physically associated with.

[0087] In some embodiments, an authentication element includes one or more portions that indicate a start point and / or end point of the at least a portion of an authentication code encoded in the authentication element (e.g., of an authentication code). In some embodiments, an authentication element includes one or more portions that encode information indicating a start point and / or end point of the at least a portion of an authentication code encoded in the authentication element (e.g., of an authentication code). In some embodiments, an authentication element includes one or more portions that encode information indicating a start point and / or end point of a region of an authentication element that encodes at least a portion of an authentication code (e.g., that encodes an authentication code). For example, one or more portions indicating a start point may precede a portion of an authentication element that corresponds to (e g., encodes) a first character in an authentication code. For example, one or more portions indicating an end point may succeed a portion of an authentication element that corresponds to (e.g., encodes) a last character in an authentication code.

[0088] In some embodiments, different encoding portions of an authentication element are spatially separated from each other such that different portions (e.g., characters) of an authentication code are discretely encoded in an authentication element. For example there may be blank space in an authentication element in which no encoding portion is present between portions of the authentication element. The size, shape, and / or spacing (e.g., pattern of spacings) of such blank space (that is, the size, shape, and / or spacing between distinct encoding portions) may itself act to encode at least a portion of an authentication code. For example, an encoding may be based not only on characteristics within encoding portions but also how the encoding portions are separated and / or sized relative to each other.

[0089] An authentication element may encode only a portion of an authentication code or more than only a portion of an authentication code, for example an entire authentication code. In some embodiments, when an authentication element encodes only a portion of an authentication code, the remainder of the authentication code may be provided from elsewhere. For example, documentation, an invoice, or a physical or electronic file, a person’s memory (e.g., an owner’s memory), or a combination thereof for an object may include the remainder of an authentication code (e.g., as a watermark, metadata, or plaintext). In some embodiments, multiple authenticationPage 19 of 21213013588vlAttorney Docket No.: 2019150-0023 elements together encode only a portion of an authentication code. The remainder of the authentication code may be provided from elsewhere (e.g., documentation, an invoice, a physical or electronic file, for example in a watermark, in metadata, or as plaintext print). Thus, in some embodiments, to determine authenticity (e.g., of an object), the authentication element or the multiple authentication elements must be read and then a portion of an authentication code discernable from the reading is combined with the remainder of the authentication code from elsewhere in order to complete the verification. In some embodiments, a portion of an authentication code read from an authentication element may be combined (e.g., concatenated or interspersed) with another portion of the authentication code as part of an authentication (e.g., verification) process.

[0090] In some embodiments, an authentication element encodes at least a portion of an authentication code two-dimensionally, for example as a QR code. In some embodiments, an authentication element encodes at least a portion of an authentication code one-dimensionally, for example as a barcode. (A barcode may be present as a two-dimensional element but generally only one-dimension of spacing encodes information in a barcode.) In some embodiments, an authentication element encodes at least a portion of an authentication code three-dimensionally. For example, an arrangement of encoding portions of an authentication element in three dimensions may correspond to at least a portion of an authentication code. In some embodiments, an authentication element that encodes at least a portion of an authentication code may be read using perpendicular probes (x-rays).

[0091] An object may be physically associated with multiple authentication elements. In some embodiments, each one of multiple authentication elements encodes a portion of a common authentication code. The portion may be a distinct portion. For example, each of four authentication elements may encode a quarter of an authentication code or a quarter of a specific portion of an authentication code. The portion may not be a distinct portion in that there may be some overlap. Such overlap may provide additional security because it can be known what the extent of overlap should be and / or whether the overlap should be considered or discarded in reading an authentication element to determine at least a portion of an authentication code. In some embodiments, multiple authentication elements together encode an entirety of an authentication code. In some embodiments, each of multiple authentication elements encodes a same authentication code or encodes a same portion of an authentication code. Thus, multiplePage 20 of 21213013588vlAttorney Docket No.: 2019150-0023 authentication elements physically associated with an object may be redundant to each other. Such redundancy may reduce the impact of intentional or unintentional damage to an object or packaging for an object that degrades or destroys one or more of the authentication elements and / or provide additional security as described below. In some embodiments, each of multiple authentication elements encodes at least a portion of a distinct authentication code (e.g., an entire distinct authentication code).

[0092] Multiple authentication elements physically associated with an object may be physically associated with different portions of the object. For example, one authentication element may be disposed on an outer surface and one authentication element may be disposed on an inner surface. As another example, different authentication elements may be disposed at different edges, different surfaces, or different corners of an object. As another example, different authentication elements may be physically associated with different components of an object. Different authentication elements physically associated with an object may be physically separated.

[0093] Different portions of an authentication element physically associated with an obj ect may be physically associated with different portions of the object. For example, one portion of an authentication element may be disposed on an outer surface and another portion may be disposed on an inner surface. As another example, different portions of an authentication element may be disposed at different edges, different surfaces, or different corners of an object. As another example, different portions of an authentication element may be physically associated with different components of an object. Different portions of an authentication element physically associated with an object may be physically separated.

[0094] An authentication element may be tamper-proof. An authentication element may be included in a tamper-proof mechanism. An authentication element may be unable to be read if a tamper-proof mechanism has been tampered with. In some embodiments, a tamper-proof mechanism (e.g., label) includes an authentication element that encodes at least a portion of the authentication code, which cannot be obtained from the authentication element if the tamper-proof mechanism has been tampered with. An authentication element may be included in a label, for example a product label (e.g., that includes information about an object) or a security or authenticity label. Such a label may be affixed to (e.g., adhered to) an obj ect or packaging in which an object is packaged (e g., shrink wrap). An authentication element may be included inPage 21 of 21213013588vlAttorney Docket No.: 2019150-0023 packaging. An authentication element may be included in shrink wrap. In some embodiments, an authentication element is included in (e.g., embedded in) a tamper evident portion of a tamperproof mechanism (e.g., label). A tamper-proof mechanism may be a seal or lock or label. A tamper-proof label may be a seal. An object may be packaged by a packaging [e.g., box (e.g., cardboard box) or shrink-wrap] where the packaging includes an authentication element. Such packaging may be tamper-proof. Alternatively or additionally, the authentication element may be included in a tamper-proof portion of the packaging.

[0095] A tamper-proof mechanism, for example that includes an authentication element, may be structured to degrade upon exposure to one or more particular chemical species, for example upon exposure to oxygen and / or humidity. A tamper-proof mechanism may be chemically sensitive, for example such that an authentication element degrades upon exposure to one or more particular chemical species. In some embodiments, a tamper-proof mechanism is constructed such that an authentication element becomes unreadable (e.g., obfuscated) upon exposure to one or more chemical species, such as, for example, oxygen and / or humidity. For example, a tamper-proof mechanism may attenuate sound waves in a manner such that an authentication element is readable unless the tamper-proof mechanism is exposed to one or more particular chemical species that alter a manner in which the tamper-proof mechanism attenuates sounds waves such that the authentication element is no longer discernable against altered portion(s) of the tamper-proof mechanism. As another example, a similar scheme may be used for analogous MRI-based embodiments, for example where tampering results in an authentication element no longer being discernable in MRI.

[0096] Likewise, a tamper-proof mechanism that includes an authentication element may be physically sensitive, for example such that the authentication element is physically degraded (e.g., broken and / or tom) if the tamper-proof mechanism is tampered with. Likewise, a tamperproof mechanism, for example that includes an authentication element, may be structured to degrade upon exposure to a specific temperature or range of temperature. A tamper-proof mechanism may be thermosensitive, for example such that an authentication element degrades upon exposure to a specific temperature or range of temperature or to temperature outside of a specific range. In some embodiments, a tamper-proof mechanism is constructed such that an authentication element becomes unreadable (e.g., obfuscated) upon exposure to a specific temperature or range of temperature or to temperature outside of a specific range. Similarly, aPage 22 of 21213013588vlAttorney Docket No.: 2019150-0023 tamper-proof mechanism, for example that includes an authentication element, may be structured to degrade upon exposure to light. A tamper-proof mechanism may be photosensitive, for example such that an authentication element degrades upon exposure to certain amount of light and / or to one or more wavelengths within the visible light spectrum. In some embodiments, a tamper-proof mechanism is constructed such that an authentication element becomes unreadable (e.g., obfuscated) upon exposure to certain amount of light and / or to one or more wavelengths of light (e.g., within the visible light spectrum). A tamper-proof mechanism may be chemically sensitive, physically sensitive, thermosensitive, photosensitive, or a combination thereof.

[0097] An authentication element may be embedded into an object. An authentication element may be integrated with (e.g., within) an object. An authentication element may be a portion of an object. An authentication element may be covered, for example by a label, by packaging, or by a portion of an object (e.g., by paint of a painting). An authentication element may be printed (e.g., inkjet printed) onto an object. An authentication element may be disposed on an interior of an object. An authentication element may be disposed on a surface of an object. An authentication element may be internal to an object. An authentication element may be covered from view by unaided human eyes, for example by a portion of an object. An authentication element may be affixed (e.g., adhered) to an object. An object may contain an authentication element. Distinct portions of an authentication element may be disposed on (e.g., printed onto, embedded in, integrated with, or woven into) different portions of an object. An authentication element may not be visible to unaided human eyes. For example, an authentication element may be covered (e.g., by a portion of an object) or may be constructed such that it blends into an object or label affixed to an object (e.g., due to material selection and / or size). An authentication element may be integrated with an object in that it is not removable without noticeably damaging the object. An authentication element may be woven into a substrate of an object (e.g., woven into a canvas of an artwork). An authentication element may have been applied to an object (e.g., printed on the object) after the object has been at least partially formed. In some embodiments, an authentication element has been applied to a substrate that is subsequently processed, for example applied to (e.g., woven into) a canvas (e.g., during fabrication of the canvas) that is then made into an artwork. An authentication element may be deposited, for example printed, such as inkjet printed, onto an object or a label physically associated with an object (e.g., disposed on the object or on packagingPage 23 of 21213013588vlAttorney Docket No.: 2019150-0023 for the object). An authentication element may be deposited on a surface of an object or a label physically associated with an object.

[0098] An authentication element may be incorporated into an object. An authentication element may be embedded into an object. An authentication element may be braided into an object. An authentication element may be woven into an object. An authentication element may be a thread that is colored. An authentication element may be a string that is colored. An authentication element may be a cord that is colored. An authentication element may be a yam that is colored. An authentication element may be a wire that is colored. An authentication element may be a thread that is dyed with a visible color. An authentication element may be a string that is dyed with a visible color. An authentication element may be a cord that is dyed with a visible color. An authentication element may be a yam that is dyed with a visible color. An authentication element may be a wire that is dyed with a visible color. An authentication element may be braided into a textile or fabric. An authentication element may be embroidered into a textile or fabric. For example, an authentication element may be embroidered into a textile as a logo. An authentication may be woven into a textile or fabric. For example, an authentication element may be woven into a textile as a logo.

[0099] In some embodiments, an authentication element is shaped into a readable pattern (e.g., forming one or more characters, such as one or more letters and / or one or more numbers) that is discernable (e.g., only discernable) using x-rays, radio waves (e.g., in combination with a magnetic field), sound waves, or a combination thereof. For example, an authentication element may be embroidered. Such a readable pattern may or may not encode at least a portion of an authentication code. An authentication element may be or include a logo, tag, patch, emblem, badge, crest, seal, or token, for example included in or on (e.g., embroidered onto) an object, such as textile. One or more encoding portions of an authentication element may be incorporated into a logo, tag, patch, emblem, badge, crest, seal, or token. For example, a logo or branding patch may include one or more encoding portions. Since one or more encoding portions may not be visible to and / or may be covered by one or more non-encoding portions of an authentication element, an observer may not be able to tell that there is an authentication element present in a logo, tag, patch, emblem, badge, crest, seal, or token. Moreover, alternatively or additionally, because an authentication element may be or include a fiber or thread (e.g., one or more encoding portions that is / are one or more fibers and / or one or more threads), such an authentication elementPage 24 of 21213013588vlAttorney Docket No.: 2019150-0023 may be easily integrated into a standard manufacturing process for a logo, tag, patch, emblem, badge, crest, seal, or token. For example, a standard embroidery process that applies a logo to an object (e.g., textile) may be adapted to also use a radiopaque thread or fiber such that an authentication element is incorporated into the logo during the embroidery of the object.

[0100] An authentication element may include one or more encoding portions that are spatially arranged and constructed to form a secondary logo, tag, patch, emblem, badge, crest, seal, or token different from a primary, human visible logo, tag, patch, emblem, badge, crest, seal, or token (e.g., for a brand). For example, a secondary logo, tag, patch, emblem, badge, crest, seal, or token may form a radiopaque and / or sound attenuating pattern (e.g., text) that is readable using an appropriate imaging modality (e.g., x-ray, MRI, CT, or ultrasound). For example, a secondary logo, tag, patch, emblem, badge, crest, seal, or token may form a radiopaque and / or sound attenuating pattern (e.g., text) that is discernable using x-rays, radio waves (e.g., in combination with a magnetic field), sound waves, or a combination thereof. For example, a brand logo may be applied as embroidery to an article of clothing (e.g., a chest area of a shirt) using a radiopaque thread that forms a secondary pattern within the logo that identifies the article of clothing as authentic. As another example, radiopaque and / or sound attenuating particles may be applied during patch construction in a manner that encodes at least a portion of an authentication code within the patch and the patch may be subsequently applied (e.g., stitched into) an article of clothing or fashion accessory (e.g., handbag).

[0101] In some embodiments, at least a portion of an authentication code is encoded in an authentication element by combination of (i) a readable pattern in which the authentication element is shaped [e.g., that is discernable (e.g., only discernable) using x-rays, radio waves (e.g., in combination with a magnetic field), sound waves, or a combination thereof] and (ii) a particular spatial arrangement, spatial distribution, phase, position, orientation, size, construction to produce a responsive signal, or combination thereof of one or more encoding portions one or more encoding portions within the authentication element.

[0102] In some embodiments, an authentication element is shaped into a readable pattern (e.g., forming one or more characters, such as one or more letters and / or one or more numbers) to act as a decoy. Thus, in some embodiments, an authentication element is shaped into a readable pattern that does not encode at least a portion of an authentication code. For example, an authentication element may be shaped into a readable pattern in order to lead potentialPage 25 of 21213013588vlAttorney Docket No.: 2019150-0023 counterfeiters to believe that the readable pattern is what provides security even though a different aspect of the authentication element is what encodes at least a portion of an authentication code (e.g., a spatial arrangement and / or distribution of one or more encoding portions of the authentication element). In general, a readable pattern may be at a larger size scale (e.g., on the order of the size of the authentication element) than an encoding mechanism (or another encoding mechanism) that encodes at least a portion of an authentication code. For example, an authentication element may be shaped into a readable pattern that is approximately centimeter scale while at least a portion of an authentication code is encoded based on a particular spatial arrangement, spatial distribution, phase, position, orientation, size, construction to produce a responsive signal, or combination thereof of one or more encoding portions that is on a millimeter or submillimeter scale. For example, at least a portion of an authentication code may be encoded by spacing in a braiding pattern of one or more encoding portions in a thread or fiber where the thread or fiber may be shaped (e.g., due to how it is stitched or embroidered) into a readable pattern. The readable pattern may show up in one or more non-visible imaging modalities but not serve to encode any portion of an authentication code and, moreover, depending on the magnification used, may appear to be of constant radiodensity and / or sound attenuation. One would need to know to look at a smaller scale (higher magnification) in order to read the at least a portion of the authentication code from the authentication element.

[0103] In some embodiments, an authentication element is no more than 10 cm, no more than 5 cm, no more than 4 cm, no more than 3 cm, no more than 2 cm, no more than 1 cm, or no more than 0.5 cm in at least one dimension (e.g., a length dimension). In some embodiments, an authentication element is at least 0.5 cm, at least 1 cm, at least 2 cm, at least 3 cm, at least 4 cm, or at least 5 cm in at least one dimension (e.g., a length dimension). In some embodiments, an authentication element is no more than 1 cm, no more than 5 mm, no more than 4 mm, no more than 3 mm, no more than 2 mm, no more than 1 mm, or no more than 0.5 mm in at least one dimension (e.g., a width dimension or a diameter dimension). In some embodiments, an authentication element is at least 0.5 mm, at least 1 mm, at least 2 mm, at least 3 mm, at least 4 mm, or at least 5 mm in at least one dimension (e.g., a width dimension or a diameter dimension). In some embodiments, an authentication element has an aspect ratio (e.g., a length to width or length to diameter aspect ratio) of at least 2: 1, at least 3: 1, at least 4: 1, at least 5: 1, at least 10: 1, or at least 20: 1 and, optionally, no more than 100: 1. In some embodiments, an authentication elementPage 26 of 21213013588vlAttorney Docket No.: 2019150-0023(e.g., encoding at least a portion of an authentication code in a barcode or a QR code) occupies an area of no more than 25 cm2, no more than 20 cm2, no more than 15 cm2, no more than 10 cm2, no more than 5 cm2, or no more than 2 cm2, or no more than 1 cm2. In some embodiments, an authentication element occupies a volume of no more than 10 cm3(e.g., no more than 10 cm3, no more than 5 cm3, no more than 2 cm3, no more than 1 cm3, no more than 0.5 cm3, no more than 0.25 cm3, no more than 0.1 cm3, no more than 0.05 cm3, no more than 0.01 cm3, or no more than 0.001 cm3). In some embodiments, an authentication element has a largest surface and a surface area of the largest surface is no more than 50 cm2(e.g., no more than 40 cm2, no more than 30 cm2, no more than 20 cm2, no more than 10 cm2, no more than 5 cm2, no more than 4 cm2, no more than 3 cm2, no more than 2 cm2, no more than 1 cm2, no more than 0.5 cm2, or no more than 0.1 cm2).

[0104] In some embodiments, an encoding portion is no more than 10 cm, no more than 5 cm, no more than 4 cm, no more than 3 cm, no more than 2 cm, no more than 1 cm, or no more than 0.5 cm in at least one dimension (e.g., a length dimension). In some embodiments, an encoding portion is at least 0.5 cm, at least 1 cm, at least 2 cm, at least 3 cm, at least 4 cm, or at least 5 cm in at least one dimension (e.g., a length dimension). In some embodiments, an encoding portion is no more than 1 cm, no more than 5 mm, no more than 4 mm, no more than 3 mm, no more than 2 mm, no more than 1 mm, or no more than 0.5 mm in at least one dimension (e.g., a width dimension or a diameter dimension). In some embodiments, an encoding portion is at least 0.5 mm, at least 1 mm, at least 2 mm, at least 3 mm, at least 4 mm, or at least 5 mm in at least one dimension (e.g., a width dimension or a diameter dimension). In some embodiments, an encoding portion has an aspect ratio (e.g., a length to width or length to diameter aspect ratio) of at least 2: 1, at least 3: 1, at least 4:1, at least 5: 1, at least 10: 1, or at least 20: 1 and, optionally, no more than 100: 1. In some embodiments, an encoding portion (e.g., encoding at least a portion of an authentication code in a barcode or a QR code) occupies an area of no more than 25 cm2, no more than 20 cm2, no more than 15 cm2, no more than 10 cm2, no more than 5 cm2, or no more than 2 cm2, or no more than 1 cm2.

[0105] In some embodiments, an authentication element encodes information that is not an authentication code. An authentication element may encode such information using one or more encoding portions. An authentication element may encode information describing an object.Page 27 of 21213013588vlAttorney Docket No.: 2019150-0023For example, an authentication element may encode a serial number, a title, author / creator, creation date, dimensions of an object, or combination thereof.In some embodiments, an authentication element includes one or more secondary authentication features (e.g., security feature(s)). For example, a label may include one or more secondary authentication features in addition to one or more radiopaque and / or sound attenuating encoding portions that are included in the authentication element. One or more encoding portions of an authentication element may be integrated with (e.g., embedded in, woven in, and / or laminated in) one or more secondary authentication features. For example, a radiopaque thread may be woven into a secondary authentication feature or radiopaque particles may be embedded and / or laminated into a secondary authentication feature, such as a security label or sticker. A secondary authentication feature, for example, may include a light shift feature, a holographic feature, a UV security feature, an infrared security feature, or a combination thereof. A secondary authentication feature may be visible to an unaided human, for example be a particular design and / or include optically variable ink. In some embodiments, at least a portion of particles of an authentication element are interspersed within a secondary authentication feature. One or more encoding portions of an authentication element may be covered by a secondary authentication feature. Because encoding portion(s) may be small and / or not visible to an unaided human (e.g., visibly transparent), such encoding portion(s) may be integrated with one or more secondary security features without interfering with performance of the one or more secondary security features (e.g., without obfuscating or otherwise altering visual appearance of the one or more secondary security features).Authentication Codes

[0106] Authentication codes may be complex (e.g., long), for example when an object is high-value or simple (e.g., short), for example where authenticity concerns exist but complexity may incur prohibitive cost, such as with certain low-value objects, or where an encoding scheme limits the amount of information that can be reliably encoded. Additionally, form of an object may lend itself to using a particular complexity of authentication code. For example, QR codes or barcodes can generally encode larger amounts of information but are more amenable to being used with certain objects (e.g., that include a flat surface) than others (e.g., certain textiles). An authentication code may be unique such that it uniquely authenticates a single object. SuchPage 28 of 21213013588vlAttorney Docket No.: 2019150-0023 authentication codes may be useful for high-value objects, such as artwork. An organization (e.g., manufacturer or producer) or person (e.g., creator or owner) may use a same unique authentication code for multiple objects such that the authentication code uniquely identifies them. A manufacturer may use a same authentication code for a set of objects (e.g., a lot or batch) or for every object of a certain model.

[0107] An authentication code may be unique to, or uniquely identify, an object (e.g., be a serial number). An authentication code may be unique to or correspond to a type of object, for example may correspond to a model, a lot, or a batch. An authentication code may be unique to or correspond to a manufacturer of an object. An authentication code may be unique to or correspond to an organization (e.g., company or hospital) (e.g., manufacturer). An authentication code may identify a manufacturer and / or model of an object. An object may be identifiable based on an authentication code. In some embodiments where an authentication code is not unique to a particular object, an authentication code may be relatively short or simple, for example where it is used for multiple objects (e.g., each of a batch or lot or every one of a certain model).

[0108] An authentication code may be multiple digits. An authentication code may be multiple characters. An authentication code may include one or more letters and / or one or more numbers. An authentication code may be unique to an object (e.g., particular artwork) or to a type of object (e.g., a stock keeping unit (SKU)). An authentication code may be unique to a person (e.g., a creator of an object or an authenticator, such as an appraiser or owner). An authentication code may be unique to an organization (e.g., company) (e.g., a manufacturer). An authentication code may be an alphanumeric string, a PIN, a serial number, a passcode, a password, a passphrase, or a combination thereof. An authentication code may include, be derived from, or correspond to information describing an object (e.g., a title, author, creation date, or combination thereof). An encoding portion may encode a single character (e.g., letter or number) of an authentication code. Multiple encoding portions may together encode a single character (e.g., letter or number).

[0109] One or more encoding portions of an authentication element may be spatially arranged, spatially distributed, phased, positioned, oriented, shaped, sized, constructed to produce a responsive signal, or a combination thereof to encode one or more characters (e.g., letter(s) and / or number(s)) of an authentication code. For example, a spacing between adjacent encoding portions may correspond to a character (e.g., a 1 or a 0 in a binary authentication code or an authentication code encoded as a binary code). For example, a spacing between adjacent portions of one or morePage 29 of 21213013588vlAttorney Docket No.: 2019150-0023 braided elements (e.g., between adjacent braided elements or portions thereof) may encode at least a portion of an authentication code. One or more encoding portions may be phased (e.g., relative to each other) to encode at least a portion of an authentication code, for example a phase difference between portions of an encoding portion and / or between different encoding portions. Such phasing may be applied using, for example, spiraled elements (e.g., braided elements). An encoding portion may be constructed to produce a responsive signal in that the responsive signal has a specific wavelength (e.g., due to down-conversion and / or fluorescence and / or amount of attenuation) and / or intensity (e.g., based on radiodensity of the encoding portion and / or amount of attenuation). An encoding portion may produce a responsive signal by, for example, absorption, attenuation, absorption and emission (e.g., down-conversion) (e.g., of a different characteristic particle or signal from an excitation particle or signal, for example fluorescence), reflection, refraction, or a combination thereof. At least a portion of an authentication code may be encoded by a spatial distribution, position, and / or size of one or more encoding portions of an authentication element. An encoding portion may encode at least a portion of a character of more than one authentication code. For example, a size of an encoding portion (e.g., particle) may correspond to a first authentication code and orientation (or shape or spacing) of the encoding portion may correspond to a second authentication code. As another example, a size of an encoding portion (e.g., particle) may encode a first portion of an authentication code and orientation (or shape or spacing) of the encoding portion may encode a second portion of the authentication code.

[0110] An authentication code may be encoded using an ASCII code. An authentication code may be at least 10 (e.g., at least 20, at least 30, or at least 50) characters long. An authentication code may be at least 64 bits (e.g., at least 128 bits, at least 256 bits, or at least 512 bits). An authentication element may encode at least a portion of an authentication code in a base that is not base 10. For example, an authentication element may encode at least a portion of an authentication code in binary (base 2) or in hexadecimal. An authentication code may be encoded in binary using, for example, two types of encoding portions having different radiodensities. An authentication element may encode at least a portion of an authentication code not in plaintext. An authentication code may be encoded as a readable pattern (e.g., a QR code or barcode). An authentication element may encode at least a portion of an authentication code as a QR code or barcode.Page 30 of 21213013588vlAttorney Docket No.: 2019150-0023

[0111] An authentication element may encode at least a portion of an authentication code in an encrypted manner. A one-way cryptographic cypher may be used to encode at least a portion of an authentication code in an encrypted manner. For example, at least a portion of an authentication code may be encoded using a secure hashing algorithm (SHA) encryption (e.g., SHA-256) or pretty good privacy (PGP) encryption. Thus, in some embodiments, verification of an object with an associated authentication element may include a person with knowledge of a correct authentication code producing a SHA encrypted version of the authentication code and comparing that to information read from the authentication element.

[0112] In some embodiments, where a PGP encryption scheme is used, at least a portion of an authentication code may be encoded in an encrypted manner with a public key and then only those with a corresponding private key can unencrypt it to verify authenticity using the authentication code itself. In some embodiments, a version of a public key encrypted at least a portion of an authentication code may be made publicly accessible. A public key encrypted at least a portion of an authentication code read from an authentication element may be compared to the publicly available version as an intermediate verification of authenticity. This can be performed without compromising the underlying authentication code which can only be unencrypted with the private key (e.g., possessed by one or more parties related to the document). Thus, those with the private key can make a final verification of authenticity (e.g., after accessing the related object). For example, a document sender (e.g., one party to a contract) may use the public key of a document receiver (e.g., another party to a contract) to encrypt an authentication code that is then encoded in an authentication element physically associated with the document before the document is sealed in a security envelope and also given to a logistics company. The logistics company can then use the public key encrypted authentication code to track the document in an authenticated manner without accessing the envelope (intermediate authentication), in this case even though it does not have access to the public key, and the document receiver can verify the ultimate authenticity by confirming the authentication code encoded on the document as received is correct using its private key. A cipher key (e.g., public or private key) for an authentication code that is encoded in an authentication element physically associated with an object in an encrypted manner may be provided separately, for example on documentation or an invoice for the object (e.g., as a watermark or plaintext print) or a physical or electronic file (e.g., as metadata) corresponding to the object, or stored in a registry in which the object is registered.Page 31 of 21213013588vlAttorney Docket No.: 2019150-0023

[0113] By encoding authentication codes in an encrypted manner, counterfeiters can be further deterred because they will not know the ultimate authentication code even if they are able to read one or more authentication elements. Encryption details can be changed, for example, between lots or batches of objects that would render old authentication elements useless without needing to change authentication codes. So long as appropriate entities are kept apprised of current encryption details (e.g., keys), the same authentication codes can be reused while staying ahead of counterfeiters.

