A financial model automatic verification method based on a lean prover

Abstract

The application discloses a kind of financial model automation verification methods based on Lean prover, belong to financial technology and formal verification technical field, the application is by converting financial model into formal specification recognizable by Lean language, constructs the specialized axiom library of fusing mathematical axiom and financial field common sense, realizes the mathematical level automation proof of financial model correctness relying on Lean theorem prover, generates executable code with correctness certificate after verification, and verification efficiency can also be optimized by parallel proof, machine learning auxiliary strategy.The application realizes the correctness verification of the whole input space of financial model, and the verification result is logically transparent and highly interpretable.The automation verification is completed in minutes, and a compliance report is automatically generated.The generated code can be directly deployed in a secure manner, perfectly adapting to regulatory requirements such as Basel III agreement, EU AI Act, etc., and is suitable for model risk management and regulatory compliance in all scenarios of financial institutions such as banks, securities, funds, etc.

Description

Technical Field

[0001] This invention relates to the fields of financial technology and formal verification, specifically to an automated verification method for financial models based on Lean provers. Background Technology

[0002] Financial models are key tools for financial institutions in conducting core business operations such as financial product pricing, risk control, investment decision-making, and credit assessment. They are mainly divided into two categories: traditional analytical financial models (such as Black-Scholes option pricing models, VaR (Value at Risk) models, and classic credit scoring models) and next-generation AI-powered intelligent financial models (such as neural network risk control models, machine learning pricing models, and large-scale model-assisted investment decision-making models). With the increasing complexity of financial markets and the growing stringency of financial regulations, the correctness, interpretability, and compliance of financial models have become core aspects of risk management for financial institutions. However, existing financial model validation methods still have many technical shortcomings and are difficult to meet actual business needs. Specific problems include: Validation has inherent blind spots and there is no strict guarantee of correctness: Traditional financial model validation mainly adopts sampling testing methods, which select a limited number of input samples to test the model output results. This cannot cover all input spaces of the model and has an inherent blind spot of "untested is risk". It can only provide statistical-level correctness guarantees and cannot prove the global correctness of the model from a mathematical perspective. Once an untested input scenario occurs, it is very easy to cause the model output error, which can lead to financial losses.

[0003] AI financial models suffer from a black box problem and poor interpretability: For AI intelligent financial models such as neural networks and machine learning, their internal decision-making logic is highly complex and unexplainable. Traditional verification methods cannot clarify the model's reasoning process, nor can they prove the rationality of the model's decisions or locate the root cause of the model's errors. At the same time, they are difficult to meet the regulatory requirements for model transparency and interpretability.

[0004] The verification efficiency is low and it cannot be adapted to high-frequency financial scenarios: The verification of existing financial models relies heavily on manual work. From the design of model test cases and test execution to result analysis and compliance report writing, the entire process takes several weeks to several months. The verification efficiency is extremely low and it is difficult to adapt to financial scenarios such as high-frequency trading and real-time risk control, which have high requirements for model iteration and verification speed.

[0005] Passive response to regulatory compliance and cumbersome report generation: Regulatory regulations such as Basel III and the EU AI Act clearly require financial institutions to have interpretable and correct models with complete verification records. However, traditional verification methods lack standardized verification processes and compliance report generation mechanisms. Financial institutions can only passively respond to regulatory inspections and manually compile verification materials and reports, which is not only time-consuming and labor-intensive, but also prone to problems such as incomplete information and illogical reasoning in reports, increasing regulatory compliance risks.

[0006] Currently, formal verification technology has been maturely applied in fields such as computer software and integrated circuits. By transforming the system into mathematical propositions and completing theorem proofs, mathematical-level guarantees of the system's global correctness can be achieved. The Lean theorem prover, as a high-performance interactive theorem prover, possesses powerful formal description and automated reasoning capabilities, but it has not yet been applied to the field of financial model verification. Therefore, there is an urgent need to combine the Lean prover with financial model verification to provide an automated financial model verification method that achieves mathematical-level correctness guarantees, high automation, strong interpretability, and complies with regulatory requirements, thereby addressing the aforementioned pain points of existing technologies. Summary of the Invention

[0007] The purpose of this invention is to provide an automated verification method for financial models based on Lean provers, in order to solve the problems mentioned in the background art.

