Method for verifying dynamic stability of distributed consensus system based on complex network dynamics and corresponding product

Abstract

This application relates to the field of software testing technology, providing a method and corresponding product for dynamic stability verification of distributed consensus systems based on complex network dynamics. The method includes: modeling the distributed consensus system under test as a time-varying dynamic graph and defining an energy feedback function based on consensus protocol rules; initializing the simulation environment and loading the configuration parameters and initial state of the distributed consensus system under test; discretizing the continuous spatiotemporal perturbation search space to generate a spatiotemporal topological perturbation vector; intercepting node messages at the communication layer for message matching; when the intercepted node message matches the characteristics of the generated spatiotemporal topological perturbation vector, modifying the message content or delaying message release based on the perturbation components; real-time acquisition of system state update data after driving evolution and calculation of a divergence index; using the calculated divergence index as a feedback signal to adaptively adjust the spatiotemporal topological perturbation vector and repeating the process until the divergence index converges or a stability anomaly is detected.

Description

Technical Field

[0001] This application relates to the field of software testing technology, and in particular to a dynamic stability verification method and corresponding product for a distributed consensus system based on complex network dynamics. Background Technology

[0002] With the rapid development of technologies such as blockchain and distributed ledgers, the stability and reliability of distributed consensus systems, as their core foundation, are of paramount importance. These systems typically operate in complex network environments, with multiple independent nodes following consensus protocols working collaboratively to achieve state consistency. The stability of a system is not only reflected in its ability to tolerate routine anomalies such as node failures or network latency, but also, at a deeper level, in its ability to maintain the convergence and fairness of the consensus process in a game environment where nodes adhere to the "rational actor assumption" (i.e., pursuing their own self-interest maximization), thus avoiding systemic instability caused by incompatible incentives.

[0003] In existing technologies, the verification of distributed consensus systems mainly relies on two types of methods. The first is formal verification, which rigorously proves the security and liveness properties of the protocol design itself through mathematical logic, but it is difficult to cover the engineering implementation details and complex dynamic operating environments. The second is fuzz testing, which triggers immediate errors (such as program crashes) on the client by randomly or heuristically mutating input data (such as transactions and blocks), focusing on discovering defects at the code level.

[0004] However, when faced with complex systems with excitation-dynamic coupling, existing verification techniques have the following obvious limitations: 1) They lack the ability to verify the long-term dynamic evolution behavior of the system; 2) They are inefficient in high-dimensional continuous perturbation search spaces; 3) Existing methods cannot effectively detect soft failures caused by excitation incompatibility. Summary of the Invention

[0005] Based on this, it is necessary to address the shortcomings of the existing technologies, such as the difficulty in verifying the long-term dynamic evolution behavior of the system and the inability to effectively detect soft failures caused by incentive incompatibility. Therefore, a dynamic stability verification method and corresponding product for distributed consensus systems based on complex network dynamics are proposed.

[0006] Firstly, a dynamic stability verification method for a distributed consensus system based on complex network dynamics is provided, the method comprising: S101: Model and initialize the system, that is, model the distributed consensus system under test as a time-varying dynamic graph and define an energy feedback function based on the consensus protocol rules, initialize the simulation environment, load the configuration parameters and initial state of the distributed consensus system under test, the energy feedback function is used to quantify the change of the equity utility value of the nodes in the time-varying dynamic graph, the nodes represent consensus participants, and the edges of the time-varying dynamic graph represent communication connections. S102: Generate a perturbation vector, that is, discretize the continuous spatiotemporal perturbation search space to generate a spatiotemporal topological perturbation vector. The spatiotemporal topological perturbation vector includes a temporal perturbation component and a topological perturbation component. The temporal perturbation component is used to control the timing of message delay, and the topological perturbation component is used to modify the message target or content. S103: Perform non-intrusive simulation, that is, intercept node messages at the communication layer through the signal injection adapter for message matching. When the intercepted node message matches the characteristics of the spatiotemporal topology disturbance vector generated in step S102, modify the message content or delay message release according to the disturbance component to drive the dynamic evolution of the system. S104: Detect stability, that is, collect the system state update data after the driving evolution in step S103 in real time, and calculate the divergence index. The divergence index is used to quantify the degree of deviation of the system state from the synchronous steady state. S105: Closed-loop optimization iteration, that is, using the divergence index calculated in step S104 as a feedback signal, adaptively adjusting the spatiotemporal topological perturbation vector in step S102, and repeating steps S103 to S104 until the divergence index converges or a stability anomaly is detected.