[0114] An authentication code may be a particular arrangement (e.g., pattern) of one or more encoding portions. Thus, an authentication code need not necessarily correspond to a set (e.g., string) of characters (e.g., a string of letters and / or numbers). For example, an authentication code may be a particular spatial arrangement, spatial distribution, phase, position, orientation, size, construction to produce a responsive signal, or combination thereof of one or more encoding portions. For example, a person, organization, or object may use an authentication code that is a particular spiral arrangement (e.g., pattern) (e.g., that produces a particular signal in response to x- rays) and an authentication element that includes one or more encoding portions with characteristics that correspond to the spiral arrangement (e.g., when x-rays are applied) therefore encodes the authentication code. Such a spiral arrangement may be based on phase, for example such that one or more encoding portions are phased relative to each other to encode at least a portion of an authentication code. In some embodiments, for example where an authentication code is a string (e.g., of letter(s) and / or number(s)), a mapping is used to correspond arrangements (e.g., patterns) to a character set used for the string.

[0115] As another example, a set of ordered spacings of encoding portions or a set of ordered spacings of a single encoding portion may be used as an authentication code without the set corresponding to certain characters (e.g., letter(s) or number(s)). For example, a Morse code type arrangement of particles or clusters of particles or of spiral spacing and / or phase in a fiber, thread, a string, a cord, or filament, may be used as an authentication code whether or not the arrangement actually corresponds to a password, passcode, or PIN represented in Morse code. In some embodiments, an interpretation threshold may be applied when determining at least a portion of an authentication code when reading an authentication element. In some embodiments, a mixed-integer programming (MIP) algorithm can be applied to threshold differences in radiodensity. In some embodiments, a spacing between adjacent portions of an encoding portionPage 32 of 21213013588vlAttorney Docket No.: 2019150-0023 or adjacent portions of two different encoding portions above a first threshold may be interpreted differently than a spacing below a second threshold. The first threshold need not be the same as the second threshold. In some embodiments, an authentication code corresponds to a certain arrangement (e.g., pattern) of above threshold and below threshold spacings.

[0116] In some embodiments, different encoding portions with different radiodensities may be used as an arrangement (e.g., pattern) that encodes at least a portion of an authentication code. In some embodiments, an arrangement may be formed by a particular (e.g., ordered) sequence of one or more encoding portions different radiodensities. For example, a particular sequence of one or more particles / cluster of particles or one or more filaments (e.g., in a spiral) may be used as an authentication code (or portion thereof). For example, a certain alternation of two or more (e.g., three or four) encoding portion(s) of different radiodensities may be used, like an AB-type sequence (e.g., AABABBABB) or ABC-type sequence (e.g., ABBCBAAC).

[0117] In some embodiments, a variable radiodensity may be used as an arrangement (e.g., pattern) that is an authentication code. For example, a length over the variation occurs and / or a function of intensity over distance may define an arrangement that is an authentication code. In some embodiments, such an authentication code may be distinguishable as authentic or inauthentic based on whether radiodensity is too high or too low at one or more given points along an encoding portion of an authentication element that encodes the authentication code. In some embodiments, an arrangement that is an authentication code is a QR code or barcode. For example, in some embodiments, a QR code or barcode itself is an authentication code.

[0118] In some embodiments, radiodensity may be used as part of encoding an authentication code. For example, radiodensity being too high or too low (e.g., as observed in a human readable image formed by applying appropriate waves to an authentication element that encodes the authentication code) may be an indication that an object is inauthentic and / or an authentication element is fake. In this way, particular material selection, which may be hard to determine from examination of an object, may play a role in producing secure. For example, an authorized person may know the appropriate material to use for an encoding portion of an authentication element such that it appears to be of correct radiodensity when verifying authenticity whereas a potential counterfeiter does not such that, even if the potential counterfeiter gains access to an authentication code itself, he or she could not produce a suitable counterfeit. In some embodiments, an encoding of an authentication code may be agnostic to radiodensity so longPage 33 of 21213013588vlAttorney Docket No.: 2019150-0023 as an arrangement is correct, for example as long the correct spacing, shape, and / or size of encoding portions is correct.

[0119] In some embodiments, an image (e.g., a human-readable image) of an authentication element is an authentication code encoded by the authentication element against which other images can be compared for authentication purposes. Thus, an authentication code may be a fingerprint (e.g., a radiological fingerprint) that can be compared against for future authentication purposes. A fingerprint may be based on using one or more predetermined conditions (e g., one or more predetermined imaging conditions, such as x-ray machine setting(s)). A registry may include one or more registered fingerprints. A fingerprint of an authentication element may be registered before and / or after the authentication element has been physically associated with an object. In some embodiments, a registration of a fingerprint may only be made under certain conditions, for example if a registrant pays a fee to register his / her object (e.g., artwork).Surface Functionalization Based Encoding Portions and Authentication Elements

[0120] An encoding portion may include molecules (e.g., polymer chains). An encoding portion may include individual molecules (e.g., individual polymer chains). An encoding portion may be a molecular ink (e.g., polymer ink). Such molecules (e.g., polymer chains) may be radiopaque. Such molecules (e g., polymer chains) may be x-ray sensitive. Such molecules (e.g., polymer chains) may include an x-ray sensitive moiety.

[0121] An authentication element may include molecules (e.g., polymer chains). An authentication element may include individual molecules (e.g., individual polymer chains). An authentication element may be formed from a molecular ink (e.g., polymer ink). Such molecules may be disposed in an arrangement to encode information, for example at least a portion of an authentication code. Such molecules may be disposed in a patterned arrangement to encode information, for example at least a portion of an authentication code. Such molecules may be disposed in a watermark arrangement to encode information, for example at least a portion of an authentication code. Such molecules may be disposed in a watermark. Such molecules (e.g., polymer chains) may be radiopaque. Such molecules (e.g., polymer chains) may be x-ray sensitive. Such molecules (e.g., polymer chains) may include an x-ray sensitive moiety.Page 34 of 21213013588vlAttorney Docket No.: 2019150-0023

[0122] An authentication element may include molecules (e.g., polymer chains) attached (e.g., primary bonded, preferably covalently bonded) to a polymer surface (e.g., of packaging or of an object). An authentication element may include individual molecules (e.g., individual polymer chains) attached (e.g., primary bonded, preferably covalently bonded) to a polymer surface (e.g., of packaging or of an object). Such molecules may be attached to a polymer surface in an arrangement to encode information, for example at least a portion of an authentication code. Such molecules may be disposed in a patterned arrangement to encode information, for example at least a portion of an authentication code. Such molecules may be attached to a polymer surface in a watermark arrangement to encode information, for example at least a portion of an authentication code. Such molecules may be attached to a polymer surface in a watermark. Such molecules (e.g., polymer chains) may be radiopaque. Such molecules (e.g., polymer chains) may be x-ray sensitive. Such molecules (e.g., polymer chains) may include an x-ray sensitive moiety.

[0123] Molecules (e.g., polymer chains) may be arranged in an authentication element e.g., attached to a polymer surface, e.g., of packaging for an object or of an object) to encode at least a portion of an authentication code (e.g., corresponding to the object) in one dimension (e.g., as a barcode) or two dimensions (e.g., as a QR code), for example.

[0124] In some embodiments, an authentication element includes molecules (e.g., polymer chains) that are attached to a polymer surface (e.g., of packaging or of an object). The molecules may be x-ray sensitive. The molecules may be radiopaque. The molecules may each comprise an x-ray sensitive moiety. In some embodiments, an authentication element includes individual molecules (e.g., polymer chains) attached to a polymer surface (e.g., of packaging or of an object). The molecules may each comprise an x-ray sensitive moiety.

[0125] In some embodiments, a composite authentication element includes molecules (e.g., polymer chains) that are attached to polymer surfaces (e.g., of packaging(s) or of one or more objects). The molecules may be x-ray sensitive. The molecules may be radiopaque. The molecules may each comprise an x-ray sensitive moiety. In some embodiments, a composite authentication element includes individual molecules (e.g., polymer chains) attached to a polymer surface (e.g., of packaging(s) or of one or more objects). The molecules may each comprise an x- ray sensitive moiety.

[0126] In some embodiments, molecules (e.g., polymer chains) are primary bonded to a polymer surface (e.g., of packaging or of an object). In some embodiments, molecules (e.g.,Page 35 of 21213013588vlAttorney Docket No.: 2019150-0023 polymer chains) are covalently bonded to a polymer surface (e.g., of packaging or of an object). In some embodiments, molecules (e.g., polymer chains) are grafted onto a polymer surface (e.g., of packaging or of an object). In some embodiments, each of a plurality of molecules (e.g., polymer chains) is individually primary bonded to a polymer surface (e.g., of packaging or of an object). In some embodiments, each of a plurality of individual molecules (e.g., polymer chains) is individually covalently bonded to a polymer surface (e.g., of packaging or of an object). In some embodiments, each of a plurality of molecules (e.g., polymer chains) comprises a carbene derived or nitrene derived moiety primary bonded to a polymer surface (e g., of packaging or of an object). In some embodiments, molecules (e.g., polymer chains) are primary bonded to a polymer surface (e.g., of packaging or of an object) at one or more side groups of the molecules (e.g., polymer chains) (e.g., each comprising a surface attachment moiety). In some embodiments, each of a plurality of individual molecules (e.g., polymer chains) comprises a surface attachment end group, wherein the molecules (e.g., polymer chains) are attached to a polymer surface (e.g., of packaging or of an object) by the attachment end group for the individual polymer chains.

[0127] In some embodiments, molecules (e.g., polymer chains) are distributed over all of an outer polymer surface. In some embodiments, a polymer surface (e.g., of packaging or of an object) to which molecules (e.g., polymer chains) are attached) is an outer surface. In some embodiments, molecules (e.g., polymer chains) are distributed over an entire outer polymer surface (e.g., of packaging or of an object) (e.g., an entire longitudinal outer surface).

[0128] In some embodiments, molecules (e.g., polymer chains) are disposed in a monolayer over a polymer surface (e.g., of packaging or of an object). Thus, molecules (e.g., polymer chains) may form a very thin layer on a polymer surface while still imparting x-ray visibility. Molecules (e.g., polymer chains) may be disposed in a layer that is no more than 200 nm thick, e.g., no more than 150 nm, no more than 100 nm, no more than 75 nm, no more than 50 nm, no more than 40 nm, no more than 30 nm, no more than 25 nm, no more than 20 nm, no more than 15 nm, or no more than 10 nm thick. Molecules (e.g., polymer chains) may be disposed in a region extending from a surface of a fiber or thread that is 200 nm thick, e.g., no more than 150 nm, no more than 100 nm, no more than 75 nm, no more than 50 nm, no more than 40 nm, no more than 30 nm, no more than 25 nm, no more than 20 nm, no more than 15 nm, or no more than 10 nm thick. Molecules (e.g., polymer chains) may extend 200 nm thick, e.g., no more than 150 nm, no more than 100 nm, no more than 75 nm, no more than 50 nm, no more than 40 nm, noPage 36 of 21213013588vlAttorney Docket No.: 2019150-0023 more than 30 nm, no more than 25 nm, no more than 20 nm, no more than 15 nm, or no more than 10 nm from a surface of a fiber or thread to which they are attached. Such thin layers (e.g., monolayers) may impart x-ray absorptivity without (materially) impacting mechanical properties of a polymer surface.

[0129] In some embodiments, an x-ray sensitive moiety is in a repeat unit of a polymer chain. In some embodiments, an x-ray sensitive moiety is in a pendant group of a repeat unit of a polymer chain. In some embodiments, x-ray sensitive moiety is bonded to a backbone of a polymer chain by a linker. In some embodiments, a linker is an oligomer or a polymer. In some embodiments, a linker separates an x-ray sensitive moiety from an backbone by at least 5 atoms, at least 10 atoms, at least 15 atoms, or at least 20 atoms. In some embodiments, an x-ray sensitive moiety is in a backbone of a polymer chain. A polymer chain may have a polyethylene glycol, acrylate, or polyoxazoline backbone, for example (among others). In general, a wide variety of repeat units (e.g., back bone moieties) may be used.

[0130] A polymer chain may be formed by a ring opening metathesis polymerization (ROMP). In some embodiments, a polymer chain is formed by a ring-opening metathesis polymerization (ROMP). ROMP is an attractive methodology because it is controllable and can form tailored architectures, for example copolymers with a well-defined ratio of repeat units. Moreover, ROMP can easily be performed to include a backbone of ring moieties with each ring including two side groups (e.g., that are substituents of the ring) where one of the side groups may be highly reactive (e.g., a carboxylic acid), for example in order to react it to form a chain grafting (e.g., photoreactive) moiety, and the other may be x-ray sensitive. Therefore, many surface attachment moieties may be provided using a side group of a ring such that a polymer chain can individually attach to at one or more positions along its length (e.g., increasing the likelihood of attaching). In some embodiments, a polymer chain includes surface attachment moieties disposed along its length.

[0131] In some embodiments, an x-ray sensitive moiety comprises iodine. In some embodiments, an x-ray sensitive moiety comprises a mono-, bi-, tri-, quad-, or penta-iodinated moiety. In some embodiments, an x-ray sensitive moiety comprises an arene comprising one, two, three, four, or five iodine-containing substituents.

[0132] In some embodiments, a polymer chain is a copolymer. In some embodiments, a copolymer is a gradient copolymer. In some embodiments, a copolymer is a block copolymer. InPage 37 of 21213013588vlAttorney Docket No.: 2019150-0023 some embodiments, a block copolymer comprises a block of a repeat unit comprising an x-ray sensitive moiety. In some embodiments, a block copolymer comprises a block of a repeat unit comprising a surface attachment moiety. In some embodiments, a copolymer is a random copolymer. In some embodiments, a copolymer comprises a repeat unit comprising an x-ray sensitive moiety. In some embodiments, a copolymer comprises a repeat unit comprising a surface attachment moiety. In some embodiments, at least 50% (e.g., at least 60%, at least 70%, at least 80%, at least 90%, at least 95%, or at least 99%) of the repeat units in a copolymer comprise at least one x-ray sensitive moiety. In some embodiments, no more than 20% of the repeat units in a copolymer comprise a surface attachment moiety.

[0133] Molecules (e.g., polymer chains) may include a photoreactive attachment moiety such that irradiation of the molecules (e.g., polymer chains) when near a corresponding polymer surface (e.g., polymer fiber or thread) causes attachment (e.g., primary bonding, e.g., covalent bonding) of the molecules to the polymer surface (e.g., via an insertion reaction). For example, a polymer surface (e.g., outer surface) may be irradiated while in contact with a mixture (e.g., solution) of x-ray sensitive molecules (e.g., polymer chains) that include a photoreactive attachment moiety in order to attach the molecules. Different photoreactive attachment moieties may be used based on which polymer is being attached (e.g., grafted) to. In this manner, molecules (e.g., polymer chains) may be attached to a polymer surface by contacting the polymer surface with the molecules (e.g., a solution of the molecules) and then irradiation may be supplied for an appropriate time (e.g., in a range of 3 seconds to 5 minutes). Irradiation based attachment of molecules (e.g., polymer chains) allows for easy integration into a manufacturing process for a polymer surface. For example, using methods disclosed herein, attachment of x-ray molecules (e.g., polymer chains) may be easily integrated into a manufacturing process for packaging and / or for packaging an object without the need for significant retooling. A polymer surface be moved through a mixture (e.g., solution) and radiation may applied during or after the mixture is contacted. Such a process may be used before or after braiding. Because such molecules (e.g., polymer chains) are generally relatively very small and therefore minimally impact both dimensionality and mechanical properties of polymer surface to which they are applied and irradiation application functionality is easy to add to an assembly line, irradiation based attachment schemes as disclosed herein can avoid the need for significant retooling of an existing packaging manufacturing and / or packaging assembly line. In general, because a primary goal for manyPage 38 of 21213013588vlAttorney Docket No.: 2019150-0023 embodiments of authentication elements is x-ray visibility, it is generally desirable to include as many x-ray sensitive moieties as possible (e.g., comprising as much iodine as possible) and therefore maximalize surface attachment of x-ray sensitive molecules (e.g., polymer chains). Blanket irradiation of a polymer surface may be preferred to increase (e.g., maximize) attachment (e.g., as compared). In some embodiments, selective irradiation may be used (e.g., using a mask or directed beam) in order to encode information, such as at least a portion of an authentication code. Blanket irradiation may be applied from only one direction or multidirectionally (e.g., omnidirectionally). In some embodiments, it may be preferable to patternwise disposing (e.g., inkjet print) molecules (e.g., polymer chains) and then blanket irradiate the molecules to attach the molecules in a patterned arrangement.

[0134] Irradiation may be applied as a blanket irradiation, for example if blanket coverage of a surface with molecules (e.g., polymer chains) is desired. Irradiation may be applied selectively (e.g., using a mask or a directed radiation beam), for example in order to attach molecules (e.g., polymer chains) in a particular arrangement (e.g., pattern), for example to encode information as described elsewhere herein.

[0135] Irradiation of polymer chains and / or molecules to attach them to a polymer surface (e.g., of packaging or of an object) may include using lights at one or more wavelengths. Irradiation of polymer chains may include light sources of different wavelengths. Polymer chains may be irradiated by lights of varying wavelengths to bond to a polymer surface. Irradiation of polymer chains may include using light at varying exposure times. Polymer chains may be irradiated at varying exposure times to bond to a polymer surface.

[0136] In some embodiments, an entire polymer surface is irradiated to bond all molecules (e.g., polymer chains) to the polymer surface. Molecules (e.g., polymer chains) may be disposed on a portion of a polymer surface, and therefore, irradiating the entire polymer surface results in bonding of the molecules (e.g., polymer chains) to the portion of the polymer surface. Molecules (e.g., polymer chains) may be disposed on an entire surface of a polymer surface, and therefore, irradiating the entire surface results in bonding of the molecules (e.g., polymer chains) to the entire surface of the polymer surface. Molecules (e.g., polymer chains) may be disposed on a polymer surface in a particular arrangement (e.g., a pattern), and therefore, irradiating the entire surface results in bonding of the molecules (e.g., polymer chains) to the polymer surface in the particular arrangement (e.g., the particular pattern).Page 39 of 21213013588vlAttorney Docket No.: 2019150-0023

[0137] In some embodiments, a selective irradiation is used to bond molecules (e.g., polymer chains) to a polymer surface (e.g., of packaging or an object). A selective irradiation may create an arrangement (e.g., a pattern) of molecules (e.g., polymer chains) on a polymer surface (e.g., of packaging or an object). A selective irradiation may bond molecules (e.g., polymer chains) to a polymer surface (e.g., of packaging or an object) such that the bonded molecules (e.g., polymer chains) form an arrangement (e.g., a pattern), for example encode at least a portion of an authentication code.

[0138] A selective irradiation may create an arrangement of molecules (e.g., polymer chains) repeatedly (e.g., across a polymer surface). A selective irradiation may create multiple copies of an arrangement of molecules (e.g., polymer chains) on a polymer surface. A selective irradiation may create multiple copies of an arrangement of molecules (e.g., polymer chains) periodically (e.g., with or without any spacing between the copies, whether or not a start point and / or end point of each copy is indicated). A selective irradiation may create multiple copies of an arrangement of molecules (e.g., polymer chains) with or without any spacing between the copies (e.g., whether or not a start point and / or end point of each copy is indicated).

[0139] A selective irradiation may create multiple arrangements of molecules (e.g., polymer chains) on a polymer surface. Each one of multiple arrangements of molecules (e.g., polymer chains) may encode a portion of information. For example, each of four arrangements of molecules (e.g., polymer chains) may encode a quarter of information. Multiple arrangements of molecules (e.g., polymer chains) together may encode an entirety of information.

[0140] An arrangement of molecules (e.g., polymer chains) may be or include a readable pattern, such as one or more letters and / or one or more numbers. An arrangement of molecules (e.g., polymer chains) may be multiple digits. An arrangement of molecules (e.g., polymer chains) may be multiple characters. An arrangement of molecules (e.g., polymer chains) may include one or more letters and / or one or more numbers. An arrangement of molecules (e.g., polymer chains) may be or include a logo, tag, patch, emblem, badge, crest, seal, or token.

[0141] A selective irradiation may create an arrangement of molecules (e.g., polymer chains) two-dimensionally, for example as a QR code, for example when used in a mesh. A selective irradiation may create an arrangement of molecules (e.g., polymer chains) one- dimensionally, for example as a barcode. (A barcode may be present as a two-dimensional element but generally only one-dimension of spacing encodes information in a barcode.) A selectivePage 40 of 21213013588vlAttorney Docket No.: 2019150-0023 irradiation may create an arrangement of molecules (e.g., polymer chains) three-dimensionally. An arrangement of molecules (e.g., polymer chains) may be read using perpendicular probes (x- rays).

[0142] A selective irradiation may include using a mask to create an arrangement of molecules (e g., polymer chains). A mask corresponding to an arrangement may be positioned between a light source and a fiber, such that the irradiation results in the bonding of the molecules (e.g., polymer chains) in the arrangement included in the mask. A mask may be constructed to correspond to any desired arrangement of polymer fibers. Using a mask may provide a flexible, and easily implemented approach to create an arrangement of molecules (e.g., polymer chains) that encodes information.

[0143] A mask corresponding to an arrangement of molecules (e.g., polymer chains) may be used repeatedly (e.g., along a polymer surface’s length). A mask corresponding to an arrangement of molecules (e.g., polymer chains) may be used multiple times to create multiple copies of the arrangement of polymer fibers on a polymer surface. A mask corresponding to an arrangement of molecules (e.g., polymer chains) may be used periodically (e.g., with or without any spacing between the copies, whether or not a start point and / or end point of each copy is indicated). A mask corresponding to an arrangement of molecules (e.g., polymer chains) may be used multiple time to create copies of an arrangement of molecules (e.g., polymer chains) with or without any spacing between the copies (e.g., whether or not a start point and / or end point of each copy is indicated).

[0144] A mask may correspond to a repeated arrangement of molecules (e.g., polymer chains) (e.g., across a polymer surface). A mask may correspond to multiple copies of an arrangement of polymer fibers on a polymer surface. A mask may correspond to a periodic arrangement of molecules (e.g., polymer chains) (e.g., with or without any spacing between the copies, whether or not a start point and / or end point of each copy is indicated). A mask may correspond to multiple copies of an arrangement of molecules (e.g., polymer chains) with or without any spacing between the copies (e g., whether or not a start point and / or end point of each copy is indicated).

[0145] Multiple masks may be used to create multiple arrangements of molecules (e.g., polymer chains) on a polymer surface. Each one of the multiple masks may correspond to an arrangements of molecules (e.g., polymer chains) that encodes a portion of information. ForPage 41 of 21213013588vlAttorney Docket No.: 2019150-0023 example, each of four masks may correspond to an arrangements of molecules (e.g., polymer chains) that encodes a quarter of information. Multiple masks may correspond to multiple arrangements of molecules (e.g., polymer chains) that together encode an entirety of information.

[0146] A mask may correspond to multiple arrangements of molecules (e.g., polymer chains) on a polymer surface. Each one of the multiple arrangements of molecules (e.g., polymer chains) of the mask may encode a portion of information. For example, each of four arrangements of molecules (e.g., polymer chains) of a mask may encode a quarter of information. Multiple arrangements of molecules (e.g., polymer chains) of a mask may together encode an entirety of information.

[0147] A mask may correspond to an arrangement of molecules (e.g., polymer chains) that is a readable pattern, such as one or more letters and / or one or more numbers. A mask may correspond to multiple digits. A mask may correspond to multiple characters. A mask may correspond to one or more letters and / or one or more numbers. A mask may correspond to a logo, tag, patch, emblem, badge, crest, seal, or token. A mask may correspond to a two-dimensional pattern, for example a QR code. A mask may correspond to a one-dimensional pattern, for example a barcode. (A barcode may be present as a two-dimensional element but generally only one-dimension of spacing encodes information in a barcode.)

[0148] In some embodiments, a method includes covalently bonding the polymer chains to the polymer surface with carbene or nitrene moieties. The method may further include forming the carbene or nitrene moieties by exposing the polymer chains to light and / or irradiating the polymer chains. For example, attaching the polymer chains to the polymer surface may include selectively irradiating (e.g., with light) different portions of the polymer surface. Carbene chemistry (e.g., surface attachment with a carbene derived moiety) for surface attachment (e.g., by covalent bonding) may be produce stronger bonds (e.g., tighter binding kinetics) than other chemistries (e.g., nitrene based chemistry), which may make attached molecules (e.g., polymer chains) more impervious to being removed during normal usage of a medical device for connecting tissue (e.g., when tying sliding knots in a suture).

[0149] In some embodiments, a method includes braiding the polymer fiber with one or more other polymer fibers. For example, a method may include braiding the polymer fiber with the one or more other fibers before attaching the polymer chains to the polymer surface. Alternatively, a method may include braiding the polymer fiber with the one or more other fibersPage 42 of 21213013588vlAttorney Docket No.: 2019150-0023 after attaching the polymer chains to the polymer surface. In some embodiments, a method includes providing a polymer fiber in a braided thread including polymer fibers braided together, and attaching the polymer chains to the polymer surface includes selectively irradiating (e.g., with light) different portions of an outer surface of the thread.

[0150] In some embodiments, a method includes attaching the polymer chains to the polymer surface by selectively irradiating (e.g., with light) different portions of the polymer surface. For example, different portions of the polymer surface may be spatially separated. In some embodiments, the different portions are disposed to encode information. Alternatively, or additionally, the different portions are disposed to encode at least a portion of an authentication code.

[0151] In some embodiments, attaching molecules (e.g., polymer chains) to a polymer surface (e.g., of packaging or of an object) comprises individually primary bonding the molecules to the polymer surface or thread. In some embodiments, attaching molecules (e.g., polymer chains) to a polymer surface (e.g., of packaging or of an object) comprises individually covalently bonding the molecules to the polymer surface or thread.

[0152] In some embodiments, attaching the polymer chains to the polymer surface or thread comprises covalently bonding the polymer chains to the polymer surface or thread with carbene or nitrene moieties. In some embodiments, a method includes forming carbene or nitrene moieties by exposing molecules (e.g., polymer chains) to light and / or irradiating the molecules in order to attach them to a polymer surface (e.g., of packaging or of an object).

[0153] In some embodiments, there are different types of molecules (e.g., polymer chains) attached to a polymer surface.

[0154] In some embodiments, attaching polymer chains to a surface polymer fiber or thread comprises (e.g., selectively) irradiating (e.g., with light) different portions of the polymer surface or thread.

[0155] Figs. 20A-20C illustrate examples of individual polymer chains 50, according to illustrative embodiments of the present disclosure. An individual polymer chain 50 may include one or more spacing units 5 IB, one or more x-ray sensitive moieties 51C, and a surface attachment moiety 51 A. The surface attachment moiety 5 ID may be photoreactive. In some embodiments, an x-ray sensitive moiety 51C is or includes part of a backbone of an individual polymer chain 50. In some embodiments, an x-ray sensitive moiety 51C is bonded to the backbone of an individualPage 43 of 21213013588vlAttorney Docket No.: 2019150-0023 polymer chain 50. An x-ray sensitive moiety 51C, for example, may be bonded to the backbone by a linker, such as an oligomer or a polymer. As another example, an x-ray sensitive moiety 51C may be a pendant group of a repeat unit.