[0008] To achieve the above objectives, the present invention provides the following technical solution: an automated verification method for financial models based on Lean provers, comprising the following steps: S1. Formal Specification of Financial Model: The financial model to be verified is fully described using the Lean formal language, defining the types and numerical constraints of the model input parameters, the correctness judgment criteria of the output results, and forming a formal model file that can be recognized by the Lean prover; S2. Construction of a Financial Axiom Library: Construct a structured axiom library containing fundamental mathematical axioms and financial-specific axioms. The axiom library supports expansion and reuse, providing callable axiom bases for theorem proofs. S3, Automated Theorem Proof: Call the Lean Theorem Proofer to transform the formal model obtained in S1 into a mathematical proposition to be proved, which conforms to the preset correctness judgment criteria. The proofer automatically searches for the proof path and completes the proposition proof. Based on the proof result, it outputs a correctness certificate or counterexample and error location information. S4. Compliant Executable Code Generation: For the financial models proven in S3, the Lean prover automatically generates executable code carrying a correctness certificate. This code can be directly deployed to the production environment of financial institutions. At the same time, it automatically generates a model verification compliance report to meet regulatory filing requirements.

[0009] Preferably, in S1, the financial model to be verified includes a traditional analytical financial model and an AI intelligent financial model. The traditional analytical financial model is one or more of the Black-Scholes option pricing model, VaR value at risk model, and credit scoring analytical model, while the AI ​​intelligent financial model is one or more of the neural network risk control model and machine learning pricing model.

[0010] Preferably, in S1, the type and numerical constraints of the input parameters are set according to the business logic of the financial model, including one or more of the following: asset price greater than 0, volatility range of (0,1), non-negative risk-free interest rate, and non-negative trading time; the correctness judgment criteria of the output results are set according to the compliance requirements of financial business, including one or more of the following: option price non-negative, risk exposure not exceeding a preset limit, credit score result within a set range, and model output result satisfying monotonicity constraints.

[0011] Preferably, in S2, the axiom library of mathematical foundations includes one or more of the following: axioms of real analysis, axioms of probability theory, axioms of stochastic processes, and axioms of linear algebra. The axioms specific to the financial field include one or more of the following: no-arbitrage pricing axiom, risk-neutral pricing axiom, capital asset pricing axiom, and basic axioms of financial regulatory compliance. The axiom library adopts a modular construction approach, with each axiom formally described in Lean language and given a unique identifier, supporting on-demand calling, adding, modifying, and deleting.

[0012] Preferably, the proof process of the Lean theorem prover in S3 includes four sub-steps: proposition transformation, proof strategy matching, axiom invocation, and reasoning verification. Proposition transformation is to transform the correctness verification requirements of the financial model into first-order logic propositions that the Lean prover can recognize. Proof strategy matching is to match suitable reasoning strategies from the prover's strategy library. Axiom invocation is to call relevant axioms from the financial axiom library constructed in S2 as the basis for reasoning. Reasoning verification is to complete the automated reasoning proof of the proposition according to the first-order logic rules.

[0013] Preferably, in step S3, if the proof is successful, the Lean prover generates a unique correctness certificate containing model information, verification time, a list of axiom calls, reasoning process, and verification conclusion; if the proof fails, the prover returns an input counterexample that can trigger a model error, and accurately locates the erroneous code line, logical defect location, or link that conflicts with financial axioms in the formal description of the model.

[0014] Preferably, in step S4, the programming language of the compliant executable code includes one or more of Python, C++, Java, and MATLAB. The code embeds a unique identifier and calling interface for the correctness certificate, supporting real-time verification of code correctness in the production environment. The compliance report includes basic model information, a complete verification process record, correctness proof results, axiom usage instructions, counterexamples (if any), and rectification suggestions. The report format is adapted to the filing requirements of financial regulatory agencies and supports export in multiple formats such as PDF, Excel, and XML.

[0015] Preferably, the method also includes an optimized implementation for verification efficiency. This optimized implementation employs a parallel theorem proving algorithm, decomposing the proposition to be proven into multiple independent sub-propositions, and completing the parallel proof of multiple sub-propositions through distributed computing nodes. Simultaneously, machine learning is introduced to assist in the selection of proof strategies. A strategy matching model is trained based on historical verification data to automatically match the optimal proof strategy for the proposition to be proven, thereby improving the inference efficiency of the prover. The optimized implementation also supports batch automated verification of multiple financial models. By batch importing formal model files, the Lean prover sequentially completes the verification and generates a batch verification summary compliance report. During the batch verification process, breakpoint resume and real-time monitoring of verification progress are supported.

[0016] Compared with the prior art, the beneficial effects of the present invention are: Achieving global correctness at the mathematical level and completely eliminating verification blind spots: This invention transforms the correctness verification of financial models into the theorem proof of mathematical propositions. By using the Lean prover to complete the logical reasoning verification of the entire input space, it proves the global correctness of the model from a mathematical perspective, completely eliminating the "untested is risk" blind spot of traditional sampling testing methods. This provides the most stringent correctness guarantee for financial models and significantly reduces financial losses caused by model errors.

[0017] Breaking the Black Box Problem of AI Financial Models and Enhancing Model Interpretability: This invention clarifies the internal decision-making logic of AI financial models by formally describing their network structure and decision rules, combined with the visual reasoning process of the Lean prover. The generated correctness certificate includes complete axiomatic calls and reasoning processes, giving the model's output a clear mathematical and financial theoretical basis. This completely breaks the black box problem of AI financial models and meets the regulatory requirements for model transparency and interpretability.

[0018] Significantly improves model validation efficiency and adapts to high-frequency financial scenarios: This invention automates the entire process of financial model validation, from formal specification and theorem proof to code generation and report writing, without human intervention. The validation of a single financial model can be completed in minutes. Compared with the cycle of several weeks to several months of traditional manual validation, the validation efficiency is improved, and it can be perfectly adapted to financial scenarios such as high-frequency trading and real-time risk control that have high requirements for model iteration and validation speed.

[0019] Proactively meet regulatory compliance requirements and reduce compliance risks: This invention pre-sets verification standards and report formats that comply with regulatory regulations such as Basel III and the EU AI Act. After verification, a standardized compliance report is automatically generated. The report contains all the core information required by regulatory agencies. Financial institutions can directly submit the report for filing, realizing the transformation from "passively responding to regulation" to "proactively meeting regulation." At the same time, the automated generation of the report avoids the omissions of manual compilation and significantly reduces the regulatory compliance risks of financial institutions.

[0020] The axiom library and verification methods are scalable, reusable, and highly practical: The financial axiom library of this invention adopts a modular construction approach, supporting expansion based on new financial business scenarios, mathematical theories, and regulatory requirements. Furthermore, the formalized reduction and theorem proving methods can be reused in the verification of various financial models without requiring redesign of the verification process for different models. In addition, this invention supports preferred implementation methods such as parallel proof and batch verification, adapting to verification needs across all scenarios, from simple analytical models to complex AI models, and from single models to batch models. It is suitable for various financial institutions such as banks, securities firms, and funds, and has broad application value. Attached Figure Description

[0021] Figure 1 This is a schematic diagram of the method flow of the present invention. Detailed Implementation