[0156] Fig. 20A shows an example of an individual polymer chain 50 a backbone formed by three spacing repeat units 5 IB and three x-ray sensitive moieties 51C, and a surface attachment moiety 51A as an end group. Fig. 20B illustrates an example of an individual polymer chain 50 including a backbone formed by four spacing units 5 IB, two x-ray sensitive moieties 51C, and a surface attachment moiety 51A as another end group. While the ratio of x-ray sensitive moieties 51C to spacing units 51B is different from that of individual polymer chain of Fig. 20A, the total amount of x-ray sensitive moieties 51C and spacing units 5 IB is the same in individual polymer chains of Figs. 20A and 20B, resulting in the same polymer length.

[0157] Fig. 20C illustrates an example of an individual polymer chain 50 including a backbone formed by five spacing units 5 IB and three x-ray sensitive moieties 51C, and a surface attachment moiety 51A as an end group. This individual polymer chain 51 includes a different ratio of x-ray sensitive moieties 51C to spacing units 5 IB, as well as a different total amount of x- ray sensitive moieties 51C and spacing units 5 IB, compared to those of individual polymer chains of Figs. 20A and 20B, resulting in a different polymer length.

[0158] Figs. 21A-21C illustrate examples of polymer portions 52 including multiple individual polymer chains 50, according to illustrative embodiments of the present disclosure. Each individual polymer chain 50 includes a surface attachment moiety 51 A as an end group. Individual polymer chains 50 are attached to polymer portion 52 by the surface attachment moieties 51 A. In some embodiments, individual polymer chains 50 are bonded (for example, covalently bonded) to polymer portion 52. In some embodiments, individual polymer chains 50 are grafted onto polymer portion 52.

[0159] Fig. 21 A shows a polymer portion 52 including individual polymer chains 50 that are formed by using the same amounts of each of the polymer moieties 51A, 51B, 51C, resulting in the same polymer length. Fig. 21B shows a polymer portion 52 including individual polymer chains 50 that are formed by using different amounts of each of the polymer moieties 51 A, 5 IB, 51C, at constant ratios, resulting in the same individual polymer chains 50 of varying lengths. Fig. 21C shows a polymer portion 52 including individual polymer chains 50A, 50B, 50C that arePage 44 of 21213013588vlAttorney Docket No.: 2019150-0023 formed by using different amounts of each of the polymer moi eties 51 A, 5 IB, 1 C, at varying ratios, resulting in different individual polymer chains 50A, 50B, 50C of varying lengths.

[0160] Figs. 22A-22B illustrate examples of a polymer surface 53 coated with a polymer 52, according to illustrative embodiments of the present disclosure. The polymer 52 includes multiple individual polymer chains 50. Each individual polymer chain 50 is attached to polymer 52 by a surface attachment moiety. In some embodiments, individual polymer chains 50 are bonded (for example, covalently bonded) to polymer 52. In some embodiments, individual polymer chains 50 are grafted onto polymer portion 52.

[0161] Fig. 22A shows an example of a polymer surface 53 that is coated with a polymer 52. In this example, entire surface of the thread 53 is coated with the polymer 52 including individual polymer chains 50. Fig. 22B shows an example of polymer surface 53 that is coated with a polymer 52. In this example, entire fabric 53 is coated with the polymer 52 including individual polymer chains 50. In some embodiments, fabric 53 is formed by weaving a thread that is coated with a polymer 52 (e.g., the thread example shown in Fig. 22A).

[0162] Fig. 23 illustrates an exemplary method 54 of forming a fabric 53 that is coated with a polymer 52. In this example, the method 54 includes a container 55 fdled with polymer 52 including individual polymer chains 50. In some embodiments, the fabric 53A is dipped in the container 55. In some embodiments, the fabric 53A is immersed in the container 55. In some embodiments, the fabric 53 A is soaked in the container 55. In some embodiments, the fabric 53 A is run through the container 55. The method 54 further includes irradiating the coated fabric 53B with light.

[0163] Fig. 24A is a flow chart diagram of a method 200 of manufacturing an authentication element from polymer chains, according to an illustrative embodiment. At step 202, the method 200 includes preparing polymer chains that are x-ray sensitive. At step 204, the method 200 includes patternwise disposing the chains (e.g., using inkjet printing) on a polymer surface, for example in an arrangement corresponding to at least a portion of an authentication code. At step 206, the method 200 blanket irradiating the chains to attach them to the polymer surface by primary bonds (e.g., covalent bonds).

[0164] Fig. 24B is a flow chart diagram of a method 300 of manufacturing an authentication element from polymer chains, according to an illustrative embodiment. At step 302, the method 300 includes preparing polymer chains that are x-ray sensitive. At step 304, the methodPage 45 of 21213013588vlAttorney Docket No.: 2019150-0023300 includes blanket disposing the chains (e.g., using inkjet printing) on a polymer surface. At step 306, the method 300 includes selectively irradiating the chains (e.g., using a mask or directed beam) to attach them to the polymer surface by primary bonds (e.g., covalent bonds), for example such that the attached chains are arranged in an arrangement corresponding to at least a portion of an authentication code.Exemplary Molecules and Polymer Chains for Surface Attachment

[0165] The following are non-limiting examples of x-ray sensitive and / or MRI sensitive molecules and polymer chains that may be attached to a surface of a fiber or thread according to embodiments of the present disclosure.

[0166] In some embodiments, a polymer chain (e.g., according to Formula II) is formed by a ring-opening metathesis polymerization (ROMP). ROMP is an attractive methodology because it is controllable and can form tailored architectures, for example copolymers with a well- defined ratio of repeat units. Moreover, ROMP can easily be performed to include a backbone of ring moieties with each ring including two side groups (e.g., that are substituents of the ring) (e.g., according to Formula Ila) where one of the side groups may be highly reactive (e.g., a carboxylic acid), for example in order to react it to form a chain grafting (e.g., photoreactive) moiety, and the other may be x-ray sensitive and / or MRI sensitive. Therefore, many surface attachment moieties may be provided using a side group of a ring such that a polymer chain can individually attach to at one or more positions along its length (e.g., increasing the likelihood of attaching). In some embodiments, a polymer chain includes surface attachment moieties disposed along its length. ROMPs and polymers formed by ROMP may also be advantageous in that they are able to be formed from oxygen containing rings, where the oxygen serves to impart (e.g., increased) hydrophilicity and / or biocompatibility to the resulting polymer backbone (e.g., in addition to linker hydrophilicity as described subsequently).

[0167] Molecules (e.g., polymer chains) disclosed herein may include one or more linkers (e.g., L1, L2of Formula I or L1, L2of Formula II). A linker may be used to provide space between a backbone and a functional moiety of a pendant group (e.g., an x-ray sensitive moiety or MRI sensitive moiety ). In general, x-ray sensitive moieties and MRI sensitive moieties are often bulky and / or reactive and may interfere with, e.g., polymerization to form a polymer chain that includes an x-ray sensitive moiety and / or an MRI sensitive moiety (e.g., as pendant group(s) in the chain).Page 46 of 21213013588vlAttorney Docket No.: 2019150-0023By using linkers (e.g., of intermediate length, such as oligomeric linkers), space can be provided to enhance reactivity of a backbone moiety of a monomer unit thereby promoting polymer formation. Alternatively or additionally, such linkers may also promote hydration for an MRI sensitive moiety (e.g., by providing more room for water to hydrate the moiety) and / or hydrophilicity of a polymer chain. For example, a backbone may not be hydrophilic while a linker is or may be more hydrophilic than a backbone, thereby imparting local hydrophilicity, which may be sufficient, given the length scales of the linker (e.g., degree of polymerization of 2 to 20), to well hydrate an MRI sensitive moiety (e.g., chelator complexed with a metal ion) attached to the linker in order to produce strong MRI signal when imaged (e.g., as compared to a similar molecule without the hydrophilic linker). In some embodiments, x-ray sensitive moieties and / or MRI sensitive moieties are reacted after polymerization to incorporate into one or more pendant groups of a preformed polymer backbone.

[0168] A linker may be or include a polyoxazoline or a repeat unit thereof. A backbone may be or include a polyoxazoline or copolymer thereof. Polyoxazoline (POx) is a preferred linker or backbone in some embodiments because it is hydrophilic and easily reacted to attach one or more pendant groups (e.g., x-ray sensitive moieties and / or MRI sensitive moieties) and / or end groups and can be used to form complex copolymers (e.g., using a living radical polymerization). POx may also be preferred to avoid issues with PEG allergies that certain people will have. Especially in trauma settings where immediate suturing is necessary and there is no time to determine whether a patient has a PEG allergy (as well as that medical devices for connecting tissue are often used internally and removal after determination that a patient has a PEG allergy may be quite difficult or impossible), having a default medical device composition that does not include PEG (e.g., includes POx instead) may be preferred.

[0169] In some embodiments, the present disclosure provides a molecule (e.g., compound) represented by Formula I:Formula I,Page 47 of 21213013588vlAttorney Docket No.: 2019150-0023 or a salt thereof, wherein: R1is a photoreactive moiety; each R2is independently selected from H, halogen, optionally substituted Ci-Ce aliphatic, optionally substituted C3-C7 cycloaliphatic, optionally substituted 3- to 7-membered heterocycle including 1 to 3 atoms selected from N, O, and S, optionally substituted Ce-Cio aryl, and optionally substituted 4- to 10-membered heteroaryl including 1 to 3 heteroatoms selected from N, O, and S; L1is a bond or a spacer moiety; each Ring A moiety is independently selected from an x-ray sensitive moiety, optionally substituted C3-C7 cycloaliphatic, optionally substituted 3- to 7-membered heterocycle including 1 to 3 atoms selected from N, O, and S, optionally substituted Ce-Cio aryl, and optionally substituted 4- to 10-membered heteroaryl including 1 to 3 heteroatoms selected from N, O, and S; L2is a bond or a spacer moiety; Z is an x-ray sensitive moiety and / or an MRI sensitive moiety (e.g., a metal -ion chelator); n is 1, 2, 3, or 4; and m is 0, 1, 2, 3, 4, or 5.

[0170] As described herein with respect to Formula I, R1may be a photoreactive moiety. In some embodiments, R1is a photoreactive moiety selected from a carbene-forming moiety, a nitrene-forming moiety, and a photoreactive crosslinker moiety. In some embodiments, the photo reactive moiety is a carbene-forming moiety. In some embodiments, the photoreactive moiety is a nitrene-forming moiety. In some embodiments, the photoreactive moiety is a photoreactive crosslinker moiety. In some embodiments, the photoreactive moiety is selected from diazerene, azide, and N-heterocyclic carbene (NHC). In some embodiments, the photoreactive moiety is a diazerene. In some embodiments, the photoreactive moiety is an azide. In some embodiments, the photoreactive moiety is an N-heterocyclic carbene (NHC). In some embodiments, the photoreactive moiety is an N-heterocyclic carbene (NHC) selected from optionally substituted thiazole, triazole, imidazole, and imidazoline. In some embodiments, the photoreactive moiety is an N-heterocyclic carbene (NHC), wherein the NHC is an optionally substituted thiazole. In some embodiments, the photoreactive moiety is an N-heterocyclic carbene (NHC), wherein the NHC is an optionally substituted triazole. In some embodiments, the photoreactive moiety is an N- heterocyclic carbene (NHC), wherein the NHC is an optionally substituted imidazole. In some embodiments, the photoreactive moiety is an N-heterocyclic carbene (NHC), wherein the NHC is an optionally substituted imidazoline. In some embodiments, the photoreactive moiety is an N- heterocyclic carbene (NHC), wherein the NHC is a thiazole. In some embodiments, the photoreactive moiety is an N-heterocyclic carbene (NHC), wherein the NHC is a triazole. In some embodiments, the photoreactive moiety is an N-heterocyclic carbene (NHC), wherein the NHC isPage 48 of 21213013588vlAttorney Docket No.: 2019150-0023 an imidazole. In some embodiments, the photoreactive moiety is an N-heterocyclic carbene (NHC), wherein the NHC is an imidazoline.

[0171] As described herein with respect to Formula I, each R2is independently selected from H, halogen, optionally substituted Ci-Ce aliphatic, optionally substituted C3-C7 cycloaliphatic, optionally substituted 3- to 7-membered heterocycle including 1 to 3 atoms selected from N, O, and S, optionally substituted Ce-Cio aryl, and optionally substituted 4- to 10-membered heteroaryl including 1 to 3 heteroatoms selected from N, O, and S. In some embodiments, each R2is independently selected from halogen, optionally substituted Ci-Ce aliphatic, optionally substituted C3-C7 cycloaliphatic, optionally substituted 3- to 7-membered heterocycle including 1 to 3 atoms selected from N, O, and S, optionally substituted Ce-Cio aryl, and optionally substituted 4- to 10-membered heteroaryl including 1 to 3 heteroatoms selected from N, O, and S. In some embodiments, each R2is independently selected from halogen, optionally substituted Ci-Ce aliphatic, optionally substituted 3- to 7-membered heterocycle including 1 to 3 atoms selected from N, O, and S, optionally substituted Ce-Cio aryl, and optionally substituted 4- to 10-membered heteroaryl including 1 to 3 heteroatoms selected from N, O, and S. In some embodiments, each R2is independently selected from halogen, optionally substituted Ci-Ce aliphatic, optionally substituted Ce-Cio aryl, and optionally substituted 4- to 10-membered heteroaryl including 1 to 3 heteroatoms selected from N, O, and S. In some embodiments, each R2is independently an optionally substituted Ci-Ce aliphatic. In some embodiments, each R2is independently an optionally substituted Cg-Cio aryl. In some embodiments, each R2is independently an optionally substituted 4- to 10-membered heteroaryl including 1 to 3 heteroatoms selected from N, O, and S. In some embodiments, each R2is independently a halogen. In some embodiments, each R2is independently a halogen selected from F, Cl, Br, and I. In some embodiments, each R2is independently F, Br, or I. In some embodiments, each R2is independently I. In some embodiments, each R2is independently hydrogen.

[0172] As described herein, the number of R2moieties is n, wherein n is 1-4. In some embodiments, n is 1, 2, 3, or 4. In some embodiments, n is 2, 3, or 4. In some embodiments, n is 3 or 4. In some embodiments, n is 1 or 2. In some embodiments, n is 1. In some embodiments, n is 2. In some embodiments, n is 3. In some embodiments, n is 4.

[0173] As described herein, L1is a bond or a spacer moiety. In some embodiments L1is a bond. In some embodiments, L1is spacer moiety. In some embodiments, L1is a spacer moietyPage 49 of 21213013588vlAttorney Docket No.: 2019150-0023 selected from an optionally substituted Ci-Ce aliphatic or a polymeric spacer moiety. In some embodiments, L1is a spacer moiety, wherein the spacer moiety is an optionally substituted Ci-Ce aliphatic. In some embodiments, L1is a spacer moiety, wherein the spacer moiety is selected from optionally substituted methyl, ethyl, propyl, isopropyl, butyl, sec-butyl, isobutyl, tert-butyl, pentyl, isopentyl, tert-pentyl, hexyl, and tert-hexyl. In some embodiments, L1is a spacer moiety, wherein the spacer moiety is selected from:embodiments, the spacer moiety is. In some embodiments, the spacer moiety isIn some embodiments, the spacer moiety isIn some embodiments, the spacer moietyPage 50 of 21213013588vlAttorney Docket No.: 2019150-0023 embodiments, the spacer moiety is. In some embodiments, the spacer moietysome embodiments, the spacer moietysome

[0174] In some embodiments, L1is spacer moiety, wherein the spacer moiety is a polymer spacer moiety. In some embodiments, L1is spacer moiety, wherein the spacer moiety is a polymer spacer moiety selected from poly(ethylene glycol), polyethylene oxide), poly((meth)acrylatePEG), poly((Ci-C6)alkylamino(meth)acrylate), linear poly(quatemary ammonium), zwitterionic poly(betaine), poly(vinylpyrrolidone), polylysine, polyoxazoline, and polyoxazine, or co-polymers thereof. In some embodiments, L1is spacer moiety, wherein the spacer moiety is a polymer spacer moiety selected from poly(ethylene glycol), poly(ethylene oxide), poly((meth)acrylatePEG), poly((Ci-C6)alkylamino(meth)acrylate), polyvinylpyrrolidone), polyoxazoline, and polyoxazine, or co-polymers thereof. In some embodiments, L1is spacer moiety, wherein the spacer moiety is a polymer spacer moiety selected from poly(ethylene glycol), poly(ethylene oxide), poly((meth)acrylatePEG), and poly((Ci- C6)alkylamino(meth)acrylate), or co-polymers thereof. In some embodiments, the polymeric spacer moiety is poly(ethylene glycol). In some embodiments, the polymeric spacer moiety is polyethylene oxide). In some embodiments, the polymeric spacer moiety is poly((meth)acrylatePEG). In some embodiments, the polymeric spacer moiety is poly((Ci- C6)alkylamino(meth)acrylate). In some embodiments, the polymeric spacer moiety is a copolymer.Page 51 of 21213013588vlAttorney Docket No.: 2019150-0023

[0175] As described herein, the degree of polymerization of the polymeric spacer moiety may be in a range from 2 to 500. In some embodiments, the degree of polymerization is in a range from 2 to 100. In some embodiments, the degree of polymerization is in a range from 2 to 50. In some embodiments, the degree of polymerization is in a range from 2 to 25. In some embodiments, the degree of polymerization is or at least 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, or 100. In some embodiments, the degree of polymerization is or at least 100, 110, 120, 130, 140, 150, 160, 170, 180, 190, 200, 250, 300, 350, 400, 450, or 500.

[0176] As described herein, each Ring A may be independently selected from an x-ray sensitive moiety, optionally substituted C3-C7 cycloaliphatic, optionally substituted 3- to 7- membered heterocycle including 1 to 3 atoms selected from N, O, and S, optionally substituted Cg-Cio aryl, and optionally substituted 4- to 10-membered heteroaryl including 1 to 3 heteroatoms selected from N, O, and S. In some embodiments, each Ring A is independently selected from an x-ray sensitive moiety, optionally substituted Ce-Cw aryl, and optionally substituted 4- to 10- membered heteroaryl including 1 to 3 heteroatoms selected from N, O, and S. In some embodiments, each Ring A is independently an optionally substituted Ce-Cio aryl. In some embodiments, each Ring A is independently an optionally substituted 4- to 10-membered heteroaryl including 1 to 3 heteroatoms selected from N, O, and S. In some embodiments, each Ring A is independently an x-ray sensitive moiety.

[0177] As described herein, the number of Ring A moi eties is m, wherein m may be 0-5. In some embodiments, m is 1, 2, 3, 4, or 5. In some embodiments, m is 1, 2, 3, or 4. In some embodiments, m is 1, 2, 3 or 4. In some embodiments, m is 1, 2, or 3. In some embodiments, m is 1. In some embodiments, m is 2. In some embodiments, m is 3. In some embodiments, m is 4. In some embodiments, m is 5. In some embodiments, m is 0.

[0178] As described herein, L2is a bond or a spacer moiety. In some embodiments L2is a bond. In some embodiments, L2is spacer moiety. In some embodiments, L2is a spacer moiety selected from an optionally substituted Ci-Ce aliphatic or a polymeric spacer moiety. In some embodiments, L2is a spacer moiety, wherein the spacer moiety is an optionally substituted Ci-Ce aliphatic. In some embodiments, L2is a spacer moiety, wherein the spacer moiety is selected from optionally substituted methyl, ethyl, propyl, isopropyl, butyl, sec-butyl, isobutyl, tert-butyl, pentyl, isopentyl, tert-pentyl, hexyl, and tert-hexyl. In some embodiments, L2is a spacer moiety, whereinPage 52 of 21213013588vlAttorney Docket No.: 2019150-0023. In some embodiments, the spacer moiety is. In some embodiments, the spacer moiety isIn some embodiments, the spacer moietyembodiments, the spacer moiety is. In some embodiments, the spacer moietyPage 53 of 21213013588vlAttorney Docket No.: 2019150-0023 embodiments, the spacer moiety isIn some embodiments, the spacer moiety is. In some embodiments, the spacer moiety is. In some embodiments, the spacer moiety

[0179] In some embodiments, L2is spacer moiety, wherein the spacer moiety is a polymer spacer moiety. In some embodiments, L2is spacer moiety, wherein the spacer moiety is a polymer spacer moiety selected from poly(ethylene glycol), poly(ethylene oxide), poly((meth)acrylatePEG), poly((Ci-C6)alkylamino(meth)acrylate), linear poly(quatemary ammonium), zwitterionic poly(betaine), poly(vinylpyrrolidone), polylysine, polyoxazoline, and polyoxazine, or co-polymers thereof. In some embodiments, L2is spacer moiety, wherein the spacer moiety is a polymer spacer moiety selected from poly(ethylene glycol), poly(ethylene oxide), poly((meth)acrylatePEG), poly((Ci-C6)alkylamino(meth)acrylate), polyvinylpyrrolidone), polyoxazoline, and polyoxazine, or co-polymers thereof. In some embodiments, L2is spacer moiety, wherein the spacer moiety is a polymer spacer moiety selected from poly(ethylene glycol), poly(ethylene oxide), poly((meth)acrylatePEG), and poly((Ci- C6)alkylamino(meth)acrylate), or co-polymers thereof. In some embodiments, the polymeric spacer moiety is poly(ethylene glycol). In some embodiments, the polymeric spacer moiety is poly(ethylene oxide). In some embodiments, the polymeric spacer moiety is poly((meth)acrylatePEG). In some embodiments, the polymeric spacer moiety is poly((Ci- C6)alkylamino(meth)acrylate). In some embodiments, the polymeric spacer moiety is a copolymer.

[0180] As described herein, the degree of polymerization of the polymeric spacer moiety may be in a range from 2 to 500. In some embodiments, the degree of polymerization is in a range from 2 to 100. In some embodiments, the degree of polymerization is in a range from 2 to 50. In some embodiments, the degree of polymerization is in a range from 2 to 25. In some embodiments, the degree of polymerization is or at least 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 25, 30, 35, 40, 45, 50,Page 54 of 21213013588vlAttorney Docket No.: 2019150-002355, 60, 65, 70, 75, 80, 85, 90, 95, or 100. In some embodiments, the degree of polymerization is or at least 100, 110, 120, 130, 140, 150, 160, 170, 180, 190, 200, 250, 300, 350, 400, 450, or 500.

[0181] As described herein, Z is an x-ray sensitive moiety and / or an MRI sensitive moiety (e.g., a metal-ion chelator). In some embodiments, Z is an x-ray sensitive moiety, In some embodiments, Z is a metal-ion chelator. In some embodiments, Z is an MRI sensitive moiety. In some embodiments, the MRI sensitive moiety is a metal-ion chelator. In some embodiments, the MRI sensitive moiety is a metal-ion chelator selected from DOTA (1,4,7, 10-tetraazacyclododecan- 1,4,7, 10-tetraacetic acid), DTPA (diethylenetriaminopentaacetic acid), DO3A (1,4,7,10- tetraazacyclododecan-l,4,7-triacetic acid), HPDO3A (10-(2-hydroxypropyl)-l,4,7,10- tetraazacyclododecan-l,4,7-triacetic acid), TRITA (1,4,7, 10-Tetrakis(carboxymethyl)-l, 4, 7,10- tetraazacyclotridecane), TETA (1,4,8, 1 l-Tetrakis(carboxymethyl)-l,4,8,l 1-Tetraazacyclotetradecane), BOPTA (4-carboxy-5,8,l l-tris(carboxymethyl)-l-phenyl-2-oxa- 5,8,11 -triazatridecan- 13 -oic acid), NOTA (l,4,7-triazacyclononane-N,N',N44-triacetic acid), PCTA (3,6,9, 15-tetraazabicyclo[9.3. 1 ]pentadeca- 1 (15), 11 , 13-triene-3,6,9-triacetic acid),DOTMA ((alpha, alpha', alpha", alpha" ')-tetram ethyl- 1, 4,7, 10-tetraazacyclododecan-l, 4, 7, 10- tetraacetic acid), AAZTA (6-amino-6-methylperhydro-l,4-diazepinetetraacetic acid) and HOPO (l-hydroxypyridin-2-one). In some embodiments, the MRI sensitive moiety is a metal-ion chelator selected from DOTA (1,4,7, 10-tetraazacyclododecan-l, 4, 7, 10-tetraacetic acid), DTPA (diethylenetriaminopentaacetic acid), DO3A (1,4, 7, 10-tetraazacyclododecan-l, 4, 7-triacetic acid), HPDO3A (10-(2-hydroxypropyl)-l, 4, 7, 10-tetraazacyclododecan-l, 4, 7-triacetic acid), TRITA (l,4,7,10-Tetrakis(carboxymethyl)-l,4,7,10-tetraazacyclotridecane), TETA (1,4,8,11- Tetrakis(carboxymethyl)-l,4,8,l l-Tetraazacyclotetradecane), and HOPO (l-hydroxypyridin-2- one). In some embodiments, the MRI sensitive moiety is a metal -ion chelator selected from DOTA (1,4,7, 10-tetraazacyclododecan-l, 4, 7, 10-tetraacetic acid), DTPA (diethylenetriaminopentaacetic acid), DO3A (1,4,7, 10-tetraazacyclododecan-l, 4, 7-triacetic acid), HPDO3A (10-(2- hydroxypropyl)-l, 4, 7, 10-tetraazacyclododecan-l, 4, 7-triacetic acid), and HOPO (1- hydroxypyridin-2-one). In some embodiments, the metal-ion chelator is DOTA (1,4, 7, 10- tetraazacyclododecan-l, 4, 7, 10-tetraacetic acid). In some embodiments, the metal-ion chelator is DTPA (diethylenetriaminopentaacetic acid). In some embodiments, the metal-ion chelator is DO3A (1,4,7, 10-tetraazacyclododecan-l, 4, 7-triacetic acid). In some embodiments, the metal-ion chelator is HPDO3A (10-(2-hydroxypropyl)-l, 4, 7, 10-tetraazacyclododecan-l, 4, 7-triacetic acid).Page 55 of 21213013588vlAttorney Docket No.: 2019150-0023In some embodiments, the metal-ion chelator is TRITA (l ,4,7,10-Tetrakis(carboxymethyl)-1.4.7.10-tetraazacy clotridecane). In some embodiments, the metal -ion chelator is TETA (1,4,8,11- Tetrakis(carboxymethyl)-l,4,8,l l-Tetraazacyclotetradecane). In some embodiments, the metalion chelator is BOPTA (4-carboxy-5,8,l l-tris(carboxymethyl)-l-phenyl-2-oxa-5,8,l 1- triazatridecan-13-oic acid). In some embodiments, the metal-ion chelator is NOTA (1,4,7- triazacyclononane-N,N',N44-triacetic acid). In some embodiments, the metal-ion chelator is PCTA (3,6,9,15-tetraazabicyclo[9.3.1]pentadeca-l(15),l l,13-triene-3,6,9-triacetic acid). In some embodiments, the metal-ion chelator is DOTMA ((alpha, alpha', alpha", alpha" ')-tetramethyl-1.4.7.10-tetraazacyclododecan-l,4,7,10-tetraacetic acid). In some embodiments, the metal-ion chelator is AAZTA (6-amino-6-methylperhydro-l,4-diazepinetetraacetic acid). In some embodiments, the metal-ion chelator is HOPO (l-hydroxypyridin-2-one).

[0182] As described herein, the metal-ion chelator is structured to chelate (e.g., chelates) metal ions (e.g., positively charged metal ions). In some embodiments, the metal ions carry a 2+ charge. In some embodiments, the metal ions are divalent ions. In some embodiments, the metal ions are alkaline-earth metal ions. In some embodiments, the metal ions are transition metal ions. In some embodiments, the metal ions are lanthonoid metals. In some embodiments, the metal ions are selected from Ca2+, Mg2+, Mn2+, Cu2+, Gd2+,...In some embodiments, the metal ions are gadolinium (Gd2+) ions. In some embodiments, the metal ions are manganese (Mn2) ions. In some embodiments, the metal-ion chelator chelates divalent metal ions. In some embodiments, the metal-ion chelator chelates alkaline-earth metal ions. In some embodiments, the metal-ion chelator chelates transition metal ions. In some embodiments, the metal-ion chelator chelates lanthanoid metal ions. In some embodiments, the metal-ion chelator chelates Ca2+, Mg2+, Mn2+, Cu2+, Gd2+, .... In some embodiments, the metal-ion chelator chelates gadolinium (Gd2+) ions. In some embodiments, the metal-ion chelator chelates manganese (Mn2+) ions.