[0022] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0023] Please see Figure 1 This invention provides a technical solution: an automated verification method for financial models based on Lean provers, comprising the following steps: S1. Formal Specification of Financial Model: The financial model to be verified is fully described using the Lean formal language, defining the types and numerical constraints of the model's input parameters and the correctness criteria for the output results, forming a formal model file that can be recognized by the Lean prover. The core of this step is to transform the financial model to be verified into a formal language description that can be recognized and processed by the Lean theorem prover, completing the standardization and formal definition of the model. The specific implementation process is as follows: The type of financial model to be validated is determined, including traditional analytical financial models (Black-Scholes option pricing model, VaR value at risk model, etc.) and AI intelligent financial models (neural network risk control model, machine learning pricing model, etc.). For AI intelligent financial models, the core elements such as network structure, weight parameters, and activation functions are extracted in a structured manner and then formally described. The Lean formal programming language is used to provide a complete and accurate description of the core logic, calculation formulas, and decision rules of the financial model, ensuring that the formal description is completely consistent with the logic of the original model. Based on the business logic and mathematical constraints of the financial model, define the type and numerical constraints of the model input parameters, such as asset price > 0, volatility ∈ (0,1), risk-free interest rate ≥ 0, etc., to avoid model errors caused by invalid inputs; Combining financial business compliance requirements and model application scenarios, define the correctness judgment criteria for model output results, such as option price ≥ 0, risk exposure ≤ preset regulatory limit, credit score result ∈ [0,100], etc., as the basis for judging the correctness of the model; The above formal descriptions, parameter constraints, and correctness specifications are integrated to generate a unified formal model file, which can be directly read and parsed by the Lean prover. S2. Construction of a Financial Axiom Library: A structured axiom library containing fundamental mathematical axioms and financial-specific axioms is constructed. This library supports expansion and reuse, providing callable axiom bases for theorem proofs. The axiom library is the core basis for the Lean prover to complete the theorem proofs of financial models. This invention adopts a modular and scalable approach to construct a financial axiom library that integrates fundamental mathematical axioms and financial-specific axioms. The specific implementation process is as follows: The module for constructing mathematical foundations axioms includes core mathematical axioms related to financial models, such as real analysis, probability theory, stochastic processes, and linear algebra. All mathematical axioms are formally described using the Lean language to ensure the rigor of the reasoning. We have constructed a dedicated axiom module for the financial sector, which formalizes basic financial common sense, pricing principles, risk control criteria, and basic regulatory requirements into callable axioms, including the no-arbitrage pricing axiom, the risk-neutral pricing axiom, the capital asset pricing axiom, and the basic axioms of financial regulatory compliance, covering the core business basis for financial model verification. All axioms are uniquely identified by assigning a unique identifier code to each axiom and adding detailed annotations, including applicable scenarios, mathematical basis, and financial business implications, to facilitate on-demand access by the prover and manual review. Build an axioms library management system that supports the expansion and reuse of the axioms library. It can add, modify or delete axiom modules according to new financial business scenarios, mathematical theories and regulatory requirements. It also supports batch import and export of axioms to improve the usability of the axioms library. The completed financial axiom library is integrated with the Lean prover, enabling the prover to call relevant axioms from the axiom library in real time during the reasoning process; S3. Automated Theorem Proof: This step calls the Lean theorem prover to transform the formal model obtained in S1, which conforms to a preset correctness criterion, into a mathematical proposition to be proven. The prover automatically searches for the proof path and completes the proof, outputting a correctness certificate or counterexample and error location information based on the proof result. This step is the core of financial model verification. Relying on the Lean theorem prover, the correctness verification of the financial model is transformed into an automated proof of a mathematical proposition, achieving mathematical-level verification of the model's global correctness. The specific implementation process is as follows: Proposition transformation: The verification requirement of "the formal model obtained by S1 meets the preset output correctness judgment standard" is transformed into a first-order logic proposition that can be recognized by the Lean prover, clarifying the preconditions (formal model, parameter constraints) and conclusion (output result meets the correctness standard) of the proposition. Proof strategy matching: The Lean prover matches an appropriate reasoning strategy for the proposition to be proved from its own proof strategy library. For complex propositions, they can be decomposed into multiple simple sub-strategies. At the same time, this invention can improve the accuracy and efficiency of strategy matching by using machine learning to assist in strategy selection. Axioms and Strategy Invocation: Based on the logic of the proposition to be proved and the matching proof strategy, the prover automatically invokes relevant mathematical and financial axioms from the financial axiom library constructed by S2 as the theoretical basis for reasoning and proof. Automated reasoning verification: The Lean prover completes the automated reasoning proof of propositions according to the reasoning rules of first-order logic. If all logical paths can derive the conclusion from the premises during the reasoning process, and there are no logical contradictions or conflicts with axioms, then the proposition is proven to be true; if any logical path cannot derive the conclusion, or if there are logical contradictions or conflicts with axioms, then the proposition is proven to be false. Verification result output: If the proof is successful, the Lean prover generates a unique correctness certificate, which contains core information such as basic model information, verification time, axiom call list, complete reasoning process, and verification conclusion, serving as the mathematical proof of the model's correctness; if the proof fails, the prover returns input counterexamples that can trigger model errors, and precisely locates the erroneous lines of code, logical defects, or specific links that conflict with financial axioms in the model's formal description, providing a clear basis for model modification and optimization; S4. Compliant Executable Code Generation: For the financial model proven in S3, the Lean prover automatically generates executable code carrying a correctness certificate. This code can be directly deployed to the production environment of financial institutions. Simultaneously, a model validation compliance report is automatically generated to meet regulatory filing requirements. This step transforms the validated financial model into actually deployable code and automatically generates a regulatory compliance report, achieving an integrated "validation-generation-deployment" process. The specific implementation process is as follows: Automatic Executable Code Generation: For financial models that have passed the proof in S3, the Lean prover automatically generates executable code that can be directly deployed to the production environment of financial institutions based on its formal description. It supports multiple mainstream programming languages ​​such as Python, C++, Java, and MATLAB to meet the deployment needs of different financial systems. Correctness certificate embedding: The unique identifier of the model's correctness certificate and the online verification interface are embedded in the generated executable code, so that the correctness of the code can be verified in real time when the code runs in the production environment. If the code is tampered with, the verification interface will immediately return an exception, ensuring the security of the model deployment. Automatic Compliance Report Generation: Based on the entire verification process of the model, a standardized financial model verification compliance report is automatically generated. The report includes basic model information, formal specification details, axiom call explanations, theorem proof process, correctness verification results, counterexamples (if any), and rectification suggestions. The report format strictly conforms to the filing requirements of regulatory agencies such as Basel III and the EU AI Act, and supports export in multiple formats such as PDF, Excel, and XML. Code and report delivered simultaneously: Executable code with a correctness certificate and compliance report are delivered simultaneously. Financial institutions can directly deploy the code to the production environment, while the compliance report is submitted to the regulatory agency for filing, achieving a seamless connection between model verification and online deployment.