[0183] In some embodiments, the present disclosure provides a molecule (e.g., compound) represented by Formula I’:Formula F,Page 56 of 21213013588vlAttorney Docket No.: 2019150-0023 or a salt thereof, wherein X is a chain grafting moiety, and L1, Ring A, L2, Z, and m are as described in classes and subclasses herein, both singly and in combination.

[0184] As described herein, X is a chain grafting moiety. In some embodiments, X is a chain grafting moiety is selected from a photoreactive moiety, a thermal reactive moiety, an enzyme reactive moiety, and a crosslinking moiety. In some embodiments, X is a chain grafting moiety, wherein the chain grafting moiety is a photoreactive moiety selected from a carbene- forming moiety, a nitrene-forming moiety, and a photoreactive crosslinker moiety. In some embodiments, the photo reactive moiety is a carbene-forming moiety. In some embodiments, the photoreactive moiety is a nitrene-forming moiety. In some embodiments, the photoreactive moiety is a photoreactive crosslinker moiety. In some embodiments, the photoreactive moiety is selected from diazerene, azide, and N-heterocyclic carbene (NHC). In some embodiments, the photoreactive moiety is a diazerene. In some embodiments, the photoreactive moiety is an azide. In some embodiments, the photoreactive moiety is an N-heterocyclic carbene (NHC). In some embodiments, the photoreactive moiety is an N-heterocyclic carbene (NHC) selected from optionally substituted thiazole, triazole, imidazole, and imidazoline. In some embodiments, the photoreactive moiety is an N-heterocyclic carbene (NHC), wherein the NHC is an optionally substituted thiazole. In some embodiments, the photoreactive moiety is an N-heterocyclic carbene (NHC), wherein the NHC is an optionally substituted triazole. In some embodiments, the photoreactive moiety is an N-heterocyclic carbene (NHC), wherein the NHC is an optionally substituted imidazole. In some embodiments, the photoreactive moiety is an N-heterocyclic carbene (NHC), wherein the NHC is an optionally substituted imidazoline. In some embodiments, the photoreactive moiety is an N-heterocyclic carbene (NHC), wherein the NHC is a thiazole. In some embodiments, the photoreactive moiety is an N-heterocyclic carbene (NHC), wherein the NHC is a triazole. In some embodiments, the photoreactive moiety is an N-heterocyclic carbene (NHC), wherein the NHC is an imidazole. In some embodiments, the photoreactive moiety is an N-heterocyclic carbene (NHC), wherein the NHC is an imidazoline.

[0185] In some embodiments, the present disclosure provides a molecule (e.g., compound) (e.g., polymer) represented by Formula II:Page 57 of 21213013588vlAttorney Docket No.: 2019150-0023Formula II, wherein: each M is independently a unit of the polymer backbone, wherein each M can be substituted with 0-3 RM; each RMis independently selected from H, halogen, optionally substituted Ci-Ce aliphatic, optionally substituted C3-C7 cycloaliphatic, optionally substituted 3- to 7- membered heterocycle including 1 to 3 atoms selected from N, O, and S, optionally substituted Ce-Cio aryl, optionally substituted 4- to 10-membered heteroaryl including 1 to 3 heteroatoms selected from N, O, and S, and a chain grafting moiety; each L is independently a bond or an optionally substituted Ci-Ce aliphatic; each L1is independently a bond or a spacer moiety; each A is independently selected from an x-ray sensitive moiety, optionally substituted C3-C7 cycloaliphatic, optionally substituted 3- to 7-membered heterocycle including 1 to 3 atoms selected from N, O, and S, optionally substituted Ce-Cio aryl, and optionally substituted 4- to 10-membered heteroaryl including 1 to 3 heteroatoms selected from N, O, and S; each L2is independently a bond or a spacer moiety; each Z is an MRI sensitive moiety (e g., a metal-ion chelator); n is 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, or 10; x is 0, 1, 2, or 3; and m is 0, 1, 2, or 3.

[0186] As described herein, each M independently may be a unit of the polymer backbone, wherein each M can be substituted with 0-3 RM. In some embodiments, each M is the same. In some embodiments, at two M are different. In some embodiments, the polymer backbone includes a hydrophobic polymer backbone. In some embodiments, the polymer backbone includes a hydrophobic polymer backbone including polyvinylchloride, polystyrenes,..., or co-polymers thereof. In some embodiments, the polymer backbone includes a hydrophilic polymer backbone. In some embodiments, the polymer backbone includes a hydrophilic polymer backbone including an acrylic, an epoxy, a polyethylene glycol, a polyoxazoline, a polyvinylalcohol, a polyvinylpyrrolidone, polyethylene imine, a polyester, a polyurethane, a poly(ethylene oxide), a poly((meth)acrylate), a poly((Cl-C6)alkylamino(meth)acrylate), a linear poly(quatemary ammonium), a zwitterionic poly(betaine), a polyvinylpyrrolidone), a polylysine, a polysaccharide, a glycosaminoglycan, or a polyoxazine, or a co-polymer thereof.Page 58 of 21213013588vlAttorney Docket No.: 2019150-0023

[0187] In some embodiments, the hydrophilic polymer backbone includes the structure of Formula Ila:Formula Ila, wherein RM, L1, A, L2, Z, x, n, and m are as described in classes and subclasses herein, both singly and in combination.

[0188] As described herein, each RMis independently selected from H, halogen, optionally substituted Ci-Ce aliphatic, optionally substituted C3-C7 cycloaliphatic, optionally substituted 3- to 7-membered heterocycle including 1 to 3 atoms selected from N, O, and S, optionally substituted Ce-Cio aryl, optionally substituted 4- to 10-membered heteroaryl including 1 to 3 heteroatoms selected from N, O, and S, and a chain grafting moiety. In some embodiments, each RMis independently selected from halogen, optionally substituted Ci-Ce aliphatic, optionally substituted C3-C7 cycloaliphatic, optionally substituted 3- to 7-membered heterocycle including 1 to 3 atoms selected from N, O, and S, optionally substituted Ce-Cio aryl, optionally substituted 4- to 10- membered heteroaryl including 1 to 3 heteroatoms selected from N, O, and S, and a chain grafting moiety. In some embodiments, each RMis independently selected from halogen, optionally substituted C1-C6 aliphatic, optionally substituted Ce-Cw aryl, optionally substituted 4- to 10- membered heteroaryl including 1 to 3 heteroatoms selected from N, O, and S, and a chain grafting moiety. In some embodiments, one or more RMis a chain grafting moiety. In some embodiments, at least one RMis a chain grafting moiety. In some embodiments, RMis a chain grafting moiety is selected from a photoreactive moiety, a thermal reactive moiety, an enzyme reactive moiety, and a crosslinking moiety. In some embodiments, RMis a chain grafting moiety, wherein the chain grafting moiety is a photoreactive moiety selected from a carbene-forming moiety, a nitrene- forming moiety, and a photoreactive crosslinker moiety. In some embodiments, the photo reactive moiety is a carbene-forming moiety. In some embodiments, the photoreactive moiety is a nitrene- forming moiety. In some embodiments, the photoreactive moiety is a photoreactive crosslinker moiety. In some embodiments, the photoreactive moiety is selected from diazerene, azide, and N-Page 59 of 21213013588vlAttorney Docket No.: 2019150-0023 heterocyclic carbene (NHC). In some embodiments, the photoreactive moiety is a diazerene. In some embodiments, the photoreactive moiety is an azide. In some embodiments, the photoreactive moiety is an N-heterocyclic carbene (NHC). In some embodiments, the photoreactive moiety is an N-heterocyclic carbene (NHC) selected from optionally substituted thiazole, triazole, imidazole, and imidazoline. In some embodiments, the photoreactive moiety is an N-heterocyclic carbene (NHC), wherein the NHC is an optionally substituted thiazole. In some embodiments, the photoreactive moiety is an N-heterocyclic carbene (NHC), wherein the NHC is an optionally substituted triazole. In some embodiments, the photoreactive moiety is an N-heterocyclic carbene (NHC), wherein the NHC is an optionally substituted imidazole. In some embodiments, the photoreactive moiety is an N-heterocyclic carbene (NHC), wherein the NHC is an optionally substituted imidazoline. In some embodiments, the photoreactive moiety is an N-heterocyclic carbene (NHC), wherein the NHC is a thiazole. In some embodiments, the photoreactive moiety is an N-heterocyclic carbene (NHC), wherein the NHC is a triazole. In some embodiments, the photoreactive moiety is an N-heterocyclic carbene (NHC), wherein the NHC is an imidazole. In some embodiments, the photoreactive moiety is an N-heterocyclic carbene (NHC), wherein the NHC is an imidazoline. In some embodiments, each RMis hydrogen.

[0189] As described herein, each L may independently be a bond or optionally substituted Ci-C6aliphatic. In some embodiments, each L is a bond. In some embodiments, each L is an optionally substituted Ci-Ce aliphatic. In some embodiments, each L is an optionally substituted Ci-Ce aliphatic selected from optionally substituted methyl, ethyl, propyl, isopropyl, butyl, secbutyl, isobutyl, tert-butyl, pentyl, isopentyl, tert-pentyl, hexyl, and tert-hexyl. In someO O / x embodiments, each L is selected from ' ,, ,

[0190] As described herein, L1is a bond or a spacer moiety. In some embodiments L1is a bond. In some embodiments, L1is spacer moiety. In some embodiments, L1is a spacer moiety selected from an optionally substituted Ci-Ce aliphatic or a polymeric spacer moiety. In some embodiments, L1is a spacer moiety, wherein the spacer moiety is an optionally substituted Ci-Ce aliphatic. In some embodiments, L1is a spacer moiety, wherein the spacer moiety is selected from optionally substituted methyl, ethyl, propyl, isopropyl, butyl, sec-butyl, isobutyl, tert-butyl, pentyl, isopentyl, tert-pentyl, hexyl, and tert-hexyl. In some embodiments, L1is a spacer moiety, whereinPage 60 of 21213013588vlAttorney Docket No.: 2019150-0023. In some embodiments, the spacer moiety is. In some embodiments, the spacer moiety isIn some embodiments, the spacer moietyembodiments, the spacer moiety is. In some embodiments, the spacer moietyPage 61 of 21213013588vlAttorney Docket No.: 2019150-0023 embodiments, the spacer moiety isIn some embodiments, the spacer moiety is. In some embodiments, the spacer moiety is. In some embodiments, the spacer moiety

[0191] In some embodiments, L1is spacer moiety, wherein the spacer moiety is a polymer spacer moiety. In some embodiments, L1is spacer moiety, wherein the spacer moiety is a polymer spacer moiety selected from poly(ethylene glycol), poly(ethylene oxide), poly((meth)acrylatePEG), poly((Ci-C6)alkylamino(meth)acrylate), linear poly(quatemary ammonium), zwitterionic poly(betaine), poly(vinylpyrrolidone), polylysine, polyoxazoline, and polyoxazine, or co-polymers thereof. In some embodiments, L1is spacer moiety, wherein the spacer moiety is a polymer spacer moiety selected from poly(ethylene glycol), poly(ethylene oxide), poly((meth)acrylatePEG), poly((Ci-C6)alkylamino(meth)acrylate), polyvinylpyrrolidone), polyoxazoline, and polyoxazine, or co-polymers thereof. In some embodiments, L1is spacer moiety, wherein the spacer moiety is a polymer spacer moiety selected from poly(ethylene glycol), poly(ethylene oxide), poly((meth)acrylatePEG), and poly((Ci- C6)alkylamino(meth)acrylate), or co-polymers thereof. In some embodiments, the polymeric spacer moiety is poly(ethylene glycol). In some embodiments, the polymeric spacer moiety is poly(ethylene oxide). In some embodiments, the polymeric spacer moiety is poly((meth)acrylatePEG). In some embodiments, the polymeric spacer moiety is poly((Ci- C6)alkylamino(meth)acrylate). In some embodiments, the polymeric spacer moiety is a copolymer.

[0192] As described herein, the degree of polymerization of the polymeric spacer moiety may be in a range from 2 to 500. In some embodiments, the degree of polymerization is in a range from 2 to 100. In some embodiments, the degree of polymerization is in a range from 2 to 50. In some embodiments, the degree of polymerization is in a range from 2 to 25. In some embodiments, the degree of polymerization is or at least 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 25, 30, 35, 40, 45, 50,Page 62 of 21213013588vlAttorney Docket No.: 2019150-002355, 60, 65, 70, 75, 80, 85, 90, 95, or 100. In some embodiments, the degree of polymerization is or at least 100, 110, 120, 130, 140, 150, 160, 170, 180, 190, 200, 250, 300, 350, 400, 450, or 500.

[0193] As described herein, each A may be independently selected from an x-ray sensitive moiety, optionally substituted C3-C7 cycloaliphatic, optionally substituted 3- to 7-membered heterocycle including 1 to 3 atoms selected from N, O, and S, optionally substituted Cg-Cio aryl, and optionally substituted 4- to 10-membered heteroaryl including 1 to 3 heteroatoms selected from N, O, and S. In some embodiments, each A is independently selected from an x-ray sensitive moiety, optionally substituted Cg-Cio aryl, and optionally substituted 4- to 10-membered heteroaryl including 1 to 3 heteroatoms selected from N, O, and S. In some embodiments, each A is independently an optionally substituted Cg-Cio aryl. In some embodiments, each A is independently an optionally substituted 4- to 10-membered heteroaryl including 1 to 3 heteroatoms selected from N, O, and S. In some embodiments, each A is independently an x-ray sensitive moiety.

[0194] As described herein, the number of A moieties (e.g., x-ray sensitive moieties) is x, wherein x may be 0-5. In some embodiments, the number of A moieties is x, wherein x is 0-3. In some embodiments, x is 1, 2, 3, 4, or 5. In some embodiments, x is 0, 1, 2, 3, or 4. In some embodiments, x is 1, 2, 3 or 4. In some embodiments, x is 0, 1, 2, or 3. In some embodiments, x is 1, 2, or 3. In some embodiments, x is 1. In some embodiments, x is 2. In some embodiments, x is 3. In some embodiments, x is 4. In some embodiments, x is 5. In some embodiments, x is 0.

[0195] As described herein, L2is a bond or a spacer moiety. In some embodiments L2is a bond. In some embodiments, L2is spacer moiety. In some embodiments, L2is a spacer moiety selected from an optionally substituted Ci-Cg aliphatic or a polymeric spacer moiety. In some embodiments, L2is a spacer moiety, wherein the spacer moiety is an optionally substituted Ci-Cg aliphatic. In some embodiments, L2is a spacer moiety, wherein the spacer moiety is selected from optionally substituted methyl, ethyl, propyl, isopropyl, butyl, sec-butyl, isobutyl, tert-butyl, pentyl, isopentyl, tert-pentyl, hexyl, and tert-hexyl. In some embodiments, L2is a spacer moiety, wherein the spacer moiety is selected from:Page 63 of 21213013588vlAttorney Docket No.: 2019150-0023. In some embodiments, the spacer moiety isIn some embodiments, the spacer moiety isIn some embodiments, the spacer moietyembodiments, the spacer moiety is. In some embodiments, the spacer, ,Page 64 of 21213013588vlAttorney Docket No.: 2019150-0023. In some embodiments, the spacer moiety is. In some embodiments, the spacer moiety

[0196] In some embodiments, L2is spacer moiety, wherein the spacer moiety is a polymer spacer moiety. In some embodiments, L2is spacer moiety, wherein the spacer moiety is a polymer spacer moiety selected from poly(ethylene glycol), poly(ethylene oxide), poly((meth)acrylatePEG), poly((Ci-C6)alkylamino(meth)acrylate), linear poly(quatemary ammonium), zwitterionic poly(betaine), poly(vinylpyrrolidone), polylysine, polyoxazoline, and polyoxazine, or co-polymers thereof. In some embodiments, L2is spacer moiety, wherein the spacer moiety is a polymer spacer moiety selected from poly(ethylene glycol), polyethylene oxide), poly((meth)acrylatePEG), poly((Ci-C6)alkylamino(meth)acrylate), polyvinylpyrrolidone), polyoxazoline, and polyoxazine, or co-polymers thereof. In some embodiments, L2is spacer moiety, wherein the spacer moiety is a polymer spacer moiety selected from poly(ethylene glycol), poly(ethylene oxide), poly((meth)acrylatePEG), and poly((Ci- C6)alkylamino(meth)acrylate), or co-polymers thereof. In some embodiments, the polymeric spacer moiety is polyethylene glycol). In some embodiments, the polymeric spacer moiety is poly(ethylene oxide). In some embodiments, the polymeric spacer moiety is poly((meth)acrylatePEG). In some embodiments, the polymeric spacer moiety is poly((Ci- C6)alkylamino(meth)acrylate). In some embodiments, the polymeric spacer moiety is a copolymer.

[0197] As described herein, the degree of polymerization of the polymeric spacer moiety may be in a range from 2 to 500. In some embodiments, the degree of polymerization is in a range from 2 to 100. In some embodiments, the degree of polymerization is in a range from 2 to 50. In some embodiments, the degree of polymerization is in a range from 2 to 25. In some embodiments, the degree of polymerization is or at least 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, or 100. In some embodiments, the degree of polymerization is or at least 100, 110, 120, 130, 140, 150, 160, 170, 180, 190, 200, 250, 300, 350, 400, 450, or 500.

[0198] As described herein, Z may be an x-ray sensitive moiety and / or an MRI sensitive moiety (e.g., a metal-ion chelator). In some embodiments, Z is an x-ray sensitive moiety, In somePage 65 of 21213013588vlAttorney Docket No.: 2019150-0023 embodiments, Z is a metal-ion chelator. In some embodiments, Z is an MRI sensitive moiety. In some embodiments, the MRI sensitive moiety is a metal-ion chelator. In some embodiments, the MRI sensitive moiety is a metal-ion chelator selected from DOTA (1,4,7, 10-tetraazacyclododecan-1.4.7.10-tetraacetic acid), DTPA (diethylenetriaminopentaacetic acid), D03A (1,4,7,10- tetraazacyclododecan-l,4,7-triacetic acid), HPDO3A (10-(2-hydroxypropyl)-l,4,7,10- tetraazacyclododecan-l,4,7-triacetic acid), TRITA (1,4,7, 10-Tetrakis(carboxymethyl)-l, 4, 7,10- tetraazacyclotridecane), TETA (1,4,8, 1 l-Tetrakis(carboxymethyl)-l,4,8,l 1-Tetraazacyclotetradecane), BOPTA (4-carboxy-5,8,l l-tris(carboxymethyl)-l-phenyl-2-oxa- 5,8,1 l-triazatridecan-13-oic acid), NOTA (l,4,7-triazacyclononane-N,N',N44-triacetic acid), PCTA (3,6,9,15-tetraazabicyclo[9.3.1]pentadeca-l(15),l l,13-triene-3,6,9-triacetic acid), DOTMA ((alpha, alpha', alpha", alpha"')-tetramethyl-l,4,7,10-tetraazacyclododecan-l, 4, 7, 10- tetraacetic acid), AAZTA (6-amino-6-methylperhydro-l,4-diazepinetetraacetic acid) and HOPO (l-hydroxypyridin-2-one). In some embodiments, the MRI sensitive moiety is a metal-ion chelator selected from DOTA (1, 4, 7, 10-tetraazacyclododecan- 1,4, 7, 10-tetraacetic acid), DTPA (diethylenetriaminopentaacetic acid), DO3A (l,4,7,10-tetraazacyclododecan-l,4,7-triacetic acid), HPDO3A (10-(2-hydroxypropyl)-l,4,7,10-tetraazacyclododecan-l,4,7-triacetic acid), TRITA (l,4,7,10-Tetrakis(carboxymethyl)-l,4,7,10-tetraazacyclotridecane), TETA (1,4,8,11- Tetrakis(carboxymethyl)-l,4,8,l 1-Tetraazacyclotetradecane), and HOPO (l-hydroxypyridin-2- one). In some embodiments, the MRI sensitive moiety is a metal-ion chelator selected from DOTA (1,4, 7, 10-tetraazacyclododecan-l, 4, 7, 10-tetraacetic acid), DTPA (diethylenetriaminopentaacetic acid), DO3A (1,4,7, 10-tetraazacyclododecan-l, 4, 7-triacetic acid), HPDO3A (10-(2- hydroxypropyl)-!, 4, 7, 10-tetraazacyclododecan-l, 4, 7-triacetic acid), and HOPO (1- hydroxypyridin-2-one). In some embodiments, the metal-ion chelator is DOTA (1,4,7, 10- tetraazacyclododecan-l, 4, 7, 10-tetraacetic acid). In some embodiments, the metal-ion chelator is DTPA (diethylenetriaminopentaacetic acid). In some embodiments, the metal-ion chelator is DO3A (1,4,7, 10-tetraazacyclododecan-l, 4, 7-triacetic acid). In some embodiments, the metal-ion chelator is HPDO3A (10-(2-hydroxypropyl)-l, 4, 7, 10-tetraazacyclododecan-l, 4, 7-triacetic acid). In some embodiments, the metal-ion chelator is TRITA (1,4,7, lO-Tetrakis(carboxymethyl)-1.4.7.10-tetraazacy clotridecane). In some embodiments, the metal -ion chelator is TETA (1,4,8,11- Tetrakis(carboxymethyl)-!, 4, 8,11-Tetraazacyclotetradecane). In some embodiments, the metalion chelator is BOPTA (4-carboxy-5,8,l l-tris(carboxymethyl)-l-phenyl-2-oxa-5,8,l 1-Page 66 of 21213013588vlAttorney Docket No.: 2019150-0023 triazatridecan-13-oic acid). In some embodiments, the metal-ion chelator is NOTA (1 ,4,7- triazacyclononane-N,N',N44-triacetic acid). In some embodiments, the metal-ion chelator is PCTA (3,6,9, 15-tetraazabicyclo[9.3.1]pentadeca-l(15),l l,13-triene-3,6,9-triacetic acid). In some embodiments, the metal-ion chelator is DOTMA ((alpha, alpha', alpha", alpha"')-tetramethyl- l,4,7,10-tetraazacyclododecan-l,4,7,10-tetraacetic acid). In some embodiments, the metal-ion chelator is AAZTA (6-amino-6-methylperhydro-l,4-diazepinetetraacetic acid). In some embodiments, the metal -ion chelator is HOPO (l-hydroxypyridin-2-one).

[0199] As described herein, the metal-ion chelator may chelate positively charged metal ions. In some embodiments, the metal ions carry a 2+ charge. In some embodiments, the metal ions are divalent ions. In some embodiments, the metal ions are alkaline-earth metal ions. In some embodiments, the metal ions are transition metal ions. In some embodiments, the metal ions are lanthonoid metals. In some embodiments, the metal ions are selected from Ca2+, Mg2+, Mn2+, Cu2+, Gd2+, . • In some embodiments, the metal ions are gadolinium (Gd2+) ions. In some embodiments, the metal ions are manganese (Mn2 1) ions. In some embodiments, the metal-ion chelator chelates divalent metal ions. In some embodiments, the metal-ion chelator chelates alkaline-earth metal ions. In some embodiments, the metal-ion chelator chelates transition metal ions. In some embodiments, the metal-ion chelator chelates lanthanoid metal ions. In some embodiments, the metal-ion chelator chelates Ca2+, Mg2+, Mn2+, Cu2+, Gd2+, .... In some embodiments, the metal-ion chelator chelates gadolinium (Gd2+) ions. In some embodiments, the metal-ion chelator chelates manganese (Mn2+) ions.

[0200] As described herein, the number of Z moieties (e.g., MRI sensitive moieties) is m, wherein m may be 0-5. In some embodiments, the number of Z moieties is m, wherein m is 0-3. In some embodiments, m is 1, 2, 3, 4, or 5. In some embodiments, m is 0, 1, 2, 3, or 4. In some embodiments, m is 1, 2, 3 or 4. In some embodiments, m is 0, 1, 2, or 3. In some embodiments, m is 1, 2, or 3. In some embodiments, m is 1. In some embodiments, m is 2. In some embodiments, m is 3. In some embodiments, m is 4. In some embodiments, m is 5. In some embodiments, m is 0.

[0201] As described herein, the number of spacer backbone units (M) between an x-ray sensitive moiety and an MRI-sensitive moiety may be n, wherein n is 0-10. In some embodiments, the number of spacer backbone units (M) between the x-ray sensitive moieties and the MRI- sensitive moieties is n, wherein n is 0-5. In some embodiments, n is 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9. InPage 67 of 21213013588vlAttorney Docket No.: 2019150-0023 some embodiments, n is 1, 2, 3, 4, 5, 6, 7, 8, or 9. In some embodiments, n is 0, 1, 2, 3, 4, or 5. In some embodiments, n is 1, 2, 3, 4, or 5. In some embodiments, n is 0, 1, 2, 3, or 4. In some embodiments, n is 1, 2, 3 or 4. In some embodiments, n is 0, 1, 2, or 3. In some embodiments, n is 1, 2, or 3. In some embodiments, n is 1. In some embodiments, n is 2. In some embodiments, n is 3. In some embodiments, n is 4. In some embodiments, n is 5. In some embodiments, n is 6. In some embodiments, n is 7. In some embodiments, n is 8. In some embodiments, n is 9. In some embodiments, n is 10. In some embodiments, n is 0.

[0202] As used herein, “surface attachment moiety” and “chain grafting moiety” are used interchangeably to refer to a moiety that can be used to attach a molecule (e.g., polymer chain) to a thread or fiber (e.g., a surface thereof). A surface attachment moiety may be a photoreactive moiety, a thermal reactive moiety, an enzyme reactive moiety, or a crosslinking moiety. A surface attachment moiety may be included in a pendant group of a polymer chain. A surface attachment moiety may be an end group of a polymer chain. A surface attachment moiety may be included in a molecule that includes one or more x-ray sensitive moieties and / or one or more MRI sensitive moi eties.

[0203] Aliphatic: The term “aliphatic” refers to a straight-chain (i.e., unbranched) or branched, substituted or unsubstituted hydrocarbon chain that is completely saturated or that contains one or more units of unsaturation, or a monocyclic hydrocarbon or bicyclic hydrocarbon that is completely saturated or that contains one or more units of unsaturation, but which is not aromatic (also referred to herein as “cycloaliphatic”), that has a single point or more than one points of attachment to the rest of the molecule. Unless otherwise specified, aliphatic groups contain 1-12 aliphatic carbon atoms. In some embodiments, aliphatic groups contain 1-6 aliphatic carbon atoms (e.g., Ci-e). In some embodiments, aliphatic groups contain 1-5 aliphatic carbon atoms (e.g., C1.5). In other embodiments, aliphatic groups contain 1-4 aliphatic carbon atoms (e.g., CM). In still other embodiments, aliphatic groups contain 1-3 aliphatic carbon atoms (e.g., C1-3), and in yet other embodiments, aliphatic groups contain 1-2 aliphatic carbon atoms (e.g., C1-2). Suitable aliphatic groups include, but are not limited to, linear or branched, substituted or unsubstituted alkyl, alkenyl, or alkynyl groups and hybrids thereof. A preferred aliphatic group is C1-6 alkyl.