[0024] To further improve the verification efficiency and practicality of this invention, the following preferred implementation methods are set for the verification needs of large-scale financial models and complex AI financial models: Parallel theorem proving: The parallel theorem proving algorithm decomposes the complex proposition to be proven into multiple sub-propositions according to logical independence, and performs parallel proof of multiple sub-propositions through distributed computing nodes, which greatly shortens the proof time. It is suitable for the verification of complex financial models such as high-frequency trading models and large-scale neural network risk control models. Machine learning-assisted proof strategy selection: Based on historical data of financial model verification, a machine learning strategy matching model is trained. This model can automatically match the optimal proof strategy for the Lean prover according to the characteristics of the proposition to be proved, such as its type, complexity, and financial scenario, thereby reducing the strategy search time of the prover and improving the efficiency of automated reasoning. Batch Model Automated Validation: Build a batch validation management interface to support financial institutions in importing multiple formal model files in batches. The Lean prover completes the automated validation of all models in a preset order. It also supports breakpoint resume and real-time monitoring of validation progress. After validation is completed, a batch validation summary compliance report is generated. It is suitable for financial institutions to conduct centralized risk management and validation of models of all categories. Visualized verification process display: Configure a visual interface for the Lean prover to display the process of theorem proof, the order of axiom calls, and the reasoning results of subpropositions in a graphical way. It also supports visual tracing of failed proofs, enabling technical and risk control personnel in financial institutions to intuitively understand the model verification process and solve the interpretability problem of AI financial models.

[0025] This invention discloses an automated verification method for financial models based on Lean provers, belonging to the fields of financial technology and formal verification technology. It solves the technical problems of traditional financial model verification relying on sampling tests with blind spots, the uninterpretable nature of AI financial models (being black boxes), low verification efficiency, and difficulty in meeting stringent regulatory compliance requirements. This method transforms the financial model into a formal specification recognizable by the Lean language, constructs a dedicated axiom library integrating mathematical axioms and common sense in the financial field, and achieves mathematical-level automated proof of the financial model's correctness using a Lean theorem prover. Upon successful verification, executable code with a correctness certificate is automatically generated. Verification efficiency can be further optimized through parallel proofs and machine learning-assisted strategies. This invention achieves correctness verification across the entire input space of the financial model. The verification results are logically transparent and highly interpretable, completing automated verification and automatically generating compliance reports within minutes. The generated code can be directly and securely deployed, perfectly adapting to regulatory requirements such as Basel III and the EU AI Act. It is applicable to all scenarios of model risk management and regulatory compliance for financial institutions such as banks, securities firms, and funds.

[0026] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. An automated verification method for financial models based on Lean provers, characterized in that, Includes the following steps: S1. Formal Specification of Financial Model: The financial model to be verified is fully described using the Lean formal language, defining the types and numerical constraints of the model input parameters, the correctness judgment criteria of the output results, and forming a formal model file that can be recognized by the Lean prover; S2. Construction of a Financial Axiom Library: Construct a structured axiom library containing fundamental mathematical axioms and financial-specific axioms. The axiom library supports expansion and reuse, providing callable axiom bases for theorem proofs. S3, Automated Theorem Proof: Call the Lean Theorem Proofer to transform the formal model obtained in S1 into a mathematical proposition to be proved, which conforms to the preset correctness judgment criteria. The proofer automatically searches for the proof path and completes the proposition proof. Based on the proof result, it outputs a correctness certificate or counterexample and error location information. S4. Compliant Executable Code Generation: For the financial models proven in S3, the Lean prover automatically generates executable code carrying a correctness certificate. This code can be directly deployed to the production environment of financial institutions. At the same time, it automatically generates a model verification compliance report to meet regulatory filing requirements.