[0204] Alkyl: The term “alkyl”, used alone or as part of a larger moiety, refers to a saturated, optionally substituted straight or branched chain hydrocarbon group having (unlessPage 68 of 21213013588vlAttorney Docket No.: 2019150-0023 otherwise specified) 1 -12, 1-10, 1-8, 1 -6, 1-4, 1 -3, or 1 -2 carbon atoms (e.g., C1-12, Ci-io, C1-8, Ci. 6, C 1-4, C1-3, or C1-2). Exemplary alkyl groups include methyl, ethyl, propyl, butyl, pentyl, hexyl, and heptyl.

[0205] Alkylene: The term “alkylene” is refers to a bivalent alkyl group. In some embodiments, “alkylene” is a bivalent straight or branched alkyl group. In some embodiments, an "alkylene chain" is a polymethylene group, i.e., -(CH2)n-, wherein n is a positive integer, e.g., from 1 to 6, from 1 to 4, from 1 to 3, from 1 to 2, or from 2 to 3. An optionally substituted alkylene chain is a polymethylene group in which one or more methylene hydrogen atoms is optionally replaced with a substituent. Suitable substituents include those described below for a substituted aliphatic group and also include those described in the specification herein. It will be appreciated that two substituents of the alkylene group may be taken together to form a ring system. In certain embodiments, two substituents can be taken together to form a 3- to 7-membered ring. The substituents can be on the same or different atoms. The suffix “-ene” or “-enyl” when appended to certain groups herein are intended to refer to a bifunctional moiety of said group. For example, “-ene” or “-enyl”, when appended to “cyclopropyl” becomes “cyclopropylene” or “cyclopropylenyl” and is intended to refer to a bifunctional cyclopropyl group, e.g.,.

[0206] Alkenyl: The term “alkenyl”, used alone or as part of a larger moiety, refers to an optionally substituted straight or branched chain or cyclic hydrocarbon group having at least one double bond and having (unless otherwise specified) 2-12, 2-10, 2-8, 2-6, 2-4, or 2-3 carbon atoms(e.g., C2-12, C2-10, C2-8, C2-6, C2-4, or C2-3). Exemplary alkenyl groups include ethenyl, propenyl, butenyl, pentenyl, hexenyl, and heptenyl. The term “cycloalkenyl” refers to an optionally substituted non-aromatic monocyclic or multicyclic ring system containing at least one carbon-carbon double bond and having 3 to 10 carbon atoms. Exemplary monocyclic cycloalkenyl rings include cyclopentenyl, cyclohexenyl, and cycloheptenyl.

[0207] Alkynyl: The term “alkynyl”, used alone or as part of a larger moiety, refers to an optionally substituted straight or branched chain hydrocarbon group having at least one triple bond and having (unless otherwise specified) 2-12, 2-10, 2-8, 2-6, 2-4, or 2-3 carbon atoms (e.g., C2-12, C2-10, C2-8, C2-6, C2-4, or C2-3). Exemplary alkynyl groups include ethynyl, propynyl, butynyl, pentynyl, hexynyl, and heptynyl.Page 69 of 21213013588vlAttorney Docket No.: 2019150-0023

[0208] Aryl: The term “aryl” refers to monocyclic and bicyclic ring systems having a total of six to fourteen ring members (e.g., Ce-Cw), wherein at least one ring in the system is aromatic and wherein each ring in the system contains three to seven ring members. In some embodiments, an “aryl” group contains between six and twelve total ring members (e.g., Ce-Cn). The term “aryl” may be used interchangeably with the term “aryl ring”. In certain embodiments, “aryl” refers to an aromatic ring system which includes, but not limited to, phenyl, biphenyl, naphthyl, anthracyl and the like, which may bear one or more substituents. Unless otherwise specified, “aryl” groups are hydrocarbons. In some embodiments, an “aryl” ring system is an aromatic ring (e.g., phenyl) that is fused to a non-aromatic ring (e.g., cycloalkyl). Examples of aryl rings include that are fused

[0209] Bicyclic. The term “bicyclic ring” or “bicyclic ring system” refers to any bicyclic ring system, i.e. , carbocyclic or heterocyclic, saturated or having one or more units of unsaturation, having one or more atoms in common between the two rings of the ring system. Thus, the term includes any permissible ring fusion, such as wz / m-fused or spirocyclic. As used herein, the term “heterobicyclic” is a subset of “bicyclic” that requires that one or more heteroatoms are present in one or both rings of the bicycle. Such heteroatoms may be present at ring junctions and are optionally substituted, and may be selected from nitrogen (including N-oxides), oxygen, sulfur (including oxidized forms such as sulfones and sulfonates), phosphorus (including oxidized forms such as phosphates), boron, etc. In some embodiments, a bicyclic group has 7-12 ring members and 0-4 heteroatoms independently selected from nitrogen, oxygen, or sulfur. As used herein, the term “bridged bicyclic” refers to any bicyclic ring system, i.e., carbocyclic or heterocyclic, saturated or partially unsaturated, having at least one bridge. As defined by IUPAC, a “bridge” is an unbranched chain of atoms or an atom or a valence bond connecting two bridgeheads, where a “bridgehead” is any skeletal atom of the ring system which is bonded to three or more skeletal atoms (excluding hydrogen). In some embodiments, a bridged bicyclic group has 7-12 ring members and 0-4 heteroatoms independently selected from nitrogen, oxygen, or sulfur. Such bridged bicyclic groups are well known in the art and include those groups set forth below where each group is attached to the rest of the molecule at any substitutable carbon or nitrogen atom. Unless otherwise specified, a bridged bicyclic group is optionally substituted with one or morePage 70 of 21213013588vlAttorney Docket No.: 2019150-0023 substituents as set forth for aliphatic groups. Additionally or alternatively, any substitutable nitrogen of a bridged bicyclic group is optionally substituted. Exemplary bicyclic rings include:Exemplary bridged bicyclics include:

[0210] Composition: Those skilled in the art will appreciate that the term “composition” may be used to refer to a discrete physical entity that includes one or more specified components. In general, unless otherwise specified, a composition may be of any form - e.g., gas, gel, liquid, solid, etc.

[0211] Cycloaliphatic. As used herein, the term “cycloaliphatic” refers to a monocyclic C3-8 hydrocarbon or a bicyclic Ce-12 hydrocarbon that is completely saturated or that contains onePage 71 of 21213013588vlAttorney Docket No.: 2019150-0023 or more units of unsaturation, but which is not aromatic, that has a single point or more than one points of attachment to the rest of the molecule.

[0212] Cycloalkyl. As used herein, the term “cycloalkyl” refers to an optionally substituted saturated ring monocyclic or polycyclic system of 3 to 10 ring carbon atoms. Exemplary monocyclic cycloalkyl rings include cyclopropyl, cyclobutyl, cyclopentyl, cyclohexyl, and cycloheptyl.

[0213] Halogen: The term “halogen” or “halo” means F, Cl, Br, or I.

[0214] Heteroaliphatic The term “heteroaliphatic” or “heteroaliphatic group”, as used herein, denotes an optionally substituted hydrocarbon moiety having, in addition to carbon atoms, from one to five heteroatoms, that may be straight-chain (i.e., unbranched), branched, or cyclic (“heterocyclic”) and may be completely saturated or may contain one or more units of unsaturation, but which is not aromatic. The term “heteroatom” refers to nitrogen, oxygen, or sulfur, and includes any oxidized form of nitrogen or sulfur, and any quatemized form of a basic nitrogen. The term “nitrogen” also includes a substituted nitrogen. Unless otherwise specified, heteroaliphatic groups contain 1-10 carbon atoms wherein 1-3 carbon atoms are optionally and independently replaced with heteroatoms selected from oxygen, nitrogen, and sulfur. In some embodiments, heteroaliphatic groups contain 1-4 carbon atoms, wherein 1-2 carbon atoms are optionally and independently replaced with heteroatoms selected from oxygen, nitrogen, and sulfur. In yet other embodiments, heteroaliphatic groups contain 1-3 carbon atoms, wherein 1 carbon atom is optionally and independently replaced with a heteroatom selected from oxygen, nitrogen, and sulfur. Suitable heteroaliphatic groups include, but are not limited to, linear or branched, heteroalkyl, heteroalkenyl, and heteroalkynyl groups. For example, a 1- to 10 atom heteroaliphatic group includes the following exemplary groups: -O-CH3, -CH2-O-CH3, -O-CH2- CH2-O-CH2-CH2-O-CH3, and the like.

[0215] Heteroaryl: The terms “heteroaryl” and “heteroar-”, used alone or as part of a larger moiety, e.g., “heteroaralkyl”, or “heteroaralkoxy”, refer to monocyclic or bicyclic ring groups having 5 to 10 ring atoms (e.g., 5- to 6-membered monocyclic heteroaryl or 9- to 10- membered bicyclic heteroaryl); having 6, 10, or 147t-electrons shared in a cyclic array; and having, in addition to carbon atoms, from one to five heteroatoms. Heteroaryl groups include, without limitation, thienyl, furanyl, pyrrolyl, imidazolyl, pyrazolyl, triazolyl, tetrazolyl, oxazolyl, isoxazolyl, oxadiazolyl, thiazolyl, isothiazolyl, thiadiazolyl, pyridyl, pyridazinyl, pyrimidinyl,Page 72 of 21213013588vlAttorney Docket No.: 2019150-0023 pyrazinyl, indolizinyl, purinyl, naphthyridinyl, pteridinyl, imidazo[l ,2-a]pyrimidinyl, imidazo[l,2-a]pyridyl, imidazo[4,5-b]pyridyl, imidazo[4,5-c]pyridyl, pyrrol opyridyl, pyrrolopyrazinyl, thienopyrimidinyl, triazolopyridyl, and benzoisoxazolyl. The terms “heteroaryl” and “heteroar-”, as used herein, also include groups in which a heteroaromatic ring is fused to one or more aryl, cycloaliphatic, or heterocyclyl rings, where the radical or point of attachment is on the heteroaromatic ring (i.e., a bicyclic heteroaryl ring having 1 to 3 heteroatoms). Nonlimiting examples include indolyl, isoindolyl, benzothienyl, benzofuranyl, dibenzofuranyl, indazolyl, benzimidazolyl, benzotriazolyl, benzothiazolyl, benzothiadiazolyl, benzoxazolyl, quinolyl, isoquinolyl, cinnolinyl, phthalazinyl, quinazolinyl, quinoxalinyl, 47 / quinolizinyl, carbazolyl, acridinyl, phenazinyl, phenothiazinyl, phenoxazinyl, tetrahydroquinolinyl, tetrahydroisoquinolinyl, pyrido[2,3-b]-l,4-oxazin-3(4H)-one, 4H-thieno[3,2-b]pyrrole, and benzoisoxazolyl. The term “heteroaryl” may be used interchangeably with the terms “heteroaryl ring”, “heteroaryl group”, or “heteroaromatic”, any of which terms include rings that are optionally substituted.

[0216] Heteroatom: The term “heteroatom” as used herein refers to nitrogen, oxygen, or sulfur, and includes any oxidized form of nitrogen or sulfur, and any quatemized form of a basic nitrogen.

[0217] Heterocycle: As used herein, the terms “heterocycle”, “heterocyclyl”, “heterocyclic radical”, and “heterocyclic ring” are used interchangeably and refer to a stable 3- to 8-membered monocyclic, a 6- to 10-membered bicyclic, or a 10- to 16-membered polycyclic heterocyclic moiety that is either saturated or partially unsaturated, and having, in addition to carbon atoms, one or more, such as one to four, heteroatoms, as defined above. When used in reference to a ring atom of a heterocycle, the term "nitrogen" includes a substituted nitrogen. As an example, in a saturated or partially unsaturated ring having 0-3 heteroatoms selected from oxygen, sulfur or nitrogen, the nitrogen may be N (as in 3,4-dihydro-2H-pyrrolyl), NH (as in pyrrolidinyl), or NR+(as in N-substituted pyrrolidinyl). A heterocyclic ring can be attached to its pendant group at any heteroatom or carbon atom that results in a stable structure and any of the ring atoms can be optionally substituted. Examples of such saturated or partially unsaturated heterocyclic radicals include, without limitation, azetidinyl, oxetanyl, tetrahydrofuranyl, tetrahydrothienyl, pyrrolidinyl, piperidinyl, decahydroquinolinyl, oxazolidinyl, piperazinyl, dioxanyl, dioxolanyl, diazepinyl, oxazepinyl, thiazepinyl, morpholinyl, and thiamorpholinyl. APage 73 of 21213013588vlAttorney Docket No.: 2019150-0023 heterocyclyl group may be mono-, bi-, tri-, or polycyclic, preferably mono-, bi-, or tricyclic, more preferably mono- or bicyclic. A bicyclic heterocyclic ring also includes groups in which the heterocyclic ring is fused to one or more aryl rings. Exemplary bicyclic heterocyclic groups include indolinyl, isoindolinyl, benzodi oxolyl, 1,3-dihydroisobenzofuranyl, 2,3- dihydrobenzofuranyl, and tetrahydroquinolinyl. A bicyclic heterocyclic ring can also be a spirocyclic ring system (e.g., 7- to 11 -membered spirocyclic fused heterocyclic ring having, in addition to carbon atoms, one or more heteroatoms as defined above (e.g., one, two, three or four heteroatoms)). A bicyclic heterocyclic ring can also be a bridged ring system (e.g., 7- to 11- membered bridged heterocyclic ring having one, two, or three bridging atoms.

[0218] Partially unsaturated: As used herein, the term “partially unsaturated” refers to a ring moiety that includes at least one double or triple bond between ring atoms. The term “partially unsaturated” is intended to encompass rings having multiple sites of unsaturation, but is not intended to include aromatic (e.g., aryl or heteroaryl) moieties, as herein defined.

[0219] Polycyclic'. As used herein, the term “polycyclic” refers to a saturated or unsaturated ring system having two or more rings (for example, heterocyclyl rings, heteroaryl rings, cycloalkyl rings, or aryl rings), having between 7 and 20 atoms, in which one or more carbon atoms are common to two adjacent rings. For example, in some embodiments, a polycyclic ring system refers to a saturated or unsaturated ring system having three or more rings (for example, heterocyclyl rings, heteroaryl rings, cycloalkyl rings, or aryl rings), having between 14 and 20 atoms, in which one or more carbon atoms are common to two adjacent rings. The rings in a polycyclic ring system may be fused (i.e., bicyclic or tricyclic), spirocyclic, or a combination thereof. An example polycyclic ring is a steroid.

[0220] Substituted or optionally substituted: As described herein, molecules may contain “optionally substituted” moieties. In general, the term “substituted,” whether preceded by the term “optionally” or not, means that one or more hydrogens of the designated moiety are replaced with a suitable substituent. “Substituted” applies to one or more hydrogens that are either explicit or implicit from the structure (e.g.,refers to at leastrefersPage 74 of 21213013588vlAttorney Docket No.: 2019150-0023 to at leastUnless otherwise indicated, an “optionally substituted” group may have a suitable substituent at each substitutable position of the group, and when more than one position in any given structure may be substituted with more than one substituent selected from a specified group, the substituent may be either the same or different at every position. Combinations of substituents envisioned by this invention are preferably those that result in the formation of stable or chemically feasible molecules. The term “stable,” as used herein, refers to molecules that are not substantially altered when subjected to conditions to allow for their production, detection, and, in certain embodiments, their recovery, purification, and use for one or more of the purposes provided herein. Groups described as being “substituted” preferably have between 1 and 4 substituents, more preferably 1 or 2 substituents. Groups described as being “optionally substituted” may be unsubstituted or be “substituted” as described above.

[0221] Suitable monovalent substituents on a substitutable carbon atom of an “optionally substituted” group are independently halogen; -(CH2)o-4R°; -(CFhjo^OR0; -0(CH2)o-4R°, -O- (CH2)O-4C(0)OR°; -(CH2)O 4CH(OR°)2; -(CH2)O 4SR0; -(CH2)O 4Ph, which may be substituted with R°; -(CH2)o 40(CH2)o iPh which may be substituted with R°; -CH=CHPh, which may be substituted with R°; -(CH2)O-40(CH2)O-I -pyridyl which may be substituted with R°; -NCh; -CN; -N3; -(CH2)O-4N(R°)2; -(CH2)O4N(R°)C(O)R°; -N(R°)C(S)R°; -(CH2)O-4N(R°)C(O)NRO2; -N(RO)C(S)NR°2; -(CH2)O4N(R°)C(O)OR°;N(R°)N(R°)C(O)R°; -N(Ro)N(R°)C(0)NRo2; -N(R°)N(R°)C(O)OR°; -(CH2)o4C(O)R°; C(S)R°; (CH2)O4C(O)ORO; (CH2)O4C(O)SRO; -(CH2)O4C(O)OSiR°3; (CH2)o4OC(O)R°;OC(0)(CH2)O4SR°; -(CH2)O4SC(O)R°; -(CH2)O4C(0)NRO2; -C(S)NRO2; -C(S)SR°; - SC(S)SR°, -(CH2)O 4OC(O)NRO2; -C(O)N(OR°)R°; -C(O)C(O)R°; -C(O)CH2C(O)RO; - C(NOR°)R°; -(CH2)O4SSRO; -(CH2)O4S(0)2RO; -(CH2)O4S(O)2ORO; -(CH2)O4OS(O)2RO; - S(O)2NR°2; -(CH2)O4S(O)RO; -N(RO)S(O)2NR°2; -N(RO)S(O)2R°; -N(OR°)R°; -C(NH)NRO2; - P(O)2R°; -P(O)R°2; -OP(O)R°2; -OP(O)(ORO)2; SiR°3; -(C1-4 straight or branched alkylenejO- N(R°)2; or -(C1-4 straight or branched alkylene)C(O)O-N(R°)2, wherein each R° may be substituted as defined below and is independently hydrogen, C1-6 aliphatic, -CH2Ph, -0(CH2)o Page 75 of 21213013588vlAttorney Docket No.: 2019150-0023 iPh, -CH2-(5- to 6-membered heteroaryl ring), or a 3- to 6-membered saturated, partially unsaturated, or aryl ring having 0-4 heteroatoms independently selected from nitrogen, oxygen, or sulfur, or, notwithstanding the definition above, two independent occurrences of R°, taken together with their intervening atom(s), form a 3- to 12-membered saturated, partially unsaturated, or aryl mono- or bicyclic ring having 0-4 heteroatoms independently selected from nitrogen, oxygen, or sulfur, which may be substituted as defined below.

[0222] Suitable monovalent substituents on R° (or the ring formed by taking two independent occurrences of R° together with their intervening atoms), are independently halogen, -(CH2)0 2R*, -(haloR*), -(CH2)O2OH, -(CH2)O 2OR*, -(CH2)O 2CH(OR*)2, -O(haloR’), -CN, - N3, -(CH2)O 2C(O)R*, -(CH2)O2C(O)OH, -(CH2)O2C(O)OR*, -(CH2)O2SR*, -(CH2)O2SH, - (CH2)0 2NH2, -(CH2)O 2NHR*, -(CH2)O 2NR*2, -NO2, -SiR*3, -OSiR*3, -C(O)SR*. -(Ci4straight or branched alkylene)C(O)OR*, or -SSR* wherein each R* is unsubstituted or where preceded by “halo” is substituted only with one or more halogens, and is independently selected from Ci- 4 aliphatic, -CH2Ph, -0(CH2)o iPh, or a 3- to 6-membered saturated, partially unsaturated, or aryl ring having 0-4 heteroatoms independently selected from nitrogen, oxygen, or sulfur. Suitable divalent substituents on a saturated carbon atom of R° include =0 and =S.

[0223] Suitable divalent substituents on a saturated carbon atom of an “optionally substituted” group include the following: =0 (“oxo”), =S, =NNR*2, =NNHC(O)R*,wherein each independent occurrence of R* is selected from hydrogen, Ci-6 aliphatic which may be substituted as defined below, or an unsubstituted 5- to 6-membered saturated, partially unsaturated, or aryl ring having 0-4 heteroatoms independently selected from nitrogen, oxygen, or sulfur. Suitable divalent substituents that are bound to vicinal substitutable carbons of an “optionally substituted” group include: -O(CR*2)2 3O-, wherein each independent occurrence of R* is selected from hydrogen, Ci-6 aliphatic which may be substituted as defined below, or an unsubstituted 5- 6-membered saturated, partially unsaturated, or aryl ring having 0-4 heteroatoms independently selected from nitrogen, oxygen, or sulfur.

[0224] Suitable substituents on the aliphatic group of R* include halogen, - R*, -(haloR*), -OH, -OR*, -O(haloR*), -CN, -C(O)OH, -C(O)OR*, -NH2, -NHR*, -NR*2, or - NO2, wherein each R* is unsubstituted or where preceded by “halo” is substituted only with one or more halogens, and is independently Ci-4 aliphatic, -CH2Ph, -0(CH2)o iPh, or a 3- to 6- Page 76 of 21213013588vlAttorney Docket No.: 2019150-0023 membered saturated, partially unsaturated, or aryl ring having 0-4 heteroatoms independently selected from nitrogen, oxygen, or sulfur.

[0225] Suitable substituents on a substitutable nitrogen of an “optionally substituted” group include )Rr, C(O)CH2C(O)Rt, -t; wherein each R1' is independently hydrogen, Ci-6 aliphatic which may be substituted as defined below, unsubstituted -OPh, or an unsubstituted 3- to 6-membered saturated, partially unsaturated, or aryl ring having 0-4 heteroatoms independently selected from nitrogen, oxygen, or sulfur, or, notwithstanding the definition above, two independent occurrences of R\ taken together with their intervening atom(s) form an unsubstituted 3- to 12-membered saturated, partially unsaturated, or aryl mono- or bicyclic ring having 0-4 heteroatoms independently selected from nitrogen, oxygen, or sulfur.

[0226] Suitable substituents on the aliphatic group of R' are independently halogen, - R*, -(haloR*), -OH, -OR*, -O(haloR*), -CN, -C(O)OH, -C(O)OR*, -NH2, -NHR*, -NR*2, or -NO2, wherein each R* is unsubstituted or where preceded by “halo” is substituted only with one or more halogens, and is independently Ci^i aliphatic, -CH2Ph, -0(CH2)o iPh, or a 3- to 6- membered saturated, partially unsaturated, or aryl ring having 0-4 heteroatoms independently selected from nitrogen, oxygen, or sulfur.

[0227] Those skilled in the art will further appreciate that, in molecular structures, the symbol , as used herein, refers to a point of attachment between two atoms. Additionally or alternatively, the symbol ■~wrefers to a point of attachment ring in a spirocyclic manner.Additional Security Features

[0228] Multiple authentication elements may also provide additional (or alternative) (e.g., secondary) security to an object beyond the ability to verify the object using one or more authentication codes. In some embodiments, multiple authentication elements have an arrangement (e.g., spatial distribution and / or orientation) that corresponds to an object being authentic (e.g., is verifiable). For example, an arrangement may be spatial distribution of multiple authentication elements within and / or on (e.g., a surface of) an object. An arrangement may be relative to each other and / or relative to an object, such as a fixed point of the object, a comer, an edge, or a combination thereof. For example, an arrangement may correspond to a verifiablePage 77 of 21213013588vlAttorney Docket No.: 2019150-0023 pattern. Therefore, it may be possible to determine that an object is not authentic based on how multiple authentication elements are arranged, whether or not the authentication elements encode at least a portion of one or more correct authentication codes that would authenticate the object. In this way, even if an authentication code is compromised, a counterfeiter would still need to know the correct arrangement for multiple authentication elements to create a forgery of the obj ect. Aspects of an arrangement of multiple authentication elements may be irrelevant to authenticity, for example location may matter but orientation does not, or relative orientation and absolute position may matter but relative position and absolute orientation may not. Different arrangements of multiple authentication elements may be used to ensure authenticity for different objects (e.g., different copies of a same type of object) even if an authentication code is reused. Such complex schemes can further reduce the ability of a counterfeiter to produce counterfeit objects.

[0229] Similarly, a single authentication element may also provide additional (or alternative) (e.g., secondary) security to an object beyond the ability to verify the object using one or more authentication codes. In some embodiments, has an arrangement (e.g., spatial distribution and / or orientation) that corresponds to an object being authentic (e.g., is verifiable). The arrangement may relative to an object, such as a fixed point of the object, a comer, an edge, or a combination thereof. Therefore, it may be possible to determine that an object is not authentic based on how a single authentication element is arranged relative to an object, whether or not the authentication element encodes at least a portion of one or more correct authentication codes that would authenticate the object. In this way, even if an authentication code is compromised, a counterfeiter would still need to know the correct arrangement for an authentication element relative to an object to create a forgery of the object. Aspects of an arrangement of an authentication element may be irrelevant to authenticity, for example location may matter but orientation does not. Different arrangements of a single authentication element may be used to ensure authenticity for different objects (e.g., different copies of a same type of object) even if an authentication code is reused. Such complex schemes can further reduce the ability of a counterfeiter to produce counterfeit objects, even when using only a single authentication element.

[0230] Security schemes using multiple authentication elements can also provide a first, fast means to determine authenticity. For example, in some embodiments, if multiple authentication elements are not disposed in a correct absolute and / or relative arrangement, then an associated object is not authentic. Therefore, simply checking the arrangement first may bePage 78 of 21213013588vlAttorney Docket No.: 2019150-0023 sufficient to determine a lack of authenticity without needing to actually read the authentication elements. Multiple authentication elements that encode only a rudimentary authentication code (e.g., a 1 or a 0) may be used in an arrangement (e.g., relative to each other or relative to an object) to provide simple security to an object. In some embodiments, multiple radiopaque elements are physically associated with (e.g., disposed on or in, embedded in, adhered to, integrated with) an object in an arrangement that corresponds to an object being authentic (e.g., is verifiable); such radiopaque elements may be constructed like an authentication element or encoding portion disclosed herein but need not be an authentication element or encoding portion (e.g., there may be no authentication code encoded). Nonetheless, arrangement of such simple authentication elements may not provide sufficient security, for example for high-value objects. Generally, in many applications, authentication elements that encode at least a portion of one or more complex authentication codes are preferred for additional security.

[0231] One or more additional security (e.g., error detection) techniques may be applied in connection with an authentication element that encodes at least a portion of an authentication code. Examples of additional security (e.g., error detection) techniques that may be used include parity bit, checksum, and check digit. For example, at least a portion of an authentication code may include a parity bit or a check digit. As another example, in some embodiments, at least a portion of an authentication code read from an authentication element may be verified as authentic or not based on a checksum, a parity bit, or a check digit. As another example, at least a portion of an authentication code may be verified, at least in part, by a checksum (e g., of two or more characters in the at least a portion of an authentication code). An authentication element may encode at least a portion of an authentication code including a check digit and / or parity bit thereof. An authentication element may encode (i) at least a portion of an authentication code and (ii) a check digit or parity bit. In some embodiments, one or more additional security techniques may be used whether an authentication code is characters (e.g., alphanumeric characters) or a pattern.

[0232] In some embodiments, radiodensity and / or sound wave attenuation is used as a type of parity bit and / or check digit. For example, in some embodiments, an authentication element encodes at least a portion of an authentication code as a QR code or barcode where a portion of the QR code or barcode (e.g., one or more bits of the QR code or one or more bars of the barcode) has a certain radiodensity and / or sound wave attenuation (e.g., higher or lower than one or more other bits of the QR code or one or more other bars of the barcode) that allows verification ofPage 79 of 21213013588vlAttorney Docket No.: 2019150-0023 authenticity of the at least a portion of the authentication code. Tn some embodiments, a portion that has a certain radiodensity is a particular predetermined portion (e.g., always a certain bit or bits of a QR code or always certain bar(s) of a barcode). In some embodiments, a portion that has a certain radiodensity is a portion selected by a person or organization to whom an authentication code pertains (e.g., is only known to that person or organization). In some embodiments, if one or more additional security techniques are used with an authentication element that encodes at least a portion of an authentication code, it can be determined that an object or label physically associated with the authentication element is not authentic (e.g., is counterfeit) even if the authentication code itself, determined at least in part by reading the authentication element, appears authentic. For example, an authentication code read from an authentication element (e.g., a QR code) may appear authentic but radiodensity of a certain portion of the authentication element (e.g., one or more certain bits of the QR code) is not correct and therefore an object physically associated with the authentication element can be determined to be counterfeit.