2. The automated verification method for financial models based on Lean provers according to claim 1, characterized in that: In S1, the financial models to be verified include traditional analytical financial models and AI intelligent financial models. The traditional analytical financial models are one or more of the Black-Scholes option pricing model, VaR value at risk model, and credit scoring analytical model, while the AI ​​intelligent financial models are one or more of the neural network risk control model and machine learning pricing model.

3. The automated verification method for financial models based on Lean provers according to claim 1, characterized in that: In S1, the types and numerical constraints of the input parameters are set according to the business logic of the financial model, including one or more of the following: asset price greater than 0, volatility range of (0,1), risk-free interest rate non-negative, and trading time non-negative; the correctness judgment criteria of the output results are set according to the compliance requirements of financial business, including one or more of the following: option price non-negative, risk exposure not exceeding the preset limit, credit score result within the set range, and model output result satisfying monotonicity constraints.

4. The automated verification method for financial models based on Lean provers according to claim 1, characterized in that: In S2, the axiom library of mathematical foundations includes one or more of the following: axioms of real analysis, axioms of probability theory, axioms of stochastic processes, and axioms of linear algebra. The axioms specific to the financial field include one or more of the following: axioms of no-arbitrage pricing, axioms of risk-neutral pricing, axioms of capital asset pricing, and axioms of basic financial regulatory compliance. The axiom library adopts a modular construction approach, with each axiom formally described in Lean language and given a unique identifier, supporting on-demand calling, adding, modifying, and deleting.

5. The automated verification method for financial models based on Lean provers according to claim 1, characterized in that: The proof process of the Lean theorem prover in S3 includes four sub-steps: proposition transformation, proof strategy matching, axiom invocation, and reasoning verification. Proposition transformation is to transform the correctness verification requirements of the financial model into first-order logic propositions that the Lean prover can recognize. Proof strategy matching is to match suitable reasoning strategies from the prover's strategy library. Axiom invocation is to call relevant axioms from the financial axiom library constructed in S2 as the basis for reasoning. Reasoning verification is to complete the automated reasoning proof of the proposition according to the first-order logic rules.

6. The automated verification method for financial models based on Lean provers according to claim 1, characterized in that: In S3, if the proof is successful, the Lean prover generates a unique correctness certificate containing model information, verification time, a list of axiom calls, reasoning process, and verification conclusion. If the proof fails, the prover returns a counterexample that can trigger a model error and pinpoints the erroneous lines of code, logical flaws, or points of conflict with financial axioms in the model's formal description.

7. The automated verification method for financial models based on Lean provers according to claim 1, characterized in that: In S4, the programming language of the compliant executable code includes one or more of Python, C++, Java, and MATLAB. The code embeds a unique identifier and calling interface for the correctness certificate, supporting real-time verification of code correctness in the production environment. The compliance report includes basic model information, a complete verification process record, correctness proof results, axiom usage instructions, counterexamples, and rectification suggestions. The report format is adapted to the filing requirements of financial regulatory agencies and supports export in multiple formats such as PDF, Excel, and XML.

8. The automated verification method for financial models based on Lean provers according to any one of claims 1-7, characterized in that: The S3 method, which automatically searches for proof paths and completes proposition proofs through the prover, also includes an optimized implementation for improving verification efficiency. This optimized implementation employs a parallel theorem proving algorithm, decomposing the proposition to be proven into multiple independent sub-propositions and completing the parallel proof of these sub-propositions through distributed computing nodes. Simultaneously, it introduces machine learning to assist in proof strategy selection, training a strategy matching model based on historical verification data to automatically match the optimal proof strategy for the proposition to be proven, thereby improving the prover's inference efficiency. This optimized implementation also supports batch automated verification of multiple financial models. By batch importing formal model files, the Lean prover sequentially completes the verification and generates a batch verification summary compliance report. During batch verification, it supports breakpoint resumption and real-time monitoring of verification progress.

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