[0233] Using one or more such additional security techniques provides an additional layer of security in that even if a potential counterfeiter comes into possession of an authentication code, the counterfeiter may not know that one or more additional security techniques are being employed. Similarly, a counterfeiter that comes into possession of a genuine object for which a forgery or counterfeit copy is intended to be made may identify an authentication element is present and be able to copy the authentication element in the attempted forgery or counterfeit copy but not know or appreciate by simple inspection (e.g., with x-rays, radio waves, or sound waves) that an additional security technique is being employed. For example, the counterfeiter may not know the correct parity bit, check digit, or check sum. The counterfeiter may therefore fail to incorporate that into the attempted forgery or counterfeit copy, such that security of the original is maintained. Similarly, a counterfeiter may try to incorporate an authentication element with an object that encodes at least a portion of a fake authentication code where the fake authentication code does not include the correct parity bit, check digit, or checksum for that object or type of object such that it can be determined that the forged or counterfeit object(s) are detectable as not authentic. pH Sensitive Authentication ElementsPage 80 of 21213013588vlAttorney Docket No.: 2019150-0023

[0234] In some embodiments, an authentication element is structured to be readable to indicate a pH of a local environment. For example, an authentication element may be coated with a pH sensitive coating that causes a change in state of the authentication element upon a change in local pH near the authentication element. An authentication element may be pH sensitive. In some embodiments, a conformational state of an authentication element (e.g., size, shape, and / or spacing) may change upon change of local pH. In some embodiments, spacing of one or more encoding portions of an authentication element may change in response to changes in local pH. In some embodiments, radial dimension of encoding portions of the authentication element may change in response to changes in local pH. In some embodiments, an authentication may be used to determine safety or quality of a food product in addition to or alternatively to authentication of the food product. Determining safety may include determining a relative pH relative to a baseline, for example a baseline that corresponds to a safe or acceptable food product (e g., the food product is safe to be consumed) (e.g., quality of the food meets desired standards). Because an authentication element may be able to be read without being visible, a pH sensitive authentication element may be able to be covered by food or beverage or packaging for the food or beverage and still serve its intended function. An authentication element may be disposed on an interior of food or beverage packaging such that it is in contact with a local environment for the food or beverage (e.g., in contact with the food or beverage) to be able to usefully indicate pH and therefore food safety. In some embodiments, a pH sensitive element is not also an authentication element. Such a pH sensitive element may include one or more pH sensitive subelements analogous to encoding portion(s) disclosed herein (e.g., previously in this paragraph) notwithstanding that no portion of an authentication code is encoded thereby.

[0235] In some embodiments, an authentication element may be used to indicate wine quality. When wine is exposed to oxygen for a long time, the alcohol within the wine changes into acetic acid, also known as wine turning, and therefore, higher acidity (i.e., lower pH level) may be an indicator of a spoiled wine. An authentication element that is pH sensitive may be used to determine a relative pH level of a bottle of wine. For example, an authentication element may be embedded into or integrated with an interior surface of a bottle of wine. For example, an authentication element may be affixed or adhered to an interior surface of a bottle of wine. For example, an authentication element may be embedded into or integrated with a cork that is used to seal a bottle of wine. For example, an authentication element may be affixed or adhered to a corkPage 81 of 21213013588vlAttorney Docket No.: 2019150-0023 that is used to seal a bottle of wine. When a bottle of wine is prepared, an authentication element indicates a baseline pH level that corresponds to desired wine quality. When wine turns (e.g., changes into acetic acid), an authentication element changes to indicate a lower pH level relative to the baseline. For example, an authentication element may indicate a wine has turned while the bottle of wine is sealed. Thus, such an authentication element may be able to be read without accessing the wine.

[0236] In some embodiments, an authentication element may be used to indicate safety of mayonnaise. Higher acidity (i.e., lower pH level) of mayonnaise is associated with spoilage (e.g., mayonnaise is not safe to be consumed). An authentication element that is pH sensitive may be used to determine a relative pH level of mayonnaise. For example, an authentication element may be embedded into or integrated with an interior surface of a mayonnaise container, such as, for example, a jar, a bottle, a packet. For example, an authentication element may be affixed or adhered to an interior surface of a mayonnaise container. For example, an authentication element may be embedded into or integrated with a lid of a mayonnaise container. For example, an authentication element may be affixed or adhered to a lid of a mayonnaise container. When mayonnaise is packaged, an authentication element indicates a baseline pH level that corresponds to a safe-to-consume mayonnaise. When mayonnaise spoils, an authentication element changes to indicate a lower pH level relative to the baseline. For example, an authentication element may indicate mayonnaise is spoiled while the packaging is intact.Verification Methods

[0237] Authentication elements disclosed herein may be used in methods of verifying authenticity of one or more objects. In some embodiments, a method includes receiving an authentication code for an object that has been obtained, at least in part, by reading a passive authentication element physically associated with the object that encodes at least a portion of the authentication code. For example, reading an authentication element may produce an authentication code. In some embodiments, a method includes verifying authenticity of an object using a received authentication code, for example solely based on the authentication code or based further on other information and / or observation(s) (e.g., nature of the object and / or source of the object) (e.g., location and / or position of the authentication element).Page 82 of 21213013588vlAttorney Docket No.: 2019150-0023

[0238] In some embodiments, a method includes receiving information potentially corresponding to an authentication code for an object. For example, at least a portion of the information may be received from an (e.g., passive) authentication element physically associated with (e.g., included in) the object (e.g., by reading the authentication element). The method may further include determining whether the information sufficiently corresponds to the authentication code. For example, it may be determined that the information sufficiently corresponds to the authentication code because the information at least approximates (e.g., matches) the authentication code. Alternatively or additionally, it may be determined that the information sufficiently corresponds to the authentication code because the information could not correspond to any other authentication code. Alternatively or additionally, it may be determined that the information sufficiently corresponds to the authentication code because the information could only correspond to one authentication code. In some embodiments, the method includes determining that the information corresponds to the authentication code for the object. In some embodiments, the method includes determining that the information does not correspond to the authentication code for the object (e.g., corresponds to an authentication code for a different object. The object may be authenticated based on the determination, for example solely based on the authentication code or based further on other information and / or observation(s) (e.g., nature of the object and / or source of the object) (e.g., location and / or position of the authentication element). If it is determined that the information does not correspond to the authentication code, it may be concluded that the object is counterfeit.

[0239] In some embodiments, a method includes obtaining an authentication code, for example by reading an authentication element. In some embodiments, a portion of an authentication code is obtained by reading an authentication element and another portion of the authentication code is obtained elsewhere, as described previously herein. In some embodiments, reading an authentication element includes applying x-rays, radio waves (e.g., in combination with a magnetic field), or sound waves to the authentication element and receiving a signal in response. For example, an image may be formed using applied x-rays, radio waves, or sound waves. In some embodiments, reading an authentication element includes forming a human readable image (e.g., an x-ray image, a CT image, an ultrasound image, or an MRI image). A human readable image is interpretable by a human, whether or not the image is ultimately processed or interpreted by aPage 83 of 21213013588vlAttorney Docket No.: 2019150-0023 human or a computer. Thus, in some embodiments, signal received in response to applied waves may be translated into at least a portion of an authentication code.

[0240] As described above, location and / or position of one or more authentication elements, relative to each other and / or relative to an object, may be used as a secondary security measure. Accordingly, in some embodiments, a method includes determining a location and / or orientation of an authentication element relative to (e.g., on or in) an object. In some embodiments, a method includes determining a location and / or orientation of two or more authentication elements relative to (e.g., on or in) each other. Authenticity of an object may be determined based at least in part on location and / or orientation of one or more authentication elements.

[0241] In some embodiments, a method is performed in-line. In some embodiments, authenticity of one or more objects is determined (e.g., verified) in-line. In some embodiments, a method is performed during a logistics process, for example during a sorting process (e.g., a document or postal sorting process), a package routing process, a package sorting process, a shipping process, a warehouse process, and / or a distribution process. In some embodiments, authenticity of one or more objects is determined (e.g., verified) during a logistics process, for example during a sorting process (e.g., a document or postal sorting process), a package routing process, a package sorting process, a shipping process, a warehouse process, and / or a distribution process. In some embodiments, authenticity of one or more objects is determined (e.g., verified) while an outer container, in which the one or more objects are disposed inside, is being transferred (e.g., using one or more conveyor belts). In some embodiments, a method is performed while an outer container, in which the one or more objects are disposed inside, is being transferred (e.g., using one or more conveyor belts). In some embodiments, authenticity of an object is determined (e.g., verified) while the object is being transferred (e.g., using one or more conveyor belts). In some embodiments, a method is performed while an object is being transferred (e.g., using one or more conveyor belts).

[0242] A method of verifying authenticity of an object may be performed or caused to be performed by, for example, an appraiser for the object, an employee of an auction house, a dealer for the object, a seller for the object, a prospective buyer of the object, a creator of an object, or an owner of the obj ect.

[0243] In some embodiments, a method registers a fingerprint of an object. A method may include receiving an object physically associated with an authentication element, obtaining aPage 84 of 21213013588vlAttorney Docket No.: 2019150-0023 fingerprint of the authentication element, and registering the fingerprint with the object in a registry. In some embodiments, a fingerprint is obtained by reading an authentication element using x-rays, radio waves (e.g., in combination with a magnetic field), or sound waves, for example to form a human-readable image such as a radiological image. A method of registering may be performed or caused to be performed by an appraiser for the object, an employee of an auction house, a dealer for the object, an owner of the object, or a creator of the object.

[0244] In some embodiments, a method verifies authenticity of an object using fingerprints. For example, comparing a fingerprint stored in a registry, which is assured to be authentic, against a comparative fingerprint obtained from an object, to determine whether they sufficiently correspond (e.g., match). A method may include obtaining a comparative fingerprint for an authentication element physically associated with an object; receiving, from a registry, a copy of an authentic fingerprint for the object, wherein the object has been registered with the registry; and verifying authenticity of the object by, at least in part, comparing the comparative fingerprint to the authentic fingerprint. In some embodiments, obtaining a comparative fingerprint includes reading an authentication element using x-rays, radio waves (e.g., in combination with a magnetic field), or sound waves. Such a method of verifying may be performed or caused to be performed by an appraiser for the object, an employee of an auction house, a dealer for the object, an owner of the object, a prospective buyer, or a seller of the object.

[0245] In some embodiments, a fingerprint is a radiological fingerprint. In some embodiments, a fingerprint is an image. In some embodiments, an authentication element includes one more encoding portions and the one or more encoding portions are discernable in a fingerprint. In some embodiments, an authentication code is determinable from a fingerprint.

[0246] In some embodiments, an object being registered or authenticated using a registry is an artwork. In some embodiments, the artwork is a completed artwork. In some embodiments, obtaining a fingerprint includes identifying an orientation mark that identifies an authentication element of which the fingerprint will be taken. In some embodiments, an authentication element is unique to an owner or creator of the object.

[0247] In some embodiments, a registry is owned and / or maintained by an auction house, an appraisal firm, a gallery, or a dealer.

[0248] In some embodiments, an authentication element can only be successfully read to determine at least a portion of an authentication code at a predetermined orientation (e.g., angle),Page 85 of 21213013588vlAttorney Docket No.: 2019150-0023 within a predetermined range of orientations (e.g., angles), or at one or more of a set of predetermined orientations (e.g., angles). Knowledge of which predetermined orientation or orientations can be used can therefore act as a secondary security feature. In some embodiments, a first portion of at least a portion of an authentication code encoded by an authentication element can be successfully read at a first predetermined orientation (e.g., angle), within a first predetermined range of orientations (e.g., angles), or at a first one or more of a set of predetermined orientations (e.g., angles) and a second portion of the at least a portion of the authentication code can be successfully read at a second predetermined orientation (e.g., angle), within a second predetermined range of orientations (e.g., angles), or at a second one or more of a set of predetermined orientations (e.g., angles). In some embodiments, an authentication element is readable at a first orientation and at a second orientation but only one of the two orientations corresponds to the at least a portion of an authentication code that is encoded by the authentication element. For example, a spatial arrangement and / or distribution and / or spacing of one or more encoding portions of an authentication element may appear one way at a first orientation and a different way at a second orientation, where only one of the two ways actually encodes at least a portion of an authentication code. Such embodiments may make fabricating counterfeit authentication elements more difficult, for example because attempted counterfeiters will not know which orientation or orientations matter. In some embodiments, both orientations encode separate portions of at least a portion of an authentication code.

[0249] Many obj ects have well defined shapes that lend themselves to easily being oriented correctly relative to a source and / or detector (e.g., for a non-visible imaging modality) (e.g., of an x-ray machine, a CT machine, a MRI machine, or an ultrasound machine). For example, packaged objects that are in boxes are easy to orient correctly. It may be easier, for example when working in-line, to use a machine that has an orientable source and / or detector in order to achieve a desired orientation between an authentication element and a source and / or detector. In some embodiments, a source and / or detector are rotatable about an authentication element (e.g., about an object physically associated with the authentication element) and may be so rotated in order to read the authentication element. In some embodiments, an object physically associated with an authentication element is rotated relative to a source and / or detector in order to read the authentication element.Page 86 of 21213013588vlAttorney Docket No.: 2019150-0023Contained Objects and Associated Methods of Authentication

[0250] An object (e.g., physically associated with an authentication element) may be removably disposed in an outer container. An object may be referred to as an “inner object” when it is in an outer container and / or still after it has been removed from the outer container. That is, an object need not be in an outer container at a given instant to be referred to as an inner object. An object may be removably disposed inside of an outer container. An object may be disposed entirely or only partially in (e.g., inside of) an outer container. An object may be removably enclosed in an outer container. An outer container may be enclosed (e.g., with one or more objects inside). An outer container may be opaque. An object may be disposed inside of an opaque outer container (e.g., such that the object is not visible unless the outer container is opened). An outer container may be opaque. An outer container may be a box, such as a cardboard box, or an envelope. An outer container may be packaging (e.g., for packaged objects) (e.g., a box or shrink wrap). An outer container may be disposable. An outer container may be secure, for example secured by a seal or lock. An outer container may orient and / or position one or more objects physically associated with authentication element(s) such that the authentication element(s) may be properly read. In some embodiments, an authentication element physically associated with an object disposed inside an outer container is readable without accessing inside of the outer container, such as without opening and / or unsecuring (e.g., unsealing) the outer container.

[0251] An outer container may be secured with a tamper-proof mechanism (e.g., a seal or lock). An outer container may be secured with a (e.g., tamper-proof) mechanism that itself can be authenticated. A tamper-proof mechanism may be structured to indicate tampering upon exposure to one or more particular chemical species, for example upon exposure to oxygen and / or humidity. A tamper-proof mechanism may be chemically sensitive. Likewise, a tamper-proof mechanism may be structured to indicate tampering upon exposure to a specific temperature or range of temperature or to temperature outside of a specific range. A tamper-proof mechanism may be thermosensitive. Similarly, a tamper-proof mechanism may be structured to indicate tampering upon exposure to certain amount of light and / or to one or more wavelengths of light (e.g., within the visible light spectrum). A tamper-proof mechanism may be photosensitive. A tamper-proof mechanism may be chemically sensitive, physically sensitive, thermosensitive, photosensitive, or a combination thereof. A tamper-proof mechanism may be physically sensitive, for example such that the tamper-proof mechanism physically degrades if the mechanism is tampered with.Page 87 of 21213013588vlAttorney Docket No.: 2019150-0023

[0252] One or more objects, for example each being physically associated with an authentication element, may be removably disposed in (e.g., inside of) an outer container. For example, the one or more objects may be a batch or a lot of objects. For example, an outer container may be packaging for shipping and / or storage purposes, such as an outer box in which products (objects) are stored in a warehouse or shipped by freight. In some embodiments, objects are ordered in an outer container, for example ordered by serial number. Each object in a set contained in an outer container (e.g., enclosed outer container) may be physically associated with an authentication element that encodes at least a portion of a unique authentication code (e.g., corresponding to a unique serial number). In some embodiments, objects are layered in an outer container, for example stacked on top of each other. In some embodiments, objects are flat, for example pieces of paper (e.g., a document or currency notes). In some embodiments, an authentication element is flat. Thus, systems and methods disclosed herein can be used to track and / or authenticate objects while in their natural packaging during shipping and / or storage, whether in a warehouse, a truck, a container ship, a shipyard, a shipping facility, or in transit.

[0253] In some embodiments, an object physically associated with an authentication element is disposed in an outer container where distinct portions of the authentication element are disposed in or on different portions of the object and the authentication element is readable (e.g., with x-rays, radio waves, and / or sound waves) based on a manner in which the object is distorted. For example, the authentication element may be readable based on how the object is folded. The outer container may be enclosed, such as an envelope (e g., a security envelope). The outer container may be sealed or otherwise secured, for example with a tamper-proof mechanism (e.g., seal) to maintain security of the object. The object may be a piece of paper. The authentication element may encode at least a portion of an authentication code two-dimensionally, for example as a QR code, or one-dimensionally, for example as a barcode, where the QR code or barcode is only readable as such while the object is in the outer container when the object is folded. For example, a piece of paper could have different portions of a radiopaque QR code or barcode printed (e.g., inkjet printed) onto different comers or regions along an edge of the paper such that when the paper is folded, for example in a bi-fold or tri-fold, the authentication element is readable, for example using an x-ray machine, to determine at least a portion of an authentication code without opening the envelope. By breaking up an authentication element into distinct spatially separate portions that are only readable with a certain folding, it may not be apparent what function thePage 88 of 21213013588vlAttorney Docket No.: 2019150-0023 portions serve even if the authentication element is visible to a human viewer. In some embodiments, an authentication element is readable based on an object having a particular arrangement within an outer container. In some embodiments, an authentication element is readable only if an object has a particular arrangement within an outer container. Such systems may be particularly useful for currency notes and / or other sensitive and / or high value documents.

[0254] In some embodiments, a plurality of objects are removably disposed inside an outer container. Each of the objects may be associated with an authentication element encoding at least a portion of an authentication code (e.g., an entire authentication code). In some embodiments, the authentication element can be read (e.g., to determine the authentication code) without accessing inside of the outer container. In some embodiments, the authentication code is a unique authentication code for the object. In some embodiments, the authentication code is a common authentication code used all of the objects. In some embodiments, the authentication element of the objects together encode an entirety of the authentication code. In some embodiments, the authentication element of the objects together encode an entirety of the authentication code such that a viewer can determine whether a complete set of objects is present inside of the container. In some embodiments, for each of the objects, the authentication element encodes at least a portion of (e.g., an entire) distinct authentication code. In some embodiments, each of the multiple authentication elements encodes an entire authentication code and the entire authentication code is the same for each of the multiple authentication elements. In some embodiments, the multiple authentication elements are associated with (e.g., disposed in and / or on) different portions of the object.

[0255] In some embodiments, a system includes an outer container and objects and a composite authentication element physically associated with the objects. Each object may be physically associated with a different (e.g., distinct) portion of the composite authentication element. In some embodiments, a composite authentication element physically associated with objects is readable without accessing an outer container. In some embodiments, objects are not authenticatable using a composite authentication element unless an entire set of objects is present, in some embodiments only when in an ordered manner. For example, different pages (e.g., pieces of paper) for a multi-page document may each be physically associated with a different (e.g., distinct) portion of a composite authentication element such that the composite authentication element is only readable if the entire document is present. Even so, it may be that the pages mustPage 89 of 21213013588vlAttorney Docket No.: 2019150-0023 be properly ordered. An ordering may refer to page order and / or with correct orientation and / or position of objects (e.g., pages). For example, the correct corners of pages may need to be aligned in order for a composite authentication element to be readable, for example if different portions of a composite authentication element are disposed on or in (e.g., printed on) a particular comer of pages of a document (e.g., each page of a document).

[0256] Distinct portions of a composite authentication element may be disposed on (e.g., printed onto, embedded in, integrated with, or woven into) different objects such that the distinction portions form at least a portion of a composite authentication element. In some embodiments, each object contained in an outer container (e.g., piece of paper in a multi-page document) includes a portion of a composite authentication element. In some embodiments, only a subset of objects contained in an outer container (e.g., every other page) includes a portion of a composite authentication element. In some embodiments, a composite authentication element is readable based on objects having a particular arrangement within an outer container. In some embodiments, a composite authentication element is readable only if objects have a particular arrangement within an outer container. In some embodiments, objects are arranged in a flat manner. In some embodiments, a composite authentication element is flat. In some embodiments, a composite authentication element is invisible to an unaided human viewer.

[0257] A composite authentication element may encode at least a portion of an authentication code two-dimensionally, for example as a QR code. In certain imaging modalities, such as x-ray imaging, even though a composite authentication element (e.g., QR code or barcode) is present in three dimensions (e.g., with different portions on different objects, such as sheets of paper, in a stack), the composite authentication element is readable as a two- dimensional element. That is, in some embodiments, an imaging modality acts to effectively “flatten” a composite authentication element when it is read. For example, a composite authentication element may appear two-dimensionally (e.g., as a two-dimensional feature) in an image (e.g., a human-readable image) formed when reading the composite authentication element. In some embodiments, different portions of a QR code or barcode is only readable as such while the object is in the outer container when the object is folded. For example, pieces of paper could have different portions of a radiopaque QR code or barcode printed (e.g., inkjet printed) onto different corners or regions along an edge of the papers such that, when the papers are stacked, a composite authentication element is readable, for example using an x-ray machine, to determine at least a portion of anPage 90 of 21213013588vlAttorney Docket No.: 2019150-0023 authentication code without opening an envelope in which the papers are contained (e.g., secured). In some embodiments, objects are arranged in an outer container such that a composite authentication element read from a predetermined angle (e.g., within a predetermined range of acceptable angles). For example, in some embodiments, a QR code or barcode may only be readable when viewed from an angle that is substantially front facing (e.g., not side facing). By breaking up a composite authentication element into distinct portions that are only readable when each of a set of objects is present (e.g., in a correct position and / or orientation), it may not be apparent what function the portions serve even if the authentication element is visible to a human viewer. Such systems may be particularly useful for currency notes and / or other sensitive and / or high value documents.

[0258] In some embodiments, a composite authentication element encodes at least a portion of a composite authentication code two-dimensionally, for example as a QR code. In some embodiments, a composite authentication element encodes at least a portion of a composite authentication code one-dimensionally, for example as a barcode. (A barcode may be present as a two-dimensional element but generally only one-dimension of spacing encodes information in a barcode.) In some embodiments, a composite authentication element encodes at least a portion of a composite authentication code three-dimensionally. For example, an arrangement of encoding portions of composite authentication element in three dimensions may correspond to at least a portion of an authentication code. In some embodiments, a composite authentication element that encodes at least a portion of an authentication code may be read using perpendicular probes (x- rays).

[0259] In some embodiments, an outer container may be constructed to properly orient and / or position objects to promote or ensure proper alignment, for example due to its size and / or shape. For example, an envelope may be sized and shaped to ensure that pages in a multi-page document are flat and properly aligned (e.g., matching corners), requiring at most that pages are inserted in the correct manner (e.g., each page facing the same way). In some embodiments, for example where the different portion of a composite authentication element for an obj ect is disposed in multiple locations on the object, it may not be necessary for objects to be inserted in a correct manner in order to read the composite authentication element, only that the objects are properly oriented and / or positioned relative to each other. In some embodiments, some page shift can be tolerated (e.g., relative to size of QR code or barcode pixels) as a mixed-integer programmingPage 91 of 21213013588vlAttorney Docket No.: 2019150-0023(MTP) algorithm can be applied to each pixel in an image of an authentication element to render at least a portion of an authentication code encoded by the authentication element as interpretable (e.g., to render a QR code processable).

[0260] Methods for authenticating objects disclosed elsewhere herein may be applied to authenticating one or more objects disposed in an outer container as now discussed. Because embodiments of authentication elements disclosed herein are readable with non-visible wavelengths, it is possible to authenticate objects through an outer container, even if the outer container is opaque. In various embodiments, x-rays, radio waves, and sound waves can be used to that effect. In some embodiments, an authentication element physically associated with an object may be read through an outer container.

[0261] In some embodiments, a method of authenticating objects includes reading a composite authentication element physically associated with objects removably disposed in (e.g., inside) an outer container through the outer container, for example using x-rays, radio waves (e.g., in combination with a magnetic field), or sound waves. The composite authentication element may be read without accessing the outer container. In some embodiments, a method of authenticating objects includes reading a composite authentication element physically associated with objects removably disposed in (e.g., inside) an outer container without accessing the outer container, for example using x-rays, radio waves (e.g., in combination with a magnetic field), or sound waves. Each of the objects in an outer container may be physically associated with a portion (e.g., a distinct portion) of the composite authentication element. The method may include verifying authenticity of the objects based on an authentication code, at least a portion of which is encoded by the composite authentication element. In some embodiments, reading the composite authentication element allows there to be a determination that no object is missing (e.g., from the outer container) because if any object were missing, a portion of the composite authentication element would be missing and therefore it could not be read. In some embodiments, one or more of the objects are removed after determining that the objects are authentic and / or that no object is missing. Removing the one or more objects may include breaking a tamper-proof mechanism that secures the outer container. Removing the one or more objects may include compromising security of the outer container.

[0262] In some embodiments, a method of authenticating an object includes reading an authentication element physically associated with the object removably disposed in (e.g., inside)Page 92 of 21213013588vlAttorney Docket No.: 2019150-0023 an outer container through the outer container, for example using x-rays, radio waves, or sound waves. The authentication element may be read without accessing the outer container. In some embodiments, a method of authenticating an object includes reading an authentication element physically associated with the object removably disposed in (e.g., inside) an outer container without accessing the outer container, for example using x-rays, radio waves, or sound waves. The method may include verifying authenticity of the object based on an authentication code, at least a portion of which is encoded by the composite authentication element. In some embodiments, the object is removed after determining that the object is authentic. Removing the object may include breaking a tamper-proof mechanism that secures the outer container. Removing the object may include compromising security of the outer container.

[0263] In some embodiments, a method of authenticating an object or objects disposed in an outer container is performed in-line. For example, such a method may be performed during a logistics process, such as a sorting process (e.g., a document or postal sorting process), a package routing process, a package sorting process, a shipping process, a warehouse process, and / or a distribution process. In some embodiments, a method is performed while an outer container is being transferred (e.g., using one or more conveyor belts). In some embodiments, a method of authenticating an object or objects disposed in an outer container is performed during a logistics process, such as during a sorting process (e.g., a document or postal sorting process), a package routing process, a package sorting process, a shipping process, a warehouse process, and / or a distribution process.

[0264] In some embodiments, a method includes orienting an outer container before reading an authentication element physically associated with an object in the outer container or a composite authentication element physically associated with objects disposed in the outer container. In some embodiments, a method includes positioning an outer container before reading an authentication element physically associated with an object in the outer container or a composite authentication element physically associated with objects disposed in the outer container.

[0265] In some embodiments, an outer container is enclosed during reading of an authentication element physically associated with an object in the outer container or a composite authentication element physically associated with objects disposed in the outer container. In some embodiments, an outer container is secure during reading of an authentication element physically associated with an object in the outer container or a composite authentication element physicallyPage 93 of 21213013588vlAttorney Docket No.: 2019150-0023 associated with objects disposed in the outer container (e.g., secured by a tamper-proof mechanism). In some embodiments, an object or objects are disposed inside of an outer container during reading of an authentication element physically associated with an object in the outer container or a composite authentication element physically associated with objects disposed in the outer container, respectively.

[0266] One or more additional security (e.g., error detection) techniques may be applied in connection with a composite authentication element that encodes at least a portion of an authentication code. Examples of additional security (e.g., error detection) techniques that may be used include parity bit, checksum, and check digit. For example, at least a portion of an authentication code may include a parity bit or a check digit. As another example, in some embodiments, at least a portion of an authentication code read from a composite authentication element may be verified as authentic or not based on a checksum, a parity bit, or a check digit. As another example, at least a portion of an authentication code may be verified, at least in part, by a checksum (e.g., of two or more characters in the at least a portion of an authentication code). A composite authentication element may encode at least a portion of an authentication code including a check digit and / or parity bit thereof. A composite authentication element may encode (i) at least a portion of an authentication code and (ii) a check digit or parity bit. In some embodiments, one or more additional security techniques may be used whether an authentication code is characters (e.g., alphanumeric characters) or a pattern.

[0267] In some embodiments, radiodensity and / or sound wave attenuation is used as a type of parity bit and / or check digit. For example, in some embodiments, a composite authentication element encodes at least a portion of an authentication code as a QR code or barcode where a portion of the QR code or barcode (e g., one or more bits of the QR code or one or more bars of the barcode) has a certain radiodensity and / or sound wave attenuation (e.g., higher or lower than one or more other bits of the QR code or one or more other bars of the barcode) that allows verification of authenticity of the at least a portion of the authentication code. In some embodiments, a portion that has a certain radiodensity is a particular predetermined portion (e.g., always a certain bit or bits of a QR code or always certain bar(s) of a barcode). In some embodiments, a portion that has a certain radiodensity is a portion selected by a person or organization to whom an authentication code pertains (e.g., is only known to that person or organization).Page 94 of 21213013588vlAttorney Docket No.: 2019150-0023

[0268] In a composite authentication element, overlapping portions of radi odense material (e.g., ink) may cause one or more portions (e.g., bits) of the authentication element (e.g., QR code) to appear as more radiodense than others and therefore be used as an additional security feature. For example, if different portions of a QR code are printed using radiodense ink on different pages of a multipage document, one or more certain bits may be printed on multiple pages such that the QR code has one or more bits that appear more radiodense than one or more other bits when read, thereby acting like a parity bit or check digit for the QR code and / or for at least a portion of an authentication code encoded by the QR code. Similarly, in an authentication element that is readable based on how an object is arranged (e.g., folded), overlapping portions of radiodense material (e.g., ink) may cause one or more portions (e.g., bits) of the authentication element (e.g., QR code) to appear as more radiodense than others and therefore be used as an additional security feature.

[0269] In some embodiments, if one or more additional security techniques are used with a composite authentication element that encodes at least a portion of an authentication code, it can be determined that an object or label physically associated with the composite authentication element is not authentic (e.g., is counterfeit) even if the authentication code itself, determined at least in part by reading the composite authentication element, appears authentic. For example, an authentication code read from a composite authentication element (e.g., a QR code) may appear authentic but radiodensity of a certain portion of the composite authentication element (e.g., one or more certain bits of the QR code) is not correct and therefore an object physically associated with the composite authentication element can be determined to be counterfeit.

[0270] Using one or more such additional security techniques provides an additional layer of security in that even if a potential counterfeiter comes into possession of an authentication code, the counterfeiter may not know that one or more additional security techniques are being employed. Similarly, a counterfeiter that comes into possession of a genuine object for which a forgery or counterfeit copy is intended to be made may identify a composite authentication element is present and be able to copy the composite authentication element in the attempted forgery or counterfeit copy but not know or appreciate by simple inspection (e.g., with x-rays, radio waves, or sound waves) that an additional security technique is being employed. For example, the counterfeiter may not know the correct parity bit, check digit, or check sum. The counterfeiter may therefore fail to incorporate that into the attempted forgery or counterfeit copy, such thatPage 95 of 21213013588vlAttorney Docket No.: 2019150-0023 security of the original is maintained. Similarly, a counterfeiter may try to incorporate a composite authentication element with an object that encodes at least a portion of a fake authentication code where the fake authentication code does not include the correct parity bit, check digit, or checksum for that object or type of object such that it can be determined that the forged or counterfeit object(s) are detectable as not authentic.

[0271] In some embodiments, a method is performed in-line. In some embodiments, authenticity of one or more objects is determined (e.g., verified) in-line. In some embodiments, a method is performed during a logistics process, for example during a sorting process (e.g., a document or postal sorting process), a package routing process, a package sorting process, a shipping process, a warehouse process, and / or a distribution process. In some embodiments, authenticity of one or more objects is determined (e.g., verified) during a logistics process, for example during a sorting process (e.g., a document or postal sorting process), a package routing process, a package sorting process, a shipping process, a warehouse process, and / or a distribution process. In some embodiments, authenticity of one or more objects is determined (e.g., verified) while an outer container, in which the one or more objects are disposed inside, is being transferred (e.g., using one or more conveyor belts). In some embodiments, a method is performed while an outer container, in which the one or more objects are disposed inside, is being transferred (e.g., using one or more conveyor belts). In some embodiments, authenticity of an object is determined (e.g., verified) while the object is being transferred (e.g., using one or more conveyor belts). In some embodiments, a method is performed while an object is being transferred (e g., using one or more conveyor belts).

[0272] A method of verifying authenticity of an object may be performed or caused to be performed by, for example, an appraiser for the object, an employee of an auction house, a dealer for the object, a seller for the object, a prospective buyer of the object, or an owner of the object.Cipher Elements Encoding Cipher Keys

[0273] The foregoing description has focused on authentication elements that encode at least a portion of an authentication code, generally that are physically associated with an object that can be authenticated using the authentication code. Also contemplated are cipher elements that encode cipher keys that can be used to decrypt encrypted authentication codes (or encrypt authentication codes) for authentication purposes. For example, an encrypted authentication codePage 96 of 21213013588vlAttorney Docket No.: 2019150-0023 may be provided on documentation or an invoice for an object (e.g., as a watermark or in plaintext print) or in an electronical or physical fde (e.g., as metadata) corresponding to an object and a cipher key for a cipher used to encrypt the authentication code may be encoded in a cipher element physically associated with the object. In this way, even though an authentication code may not be physically associated with an object (e.g., using an authentication element), the authentication code can still be used to verify authenticity of the object since the authentication code may only be able to be verified using a cipher key encoded by a cipher element physically associated with the object. If an incorrect cipher key were encoded with a cipher element physically associated with an object, then an authentication code may not be able to be properly decrypted, signifying that the object is counterfeit. Moreover, because cipher keys may, in some embodiments, be simpler than authentication codes (e.g., fewer characters), it may be easier to encode a cipher key into a cipher element than it would be to encode a corresponding encrypted authentication code into an authentication element. Therefore, using cipher elements may allow simpler, more reliable, and / or easier to interpret encoding schemes to be used while also facilitating use of complicated authentication codes to enhance overall security. Even if an attempted counterfeiter could somehow surreptitiously read a cipher element, without the corresponding authentication code, the counterfeiter could not create a passable counterfeit, for example could not create an accurate invoice that matches the cipher element.

[0274] In some embodiments, one party may possess an authentication code and another party may possess a cipher key and cipher. For example, a party shipping or storing an object may provide an authentication code and a shipping or storage company may provide (e.g., generate) a cipher key to encrypt the authentication code and then include the encrypted authentication code in documentation or a file for the shipment or storage and provide (e.g., produce) a cipher element that encodes the cipher key and physically associate it with the object. In some embodiments, a party shipping or storing an object provides the object physically associated with a cipher element that encodes a cipher key and separately provides (e.g., sends or mails) or maintains an encrypted authentication code. When receiving or retrieving the object, the cipher element can be read to determine the cipher key and decrypt the authentication code to verify authenticity.

[0275] In some embodiments, an object is physically associated with a cipher element. A cipher element may encode a cipher key like an authentication element encodes at least a portion of an authentication code, for example using one or more encoding portions as described herein.Page 97 of 21213013588vlAttorney Docket No.: 2019150-0023To avoid unnecessary duplication of text herein, it is expressly contemplated that the present disclosure includes embodiments of cipher elements and composite cipher elements that correspond to expressly described embodiments of authentication elements and composite authentication elements, respectively, except that the cipher elements and composite cipher elements encode cipher keys whereas the authentication elements and composite authentication elements encode at least a portion of authentication codes. Any object described as being physically associated with one or more authentication elements may be additionally or alternatively physically associated with one or more analogous cipher elements.

[0276] In some embodiments, an object is physically associated with a cipher element that encodes a cipher key. A cipher key may be used to decrypt the encrypted authentication code using a cipher. A cipher element may encode a cipher key using one or more encoding portions as disclosed herein. A cipher key may correspond to an encrypted authentication code corresponding to one or more objects. A cipher key may be for an encrypted authentication code corresponding to one or more objects. A cipher key may be used to decrypt an encrypted authentication code corresponding to one or more objects. An encrypted authentication code may be provided elsewhere than one or more objects corresponding to the authentication code. For example, documentation, an invoice, or a physical or electronic file, a person’s memory (e.g., an owner’s memory), a registry, or a combination thereof for one or more objects may include an encrypted authentication code. In some embodiments, a passive cipher element encodes a cipher key for an encrypted authentication code (e.g., corresponding to an object). In some embodiments, a plurality of cipher elements encode a cipher key for an encrypted authentication code (e.g., corresponding to an object); each of the cipher elements may encode a portion (e.g., a distinct portion) of the cipher key. In some embodiments, a plurality of cipher elements each encode a different cipher key of a set of cipher keys corresponding to an encrypted authentication code (e.g., for an object).

[0277] A method of determining authenticity of an object may include reading a cipher element physically associated with an object to determine a cipher key. A method may further include decrypting an encrypted authentication code for the object using the cipher key. A method may further include determining that the object is authentic based on the decrypted authentication code.Page 98 of 21213013588vlAttorney Docket No.: 2019150-0023

[0278] One or more cipher elements may be used in combination with one or more authentication elements. For example, an object may be physically associated with an authentication element and a cipher element. As another example, a set of objects may include (i) a first object physically associated with an authentication element that encodes an authentication code in a manner encrypted with a cipher and (ii) a second object physically associated with a cipher element that encodes a cipher key for the cipher, thereby allowing both objects in the set to be mutually authenticated by reading the authentication element and the cipher element in order to decrypt and verify the authentication code.

[0279] A cipher key may be short, for example no more than 10 characters (e.g., no more than ten binary digits), no more than 8 characters, no more than 6 characters, or no more than 4 characters.Images for Authentication and / or Verification of Authenticity

[0280] A non-transitory image of an authentication element disclosed herein, for example physically associated with an object or a label, may be used for authentication and / or verification of authenticity. Likewise, a non-transitory image of a composite authentication element disclosed herein, for example physically associated with objects that may be disposed in (e.g., enclosed in) an outer container, may be used for authentication and / or verification of authenticity.

[0281] In some embodiments, an authentication element is discernable in a non-transitory image, for example based on one or more encoding portions included in the authentication element. The authentication element may be physically associated with an object where the object is authenticatable using the image.

[0282] In some embodiments, a composite authentication element is discernable in a non- transitory image, for example based on one or more encoding portions included in the composite authentication element. The composite authentication element may be physically associated with objects where the objects are authenticatable using the image.

[0283] An object may be discernable in an image, for example because the object is radi odense. An object may not be discernable (may be undiscemible) in an image, for example because the object is not radiodense. In some embodiments, a label includes an authentication element and the label is discernable in an image, for example because the label is radiodense. InPage 99 of 21213013588vlAttorney Docket No.: 2019150-0023 some embodiments, a label includes an authentication element and the label is not discernable (may be undiscernible) in an image, for example because the label is not radiodense.

[0284] An image may be a radiological image. An image may be a sonogram (e.g., an ultrasound image). An image may be a tomographic image, such as an x-ray tomography image and / or a CT image (e.g., CT scan). An image may be an x-ray image. An image may be a dual energy x-ray absorptiometry image.

[0285] An image may be a printed image. An image may be a film image. One or more images may be stored on one or more non-transitory computer-readable media.

[0286] A method may include acquiring an image. For example, an image may be acquired from outside of an outer container. Acquiring an image may include providing (e.g., directing) x- rays, radio waves (e.g., in combination with a magnetic field), or sound waves to an authentication element and / or an object physically associated with the authentication element and / or a label physically associated with the authentication element. For example, acquiring an image may include providing (e.g., directing) x-rays, radio waves (e.g., in combination with a magnetic field), or sound waves to an authentication element (e.g., through an outer container). An image may be acquired using x-rays, radio waves (e.g., in combination with a magnetic field), or sound waves. A method may include rendering, by a processor of a computing device, an image. A method may include displaying, by a processor of a computing device, an image. A method may include constructing (e.g., by a processor of a computing device) an image. A method may include developing an image. One or more non-transitory computer-readable media may have instructions (e.g., one or more programs) stored thereon that, when executed by a processor, cause the processor to perform any such method or methods.Objects

[0287] An object may be an item. An object may be or include a fashion object, such as, for example, clothing (e.g., an article of clothing), an accessory, a handbag, a shoe. An object may be or include jewelry, such as, for example, an earring, a ring, a necklace, or a bracelet. An object may be or include a textile (e.g., fabric), such as, for example, leather (faux (e.g., plastic and / or vegan) or genuine), nylon, silk (shantung), canvas, cotton twill, cotton (e.g., shirting), denim, or a combination thereof. An object maybe or include a thread. An object maybe or include a string. An object maybe or include a cord. An object maybe or include a yarn. An object maybe orPage 100 of 21213013588vlAttorney Docket No.: 2019150-0023 include a wire. An object may be or include food packaging, such as, for example, a container, a bottle, ajar, a can, a carton, a tub, a box, a bag, a sac, or a combination thereof. An object may be or include beverage packaging, such as, for example, a container, a bottle, a carton, or a combination thereof. An object may be or include a label. A label maybe a food label. A label may be a beverage label. An object may be or include a logo. An object may be or include a patch (e.g., a logo patch) (e.g., an embroidered patch). An object may be or include embroidery. An object may be or include an emblem, badge, crest, seal, or token. An object may be or include an artwork, for example a painting, a print, or a photograph. An object may be or include a canvas. An object may be or include a sculpture. An object may be or include a substrate, for example a canvas, paper, or board (e.g., wood board), for example for an artwork or document. An object may be unfinished (e.g., a blank canvas). An object may be or include an antique. An object may be or include a weapon or ammunition for a weapon. An object may have the form a sheet-like layer, for example a currency note. An object may be or include a piece of paper, such as a document, lottery ticket or betting slip, or currency note. Objects may be or include multiple pieces of paper, such as objects that are together at least a portion of a document (e.g., a complete document) or at least a portion of a set of documents (e.g., a complete set of documents). An object may be or include a single page document or a multi -page document. A document may be, for example, a contract or agreement (e.g., insurance contract, an invoice, a purchase agreement, a non-disclosure agreement), a financial instrument (e.g., stock certificate, bearer bond, options contract, derivative contract), a lottery ticket or betting slip, a deed, an assignment, a legal document (e.g., a warrant, a will, a trust certificate), a corporate record (e.g., a record of one or more trade secrets), or a certificate of authenticity. An object may be or include a document or currency note. A document (e.g., a complete document) may include one or more objects. An object may be or include a currency note. Objects may be a set. For example, objects may be units of a single stock keeping unit (SKU). Objects may be a set of multiple SKUs. An object may be an inner object, for example when disposed inside of an outer container or when it has been removed from being disposed inside of an outer container.Exemplary Applications to Artwork

[0288] Advances in simulation of age-appropriate paints and other media have made authentication of artwork more difficult, even as non-destructive dating and other analysis methodsPage 101 of 21213013588vlAttorney Docket No.: 2019150-0023 have improved. In some embodiments, an object is a new work of art or a previously completed one. An authentication element for such an object may be a thread encoding an authentication code that is applied to a substrate (e.g., canvas or paper) of the artwork, either under paint or varnish. The authentication element may be provided in an unobtrusive location. The thread may be documented via x-ray (e.g., dual-energy x-ray absorptiometry) or another imaging modality. The authentication code may be kept as a secret by the artist or registration authority of the artwork. In the future, this piece (or a copy) can be similarly scanned via x-ray and a determination made whether the codes sufficiently correspond (e.g., match). An authentication element used in such an application may include (e.g., optically clear) radiopaque ink, preferably that does not limit the ability of the media to uptake additional inks, dyes, paints or artistic media. The authentication element may be applied to the front or back of a substrate (e.g., canvas or paper or other media). Such substrates may be sold for making art. In some embodiments, an orientation mark is included to orient an authentication element (e.g., for a person desiring to authenticate an object).

[0289] In some embodiments, once an artist has finished a piece of art and desires to register the artwork, a x-ray is taken (e.g., under predetermined conditions). The radiographic fingerprint of that canvas (e.g., aligned with an orientation mark) may be recorded. The fingerprint may then be attested to by the artist as being linked to that original art. The registration process may have an additional cost, as not all canvases or papers will result in final works intended for display. There may be a maintenance of certification fee for storage of the fingerprint (e.g., radiographic signature). When the artwork is being bought, sold, moved to a new location, for example where the transportation may have compromised the authenticity of the artwork, or at any time desired by the claimed owner, a radiological image can be taken (e.g., at the location of the artwork). By comparing the registered radiographic file with the original artists attested master file image, the object in question can be authenticated.

[0290] In some embodiments, an authentication element could be applied to the front of the canvas either before painting has begun or partway through, such that evidence that a special thread has been applied is no longer visible to the casual observer. In some embodiments, it may be the presence of or location and / or orientation of an authentication element, alternatively or additionally to an authentication code, that provides sufficient evidence of authenticity. In some embodiments, it may be the relative location and / or orientation of an authentication element to some other radio-dense part of an object (e.g., artwork), such as a metallic foil or even a portionPage 102 of 21213013588vlAttorney Docket No.: 2019150-0023 of a frame for the object, which, alone or in combination, provides evidence of authenticity. In some embodiments, an authentication element is incorporated directly into a canvas itself as part of a manufacturing process rather than being added to the canvas later. In some embodiments, an authentication element is physically associated with a frame instead of a canvas.Exemplary Applications to Document Security

[0291] Documents, such as high security documents, may need to be authenticated and verified from time to time. However, current methods of authentication and verification requires direct inspection of the documents and thereby likely exposure of the sensitive content, for example to inspect watermarks or similar security features. Additionally, the authentication may require specialized knowledge that is considered proprietary and knowing what to look for in and of itself may decrease the security of the process. Systems disclosed herein mitigate these risks.

[0292] In some embodiments, a composite authentication element is physically associated with a document (e.g., multi-page document) or set of documents, for example in such a way as to be able to verify the completeness of the document or set of documents and / or the authenticity without exposing the document or set of documents to direct inspection. For example, the document or set of documents can be disposed in a secure, enclosed, and / or opaque outer container, such as an envelope.

[0293] In some embodiments, optically-clear radiopaque ink that does not limit the ability of the document media to uptake additional inks, dyes, varnishes or coatings is used. Such ink may be applied as a composite authentication element to a document or set of documents in such a way as to uniquely identify / authenticate the document. The composite authentication element may be distributed among the pages of the document or set of documents in such a way to be able to verify the completeness of the document or set of documents.

[0294] In some embodiments, when verification is required, an x-ray image of a document can be obtained to read a composite authentication element. In some embodiments, an encrypted authentication code (e.g., encrypted with a public key) for the document can be compared with the public-key encrypted version obtained from the x-ray image. Accordingly, a match can be ensured without exposing the private key of the document. Such schemes allow for verification of authenticity and / or completeness without the need to remove a document or set of documents from an outer container (e.g., security envelope), which could or would expose contents of the documentPage 103 of 21213013588vlAttorney Docket No.: 2019150-0023 or set of documents to the inspecting party. In some embodiments, different inks with different radiopaque materials (e.g., optically clear and radiopaque materials) are used such that dual energy x-ray can be used to decipher what material is used for which pixel in a QR code or barcode based authentication element. In some embodiments, some page shift can be tolerated given the size of QR code or barcode pixels as a mixed-integer programming (MIP) algorithm can be applied to each pixel.

[0295] An authentication element or composite authentication element can be applied to an otherwise blank sheet or blank sheets (e.g., before document text is written or printed). An authentication element or composite authentication element can be applied after document text is written or printed, for example as a second print layer or varnish layer. An authentication element or composite authentication element may be applied using one or more optically clear and radiopaque material so that a document appears blank before text is added (or so there is no interference with existing text).

[0296] In some embodiments, a machine approximately the size of a countertop copy machine is employed with a printer and a “reader” together. A document to be secured may be fed into the machine and an authentication element or composite authentication element applied. For an incoming document, the lid could be lifted and a security envelope placed in a chamber of the machine. The lid may contain an x-ray DR plate, and a source would move on a gantry to expose the entire chamber from a series of exposures. A series of exposures may be preferred due to the proximity of the source to a detector and the field of view (FOV) of the image. A small source, such as dental x-ray, could be used and repeated and then stitched together to create the entire image. The devices could be synched so that only a document created on a certified device would produce a positive match.Exemplary Applications to Medication and Other Packaged Objects

[0297] Authentication elements, systems, and methods disclosed herein may include be used to verify authenticity of medical products, such as, for example medications (e.g., pills) and medical devices (e.g., clear polymer devices such as implants, tubing, valves, for example). In some embodiments, an inner object is a bottle (e.g., a pill bottle). In some embodiments, an object is a bottle (e.g., a pill bottle). In some embodiments, an object is packaging for a medication (e.g., pills), such as a blister pack. An authentication element may be an ink comprising molecules (e.g.,Page 104 of 21213013588vlAttorney Docket No.: 2019150-0023 polymer chains) [(e.g., a molecular ink) (e.g., a polymer ink)] disposed on [e.g., attached to (e.g., primary bonded to)] a polymer surface of packaging for medication. An authentication element may be formed as a watermark on packaging (e.g., such packaging). In some embodiments, a user could count the number of packages in an outer container without accessing the outer container based on radiopaque molecules (e.g., printed on and) attached to each of the packages.

[0298] In some embodiments, it is possible to observe whether an object is present or not based on how a radiopaque watermark appears. Such a watermark may appear differently in an x- ray image if an object is present (e.g., where it may not appear) than when the object is not. Thus, a watermark made with radiopaque molecules (e.g., polymer chains) as disclosed herein may be printed on (e.g., and attached to) (e.g., polymer) packaging for objects and an x-ray image of the packaging (e g., taken from outside an outer container) may allow it to be verified whether or not any of the objects are missing (and which objects are missing if any, in some embodiments, for example where the packaging individually packages each of the objects). For example, blister packs of pills could have radiopaque molecules disposed thereon [e.g., in a watermark (e.g., a repeating watermark)] such that x-ray images could indicate whether any pills from any of the blister packs are missing.

[0299] A checksum (e.g., of authentication codes, e.g., serial numbers) may be used to verify that a complete set of objects (e.g., pill bottles) is in an outer container (e.g., shipping box) (e.g., without accessing the outer container), for example a checksum based on number of objects and / or identity of objects (e.g., particular bottles or just number of bottles). For example, serial numbers may be batched to satisfy a checksum for a set of packagings or other objects in an outer container. This may avoid the need for a user to manually count objects discernable in an image, since image processing, including verifying a checksum, could be automated.Additional Exemplary Embodiments

[0300] The present disclosure also provides, inter alia, systems and devices for utilizing visibility -enhancing elements. According to some embodiments of the present disclosure, a visibility-enhancing system may include at least one visibility-enhancing element configured to be at least temporarily affixed to, integrated with, or embedded within at least one portion of at least one item. In some implementations, at least one internal component may include at least one visibility-enhancing element, wherein the visibility-enhancing element may be at least temporarilyPage 105 of 21213013588vlAttorney Docket No.: 2019150-0023 affixed to, integrated with, or embedded within at least one portion of the internal component before the internal component itself may be at least temporarily affixed to, integrated with, or embedded within at least one portion of at least one item.

[0301] In some embodiments, the internal component may be configured for use in one or more various applications, such as facilitating medical treatment or authenticating a good, product label, or document. The at least one visibility-enhancing element may include a form including one or more of: at least one contrasting agent, an amount of at least one elongated fibrous material in a structural weaving configuration, an amount of at least one elongated fibrous material configured as a tracer line, one or more substantially rigid particles or pieces, one or more metallic elements, or an amount of at least one hydrogel. In some aspects, the at least one visibilityenhancing element may be at least partially visible in one or more imaging modalities, such as x- radiation (x-ray) imaging, MRI, CT scan, or sonography (e.g., ultrasound). In some embodiments, the at least one visibility-enhancing element may be added to the at least one internal component during one or more stages of the manufacturing process of the internal component, or the at least one visibility-enhancing element may be added to at least one existing internal component after the manufacturing process has been completed.

[0302] In some embodiments, an authentication element is or includes an internal component. An internal component may be any structure, element, composition, device, or mechanism that may be configured, integrated, or embedded at least partially within an internal portion of an object or something associated with an object, for example one or more of: a good, a product, a label, an item, a article, or a document. In some embodiments, an internal component may be configured at least partially within an internal portion at least one good or item including one or more of: a handbag; product packaging; food packaging; artwork, such as a painting, canvas, or sculpture; currency; one or more bullets or other ammunition; a protection device; an article of clothing, or a piece of jewelry.

[0303] In some embodiments, an encoding portion is or includes a visibility-enhancing element. An visibility-enhancing element may include any element, structure, substance, composition, or material that may be affixed to, integrated with, embedded within, or otherwise added to at least one internal or external portion of at least one internal component, wherein the visibility-enhancing element may be at least partially visible via at least one imaging modality. By way of example, a visibility-enhancing element may include one or more of: at least onePage 106 of 21213013588vlAttorney Docket No.: 2019150-0023 contrasting agent, an amount of at least one fibrous material in a structural weaving configuration, an amount of at least one fibrous material configured as a tracer line, one or more substantially rigid particles or pieces, one or more metallic elements, or an amount of at least one hydrogel that may be integrated with, embedded within, or affixed or applied to one or more internal or external portions of at least one internal component.

[0304] In some embodiments, an additive may include any element that may be added to one or more internal or external portions of at least one internal component for one or more purposes other than or in addition to facilitating at least partial visibility of the internal component in one or more imaging modalities. By way of example, an additive may include one or more antibiotics, vitamins (such as, vitamin E in the form of one or more tocopherols or one or more tocotri enols), an amount of titanium, an amount of iron oxide, an amount of barium sulfate, an amount of manganese chloride or other manganese salt, an amount of aluminum, or one or more nanoparticles including any combination thereof. In some embodiments, while an additive may not be exclusively intended to facilitate at least partial visibility in one or more imaging modalities of at least one internal component to which it may be added, an additive may be at least partially visible in at least one imaging modality.

[0305] In some embodiments, imaging may include any imaging modality that may be used to view one or more internal portions configured at least partially within one or more of: an object, a good, a product, a label, an item, an article, a document, or other tangible entity. By way of example, imaging may include x-radiation, MRI, CT, or sonography (e.g., ultrasound).

[0306] In some embodiments, a fibrous material may include any substance, material, or member that includes at least one fiber. In some embodiments, a fibrous material may include one or more of an amount of thread, an amount of wire, an amount of cord, or an amount of string.

[0307] Fig. 1 illustrates an example of an authentication element 10 that encodes at least a portion of an authentication code, according to some embodiments of the present disclosure. The authentication element 10 may include a thread 11 and one or more encoding portions 12. The one or more encoding portions 12 encode the at least a portion of an authentication code 13. The authentication code 13 may include an alphanumeric code. The alphanumeric code, for example, may only include numbers (e.g., a decimal number, a binary number). In another example, the alphanumeric code may only include letters. In another example, the alphanumeric code may include combinations of letters and numbers. In another example, the alphanumeric code may bePage 107 of 21213013588vlAttorney Docket No.: 2019150-0023 represented in hexadecimal or another base that is not base 10. In some embodiments, the authentication code 13 may include a 2-dimensional code. The 2-dimensional code, for example, may include a QR code. The encoding portions 12 may include several ways to encode the at least a portion of authentication code 13, as further described herein in connection with Figs. 2A-D and Figs. 3A-D.

[0308] Fig. 2A illustrates an example of an authentication element 10 that encodes at least a portion of an authentication code. In this example, the authentication element 10 includes a thread 11 that includes encoding portions 12. The encoding portions are particles and / or clusters of particles. In some embodiments, the encoding portions 12 may be evenly distributed with a spacing dl between two successive encoding portions 12. In this case, the authentication code is a simple code that is set by a combination of encoding portion size, encoding portion shape (e.g., particulate), and spacing dl. In some embodiments, one or two of these may be irrelevant to the authentication code. For example, encoding portion size may be irrelevant and the authentication code is derived from only spacing and shape or shape is irrelevant and the authentication code is derived from only spacing and size or neither shape nor size matters and the authentication code is derived only from spacing. In some embodiments, when fewer characteristics are used to encode an authentication code, more precise tolerances may be used (e.g., the authentication code may be encoded by a more precise spacing if size and shape are not considered and a less precise spacing if size and / or shape is considered). Fig. 3A illustrates a related exemplary embodiment where there are one or more encoding portions 12 that is / are filament(s) or fiber(s) woven or braided into the thread 11.

[0309] Fig. 2B illustrates an example of an authentication element 10. Authentication element 10 includes a thread 11 and encoding portions 12. The encoding portions are particles and / or clusters of particles. The encoding portions 12 are distributed unevenly, resulting in varying spacings dl, d2 between the encoding portions 12, which contributes to the encoding of at least a portion of an authentication code. For example, different spacings may correspond to different characters in the authentication code 13. In another example, the number of similarly spaced encoding portions before a larger gap may correspond to different characters in the authentication code 13 (e.g., the number of encoding portions separated by distance dl before separation by a larger distance d2). Fig. 3B illustrates a related exemplary embodiment where encoding portions 12 are filament(s) or fiber(s) woven or braided into a thread 11. Still referring to Fig. 3B, differentPage 108 of 21213013588vlAttorney Docket No.: 2019150-0023 spacings and / or phase between blocks of spirals may correspond to different characters in the authentication code 13 or the number of spirals of one or more encoding portions 12 before a larger gap d2 may correspond to different characters in the authentication code 13. Each encoding portion 12 may have a same dimension d3 (e.g., thickness) (as shown) or a different dimension.

[0310] Fig. 2C illustrates an example of an authentication element 10. The authentication element 10 includes a thread 11 and encoding portions 12. The encoding portions are particles and / or clusters of particles. The encoding portions 12 include different sizes (e.g., widths wl, w2, w3) and different spacings, which contribute to the encoding of at least a portion of an authentication code. For example, different sizes of encoding portions 12 may correspond to different characters in the authentication code 13. For example, a Morse code type encoding scheme may be used using different sizes (e.g., regardless of spacings). The encoding portions 12, for example, may represent a barcode. In some embodiments, different sizes are used with constant spacings.

[0311] Fig. 2D illustrates an example of an authentication element 10. The authentication element 10 includes a thread 11 and encoding portions of different radiodensities 12A, 12B and 12C. The encoding portions are particles and / or clusters of particles. The encoding portions of different radiodensities 12A-C may appear as different contrasts in an image, for example, a two- energy x-ray absorptiometry image or fluoroscopic image. The encoding portions 12A-C may be arranged in a pattern that encodes an authentication codes. In some embodiments, the pattern corresponds to different characters in the authentication code 13. For example, a base three authentication code may be used if three different radiodensities of encoding portions are use. Figs. 3C-D illustrates a related exemplary embodiment where the encoding portions 12A-C are filament(s) or fiber(s) woven or braided into the thread 11. Fig. 3C illustrates encoding portions 12A-C an ABC pattern (but the pattern need not be repetitious as illustrated), in this case where all of the encoding portions 12A-C are spiraled in a same orientation (e.g., direction). Fig. 3D illustrates a similar pattern as Fig. 3C but here encoding portion 12C is spiraled in a different orientation (e.g., direction) from encoding portions 12A-B.

[0312] Fig. 4A is a brightfield image of an exemplary authentication element 10 that has been constructed. The authentication element 10 is a thread 11 and radiopaque encoding portions 12A-D are woven into the thread 11. In this example, there are four similar encoding portions 12A-D that are spiraled in a same orientation with a spacing between each of the spirals. ThePage 109 of 21213013588vlAttorney Docket No.: 2019150-0023 encoding portions 12A-D are discernable from the rest of the authentication element 10 in the brightfield image, at least in the magnified view shown (they may be undiscernible or less discernable in an unmagnified view). Fig. 4B shows an x-ray image 15 of the authentication element 10 of Fig. 4A showing that the different encoding portions are discernable. The parts of the authentication element 10 that are not the encoding portions 12A-D are not radiopaque (and are optically clear as seen in Fig. 4A) and therefore do not show up against background in the x- ray image. The spacing dl between successive encoding portions 12A-D is about 0.6 mm in this example. In some embodiments, there are different spacings between different adjacent pairs of the encoding portions 12.

[0313] Referring to Figs. 5A and 5B, an exemplary visibility-enhancing system 20 including an item 21 including at least one visibility-enhancing element 12, according to some embodiments of the present disclosure, is illustrated. In some embodiments, at least one visibilityenhancing element 12 may be at least temporarily secured within or upon or may be at least temporarily integrated with or embedded within at least one portion of at least one item 21, wherein the item 21 may include at least one good, product, or document, such as, a handbag, product packaging, food packaging, artwork, currency, a product label, one or more bullets or other ammunition, a protection device, an article of clothing, or a piece of jewelry.

[0314] In some embodiments, at least one visibility-enhancing element 12 may include at least one fibrous material, such as, an amount of thread or amount of string, wherein at least a portion of the fibrous material may be doped or embedded with at least one contrasting agent before being at least temporarily secured to, integrated with, or embedded within at least one portion of at least one item 21 to facilitate the detection or visibility of the fibrous material in one or more imaging modalities, such as, an x-ray, MRI, or CT scan.

[0315] In some embodiments, the fibrous material may include at least one unique structural configuration, arrangement, or pattern, wherein the unique configuration may be formed by using one or more various stitching or threading techniques or styles, or by arranging the fibrous material as a unique patch or similar material structure, for example. In some embodiments, by forming a unique structural configuration using the fibrous material, a manufacturer, producer, or other source of the item 21 may integrate a unique design, symbol, pattern, or similar identification feature with the item 21 that may be substantially imperceptible by unassisted human eyesight, but may be detectable via at least one imaging modality. In some implementations, this may allowPage 110 of 21213013588vlAttorney Docket No.: 2019150-0023 the item 21 to be authenticated as having been produced, manufactured, or otherwise provided by an indicated source when at least one imaging modality confirms the presence of the visibilityenhancing element 12 at an expected location in an expected orientation, position, or configuration. In some embodiments, the expected location, orientation, position, or configuration of the visibility-enhancing element 12 may be unknown to any entity other than the source of the item 21 due to the substantially imperceptible nature of the visibility-enhancing element 12 without the use of at least one imaging modality.

[0316] At least one visibility-enhancing element 12 may be at least partially integrated with at least one internal or external portion of an item 21, such as a handbag, wherein the visibility-enhancing element 12 may be integrated via stitching, sewing, or weaving, for example. In some embodiments, the location, orientation, position, and configuration of the visibilityenhancing element 12 may be detectable or observable via at least one imaging modality, such as x-ray imaging. In some embodiments, the visibility-enhancing element 12 integrated with the handbag 21 may include a unique structural weaving or mesh configuration or unique stitching pattern that may indicate that the handbag 21 was produced by an indicated manufacturer. In some embodiments, this may allow a purchaser of the handbag 21 to be able to confirm that the handbag 21 originated from the indicated source by scanning one or more portions of the handbag 21 using an x-ray imaging device to reveal or detect the unique configuration of the visibility-enhancing element 12 associated with the indicated source. In some embodiments, this may allow consumers to verify that one or more goods available for purchase are likely to have originated from the indicated source and are not counterfeit or copycat products.

[0317] In some embodiments, the visibility-enhancing element 12 may be substantially unobservable or undetectable without the utilization of at least one imaging device. In some implementations, the visibility-enhancing element 12 may include a unique identifier for at least one item 21. In some embodiments, the discrete nature of the visibility-enhancing element 12 may at least partially deter or hinder the item 21 associated therewith from being easily replicated or copied, which may at least partially facilitate a reduction in the unauthorized use or distribution of goods or products and may deter the production of counterfeit items 21.

[0318] In some embodiments, at least one visibility -enhancing element 12 may be added to one or more internal or external portions of at least one internal component 10 to facilitate the ability of the internal component 10 to be seen in one or more types of imaging, wherein one orPage 111 of 21213013588vlAttorney Docket No.: 2019150-0023 more internal components 10 may be at least temporarily affixed to, integrated with, or embedded within at least one portion of at least one item 21. In some embodiments, this may allow the internal component 10 to include at least one visibility-enhancing element 12 in a structural configuration that includes at least one unique identifier that may be difficult or impossible to view or detect without at least one imaging device, making the structural configuration of the visibilityenhancing element 12 difficult to replicate.

[0319] In some embodiments, a visibility-enhancing element 12 may include a form that includes one or more of: at least one contrasting agent, an amount of at least one elongated fibrous material in a structural weaving configuration, an amount of at least one elongated fibrous material configured as a tracer line, one or more substantially rigid particles or pieces (such as, one or more metallic particles or beads), one or more metallic elements (such as, metallic particles or staples), or an amount of at least one hydrogel. In some embodiments, in aspects wherein the visibilityenhancing element 12 may include at least one contrasting agent, the contrasting agent may include an amount of gadolinium, an amount of iodine, or a combination thereof. In some embodiments, at least one visibility-enhancing element 12 in the form of at least one contrasting agent may be added to one or more internal or external portions of an existing internal component 10 or may be integrated into or affixed upon one or more internal or external portions of an internal component 10 during one or more stages of the manufacturing process of the internal component 10 before the internal component 10 may be affixed to, integrated with, or embedded within at least one portion of at least one item 21.

[0320] In some embodiments, at least one visibility-enhancing element 12 may be added as a coating to at least one internal component 10, wherein the visibility-enhancing element 12 may be applied to the internal component 10 while in a liquid, resin, or gel form and may solidify to form a coating upon one or more portions of the surface of the internal component 10 as it dries. In some implementations, an amount of at least one visibility-enhancing element 12 in a liquid, resin, or gel form may be placed in at least one container, and the container may then be inserted within an internal portion of the internal component 10 prior to being affixed to, integrated with, or embedded within at least one portion of at least one item 21.

[0321] In some embodiments, an amount of thread, cord, string, or similar elongated fibrous material may be doped or embedded with at least one visibility-enhancing element 12 in the form of at least one contrasting agent, and the elongated fibrous material may be used to formPage 112 of 21213013588vlAttorney Docket No.: 2019150-0023 structural weaving or braiding that may be integrated with at least one internal component 10 such as, via stitching or sewing, wherein the structural weaving may include one or more of a plurality of different patterns or configurations upon and / or within the internal component 10. In some embodiments, the visibility-enhancing mechanism 12 may be woven into the internal component 10 either during or after the manufacturing of the internal component 10, whereafter the internal component 10 may be at least temporarily affixed to, integrated with, or embedded within at least one portion of at least one item 21.

[0322] In some embodiments, at least one visibility-enhancing element 12 may interact with a secondary design element, wherein the interaction may confirm the identity of the at least one item 21. For example, a visibility-enhancing element 12 may include an oval, and a secondary design element may include a metallic logo design located on the exterior of the item 21. When scanned with imaging technology, the metallic logo design may be centered within the oval. As an example, the secondary design element may include hardware, such as buckles, rivets, or chain links.

[0323] In some embodiments, at least one visibility-enhancing element 12 may be intentionally oriented and located within the item 21 to display known images or patterns through imaging systems from a predefined angle of view. For example, when properly aligned with an imaging system, at least one visibility-enhancing element 12 may include a predefined undistorted image. As another example, multiple visibility-enhancing elements 12 may interact with each other, wherein when properly viewed from a predefined angle, the multiple visibility-enhancing elements 12 may align to create a known composite image.

[0324] In some embodiments, a first view from a first angle may include a first composite image, and a second view from a second angle may include a second composite image. The first composite image may be taken from a standard scanning angle and may include a fake authentication that may be duplicated by counterfeiters. The second composite image may be viewable from a confidential angle or an angle specific to a batch of items 21, which may make it more difficult to create a counterfeit item.

[0325] For example, a purse could be constructed with a metal medallion 26 containing a brand logo on one side of the purse and an authentication element that includes a stitched oval 27 on the other side (where the stitching is an encoding portion 12 of radio-opaque thread), as illustrated in Figs. 5C-D (illustrating the two sides of the purse). This oval could be off-set belowPage 113 of 21213013588vlAttorney Docket No.: 2019150-0023 the level of the medallion such that when the purse is standing up, the two are not co-axial. An x- ray image of the purse parallel to the bottom of the purse would show both the logo and the oval, but not co-axial. However, if the x-ray was oriented at a specific angle, such as 30° from the plane parallel to the purse bottom, then the composite x-ray image would show the logo completely encircled by the radio-opaque thread.

[0326] In some embodiments, at least one encoding portion 12 may be intentionally oriented and located within an item 21 to display known images or patterns through imaging systems for a predefined relative orientations of two or more portions of the item 21. For example, when two or more portions of the item 21 are properly aligned, at least one encoding portion 12 may include a predefined undistorted image. As another example, multiple encoding portions 12 may interact with each other, wherein when two or more portions of the item 21 are properly aligned, the multiple encoding portions 12 may align to create a known composite image.

[0327] For example, a watch may be constructed with two authentication elements 10 stitched onto the strap, wherein the stitches are encoding portions 12 of radiopaque threads. An x-ray image of the watch would show the desired composite image, only if oriented properly. For example, if the watch is worn on a wrist, when the wrist is placed at a specific angle when imaged by an x-ray machine, the encoding portions 12 may align in a way that the predefined composite image is formed. In another example, the strap is placed on a mandrel of a predefined size which results in encoding portions to align in a way that the predefined composite image is formed. In some embodiments, the watch is set to a specific time, for an added security measure. Therefore, a watch may be authenticated if a predefined composite image is formed by x-ray and the watch shows a specific time. In some embodiments, an item 21 may include a size that may be swallowed in a material that may not be viewable on imaging systems, wherein at least one visibilityenhancing element 12 may allow a swallowed item 21 to be viewed on imaging systems. This may be particularly useful for human and pet toys that may be susceptible to swallowing by children and pets. For e...

Claims

Attorney Docket No.: 2019150-0023What is claimed is:

1. An authentication element comprising molecules [e.g., a molecular ink (e.g., that has been inkjet print)], wherein the molecules are arranged to encode at least a portion of an authentication code.

2. The authentication element of claim 1, wherein the molecules are polymer chains (e.g., individual polymer chains) [e.g., in a polymer ink (e.g., that has been inkjet print)].

3. The authentication element of claim 1 or claim 2, wherein the molecules are x-ray sensitive.

4. The authentication element of any one of claims 1-3, wherein each of the molecules comprises an x-ray sensitive moiety.

5. The authentication element of any one of claims 1 -4, wherein the molecules are radiopaque.

6. The authentication element of any one of claims 1-5, wherein a shape in which the molecules are arranged (e.g., on a surface to which they are attached) encodes the at least a portion of the authentication code.

7. The authentication element of any one of claims 1-6, wherein the molecules are arranged as a two-dimensional pattern (e.g., on a surface to which they are attached).

8. The authentication element of any one of claims 1-7, wherein the molecules are arranged as a QR-code (e.g., on a surface to which they are attached) or barcode.

9. The authentication element of any one of claims 1-8, wherein the molecules are disposed on a polymer surface.

10. The authentication element of claim 9, wherein the molecules are attached to the polymer surface.Page 202 of 21213013588vlAttorney Docket No.: 2019150-002311. The authentication element of claim 9 or claim 10, wherein the molecules are primary bonded to the polymer surface (e.g., individual polymer chains individually primary bonded to the polymer surface).

12. The authentication element of claim 11, wherein the molecules are covalently bonded to the polymer surface (e.g., individual polymer chains individually covalently bonded to the polymer surface).

13. The authentication element of any one of claims 9-12, wherein the polymer surface is a surface of packaging for an object to which the authentication code corresponds.

14. A system comprising the authentication element of claim 13, the packaging, and the object.

15. The authentication element or system of any one of claims 1-14, wherein the molecules are grafted onto the polymer surface.

16. The authentication element or system of any one of claims 1-15, wherein each of the molecules comprises a carbene derived or nitrene derived moiety primary bonded to the surface.

17. The authentication element or system of any one of claims 1-16, wherein the molecules are polymer chains that are primary bonded to the surface at one or more side groups of the polymer chains (e.g., each comprising a surface attachment moiety).

18. The authentication element or system of any one of claims 1-17, wherein each of the individual polymer chains comprises a surface attachment end group, wherein the polymer chains are attached to the polymer surface or thread by the attachment end group for the individual polymer chains.

19. The authentication element or system of any one of claims 1-18, wherein the molecules (e.g., polymer chains) are disposed in a monolayer over the surface.Page 203 of 21213013588vlAttorney Docket No.: 2019150-002320. The authentication element or system of any one of claims 1-19, wherein the molecules are polymer chains that each comprise an x-ray sensitive moiety.

21. The authentication element or system of claim 20, wherein the x-ray sensitive moiety is in a repeat unit of the polymer chain.

22. The authentication element or system of claim 20 or claim 21, wherein the x-ray sensitive moiety is in a pendant group of a repeat unit of the polymer chain.

23. The authentication element or system of any one of claims 20-22, wherein the x-ray sensitive moiety is bonded to a backbone of the polymer chain by a linker.

24. The authentication element or system of claim 23, wherein the linker is a polymer (e.g., oligomer).

25. The authentication element or system of claim 23 or claim 24, wherein the linker separates the x-ray sensitive moiety from the backbone by at least 5 atoms, at least 10 atoms, at least 15 atoms, or at least 20 atoms.

26. The authentication element or system of any one of claims 20-25, wherein the x-ray sensitive moiety is in a backbone of the polymer chain.

27. The authentication element or system of any one of claims 20-26, wherein the x-ray sensitive moiety comprises iodine.

28. The authentication element or system of any one of claims 20-27, wherein the x-ray sensitive moiety comprises a mono-, bi-, tri-, quad-, or penta-iodinated moiety.

29. The authentication element or system of claim 28, wherein the x-ray sensitive moiety comprises an arene comprising one, two, three, four, or five iodine-containing substituents.Page 204 of 21213013588vlAttorney Docket No.: 2019150-002330. The authentication element or system of any one of claims 20-29, wherein each of the polymer chains is a copolymer.

31. The authentication element or system of claim 30, wherein the copolymer is a gradient copolymer.

32. The authentication element or system of claim 30, wherein the copolymer is a block copolymer.

33. The authentication element or system of claim 32, wherein the block copolymer comprises a block of a repeat unit comprising the x-ray sensitive moiety.

34. The authentication element or system of claim 32 or claim 33, wherein the block copolymer comprises a block of a repeat unit comprising a surface attachment moiety.

35. The authentication element or system of claim 30, wherein the copolymer is a random copolymer.

36. The authentication element or system of any one of claims 30-35, wherein the copolymer comprises a repeat unit comprising the x-ray sensitive moiety.

37. The authentication element or system of any one of claims 30-36, wherein the copolymer comprises a repeat unit comprising a surface attachment moiety.

38. The authentication element or system of any one of claims 30-37, wherein at least 50% of the repeat units in the copolymer comprise at least one x-ray sensitive moiety.

39. The authentication element or system of any one of claims 30-38, wherein no more than 20% of the repeat units in the copolymer comprise a surface attachment moiety.Page 205 of 21213013588vlAttorney Docket No.: 2019150-002340. A composite authentication element comprising molecules [e g., a molecular ink (e.g., that has been inkjet print)], wherein the molecules are arranged to encode at least a portion of an authentication code.

41. The composite authentication element of claim 40, wherein the molecules are polymer chains (e.g., individual polymer chains) [e.g., in a polymer ink (e.g., that has been inkjet print)].

42. The composite authentication element of claim 40 or claim 41, wherein the molecules are x-ray sensitive.

43. The composite authentication element of any one of claims 40-42, wherein each of the molecules comprises an x-ray sensitive moiety.

44. The composite authentication element of any one of claims 40-43, wherein the molecules are radiopaque.

45. The composite authentication element of any one of claims 40-44, wherein a shape in which the molecules are arranged (e.g., on a surface to which they are attached) encodes the at least a portion of the authentication code.

46. The composite authentication element of any one of claims 40-45, wherein the molecules are arranged as a two-dimensional pattern (e.g., on a surface to which they are attached).

47. The composite authentication element of any one of claims 40-46, wherein the molecules are arranged as a QR-code (e.g., on a surface to which they are attached) or barcode.

48. The composite authentication element of any one of claims 40-47, wherein the molecules are disposed on a plurality of polymer surfaces, each of the plurality of polymer surfaces having a portion of the molecules disposed thereon.Page 206 of 21213013588vlAttorney Docket No.: 2019150-002349. The composite authentication element of claim 48, wherein the molecules are attached to the polymer surfaces.

50. The composite authentication element of claim 48 or claim 49, wherein the molecules are primary bonded to the polymer surfaces (e.g., individual polymer chains individually primary bonded to the polymer surfaces).

51. The composite authentication element of claim 50, wherein the molecules are covalently bonded to the polymer surfaces (e.g., individual polymer chains individually covalently bonded to the polymer surfaces).

52. The composite authentication element of any one of claims 48-51, wherein the polymer surfaces are surfaces of packagings for objects to which the authentication code corresponds.

53. A system comprising the composite authentication element of claim 52, the packagings, and the objects.

54. The composite authentication element or system of any one of claims 40-53, wherein the molecules are grafted onto the polymer surfaces.

55. The composite authentication element or system of any one of claims 40-54, wherein each of the molecules comprises a carbene derived or nitrene derived moiety primary bonded to the surfaces.

56. The composite authentication element or system of any one of claims 40-55, wherein the molecules are polymer chains that are primary bonded to the surfaces at one or more side groups of the polymer chains (e.g., each comprising a surface attachment moiety).

57. The composite authentication element or system of any one of claims 40-56, wherein each of the individual polymer chains comprises a surface attachment end group, wherein thePage 207 of 21213013588vlAttorney Docket No.: 2019150-0023 polymer chains are attached to the surfaces of the polymer fiber or thread by the attachment end group for the individual polymer chains.

58. The composite authentication element or system of any one of claims 40-57, wherein, for each of the polymer surfaces, the portion of the molecules (e.g., polymer chains) are disposed on the surface are disposed in a monolayer.

59. The composite authentication element or system of any one of claims 40-58, wherein the molecules are polymer chains that each comprise an x-ray sensitive moiety.

60. The composite authentication element or system of claim 59, wherein the x-ray sensitive moiety is in a repeat unit of the polymer chain.

61. The composite authentication element or system of claim 59 or claim 60, wherein the x- ray sensitive moiety is in a pendant group of a repeat unit of the polymer chain.

62. The composite authentication element or system of any one of claims 59-61, wherein the x-ray sensitive moiety is bonded to a backbone of the polymer chain by a linker.

63. The composite authentication element or system of claim 62, wherein the linker is a polymer (e.g., oligomer).

64. The composite authentication element or system of claim 62 or claim 63, wherein the linker separates the x-ray sensitive moiety from the backbone by at least 5 atoms, at least 10 atoms, at least 15 atoms, or at least 20 atoms.

65. The composite authentication element or system of any one of claims 59-64, wherein the x-ray sensitive moiety is in a backbone of the polymer chain.

66. The composite authentication element or system of any one of claims 59-65, wherein the x-ray sensitive moiety comprises iodine.Page 208 of 21213013588vlAttorney Docket No.: 2019150-002367. The composite authentication element or system of any one of claims 59-66, wherein the x-ray sensitive moiety comprises a mono-, bi-, tri-, quad-, or penta-iodinated moiety.

68. The composite authentication element or system of claim 67, wherein the x-ray sensitive moiety comprises an arene comprising one, two, three, four, or five iodine-containing substituents.

69. The composite authentication element or system of any one of claims 59-68, wherein each of the polymer chains is a copolymer.

70. The composite authentication element or system of claim 69, wherein the copolymer is a gradient copolymer.

71. The composite authentication element or system of claim 69, wherein the copolymer is a block copolymer.

72. The composite authentication element or system of claim 71, wherein the block copolymer comprises a block of a repeat unit comprising the x-ray sensitive moiety.

73. The composite authentication element or system of claim 71 or claim 72, wherein the block copolymer comprises a block of a repeat unit comprising a surface attachment moiety.

74. The composite authentication element or system of claim 69, wherein the copolymer is a random copolymer.

75. The composite authentication element or system of any one of claims 69-74, wherein the copolymer comprises a repeat unit comprising the x-ray sensitive moiety.

76. The composite authentication element or system of any one of claims 69-75, wherein the copolymer comprises a repeat unit comprising a surface attachment moiety.Page 209 of 21213013588vlAttorney Docket No.: 2019150-002377. The composite authentication element or system of any one of claims 69-76, wherein at least 50% of the repeat units in the copolymer comprise at least one x-ray sensitive moiety.

78. The composite authentication element or system of any one of claims 69-77, wherein no more than 20% of the repeat units in the copolymer comprise a surface attachment moiety.

79. The composite authentication element or system of any one of claims 48-78, wherein the polymer surfaces are surfaces of objects to which the authentication code corresponds.

80. A method of applying an authentication element, the method comprising: disposing (e.g., depositing) (e.g., printing) (e.g., inkjet printing) molecules onto a polymer surface; and irradiating at least a portion of the molecules thereby attaching the at least a portion of the molecules to the surface such that the at least a portion of the molecules are arranged in an arrangement corresponding to at least a portion of an authentication code.

81. The method of claim 80, wherein the molecules are individual polymer chains.

82. The method of claim 80 or claim 81, wherein the polymer surface is a packaging surface (e.g., and the authentication code corresponds to an object in the packaging).

83. The method of any one of claims 80-82, wherein the polymer surface is an object surface and the authentication code corresponds to the object.

84. The method of any one of claims 80-83, wherein the irradiating is a selective irradiation (e.g., applied with a mask or a directed beam).

85. The method of any one of claims 80-84, wherein the irradiating is a blanket irradiation.Page 210 of 21213013588vlAttorney Docket No.: 2019150-002386. The method of any one of claims 80-85, wherein disposing the molecules comprises disposing the molecules in the arrangement.

87. The method of any one of claims 80-86, wherein disposing the molecules comprises making a blanket disposition of the molecules.

88. The method of any one of claims 80-87, wherein the molecules are attached with primary bonds (e.g., covalent bonds).

89. The method of any one of claims 80-88, wherein irradiating the molecules causes a photoreactive moiety to attach to the polymer surface.

90. The method of any one of claims 80-89, wherein the molecules are x-ray sensitive.

91. The method of any one of claims 80-90, wherein each of the molecules comprises an x-ray sensitive moiety.

92. The method of any one of claims 80-91, wherein the arrangement is a two dimensional pattern.

93. The method of any one of claims 80-92, wherein the arrangement is a QR code.

94. The method of any one of claims 80-93, wherein the arrangement is a barcode.Page lll of 21213013588vl

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