[0007] Secondly, a dynamic stability verification device for a distributed consensus system based on complex network dynamics is provided, the device comprising: The initialization module is used to model the distributed consensus system under test as a time-varying dynamic graph and define an energy feedback function based on the consensus protocol rules, initialize the simulation environment, load the configuration parameters and initial state of the distributed consensus system under test, and the energy feedback function is used to quantify the change of the equity utility value of the nodes in the time-varying dynamic graph, where the nodes represent consensus participants and the edges of the time-varying dynamic graph represent communication connections. The generation module is used to discretize the continuous spatiotemporal perturbation search space and generate a spatiotemporal topological perturbation vector. The spatiotemporal topological perturbation vector includes a temporal perturbation component and a topological perturbation component. The temporal perturbation component is used to control the timing of message delay, and the topological perturbation component is used to modify the message target or content. The simulation module is used to intercept node messages at the communication layer through a signal injection adapter for message matching. When the intercepted node message matches the characteristics of the generated spatiotemporal topology perturbation vector, the message content is modified or the message release is delayed based on the perturbation components to drive the dynamic evolution of the system. The calculation module is used to collect system state update data after the dynamic evolution of the driving system in real time and calculate the divergence index, which is used to quantify the degree of deviation of the system state from the synchronous steady state. The iterative module is used to adaptively adjust the spatiotemporal topological perturbation vector using the divergence index as a feedback signal, and repeatedly execute the functions or actions of the simulation module and the calculation module until the divergence index converges or a stability anomaly is detected.

[0008] Thirdly, a computer device is provided, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps of the above-described dynamic stability verification method for a distributed consensus system based on complex network dynamics.

[0009] Fourthly, a computer-readable storage medium is provided, which stores a computer program that, when executed by a processor, implements the steps of the above-described method for dynamic stability verification of a distributed consensus system based on complex network dynamics.

[0010] As can be seen from the technical solution provided in this application, on the one hand, by adopting a combination of non-intrusive simulation execution and closed-loop optimization iteration, it is possible to continuously drive the dynamic evolution of the tested system over a long period of time without interfering with its normal operation. By repeatedly injecting disturbances and observing the system response, this method can simulate the long-term effects of multi-round games between nodes in the real world, thereby effectively revealing stability problems that only appear in long-term interactions, overcoming the limitation of existing technologies that can only verify instantaneous or short-term behaviors. On the other hand, thanks to the discretization of the continuous spatiotemporal search space in the generation of disturbance vectors, the originally infinite search range is reduced to a finite, structured discrete grid, which provides a feasible search basis for subsequent optimization algorithms, enabling systematic optimization. First, by strategically exploring critical perturbation parameters that may trigger system instability, this approach avoids the blindness of traditional random testing, thereby improving verification efficiency and the ability to discover boundary scenarios. Second, by introducing an energy feedback function during system modeling and initialization, and using it as the core basis for calculating the divergence index in stability testing, the method described in this application can quantify changes in node equity utility values, thus effectively identifying whether the system has deviated from the incentive-compatible equilibrium state. Whether a node gains excess benefits or the entire network experiences utility dissipation, these can be sensitively captured through the divergence index, solving the problem that traditional methods cannot quantify and evaluate soft failures. In summary, the technical solution of this application, through closed-loop dynamic verification and an energy feedback mechanism, can automatically discover deep-seated stability risks and incentive compatibility issues in the system. Attached Figure Description

[0011] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort. Wherein: Figure 1 This is a flowchart of a dynamic stability verification method for a distributed consensus system based on complex network dynamics in one embodiment; Figure 2 This is a structural block diagram of a dynamic stability verification device for a distributed consensus system based on complex network dynamics in one embodiment. Figure 3 This is a structural block diagram of a computer device in one embodiment. Detailed Implementation

[0012] 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, not all, of the embodiments of the present invention. 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.

[0013] In existing technologies, the verification of distributed consensus systems mainly relies on two types of methods. The first is formal verification, which rigorously proves the security and liveness properties of the protocol design itself through mathematical logic, but it is difficult to cover the engineering implementation details and complex dynamic operating environments. The second is fuzz testing, which triggers immediate errors (e.g., program crashes) on the client by randomly or heuristically mutating the input data (e.g., transactions, blocks), focusing on discovering defects at the code level. However, when faced with complex systems with coupled incentives and dynamics, existing verification techniques have the following obvious limitations: 1) They lack the ability to verify the long-term dynamic evolution of the system. Many stability problems in consensus systems (e.g., consensus bifurcation caused by certain perturbation strategies) are the result of multi-round game interactions between nodes, rather than being directly caused by a single input. Existing methods are difficult to simulate and evaluate this evolution process that spans multiple consensus cycles; 2) They are inefficient in high-dimensional continuous perturbation search spaces. Perturbations that may induce system instability (e.g., message delays accurate to milliseconds, specific network topology changes) have a nearly infinite parameter space. Traditional random testing methods are like finding a needle in a haystack, making it difficult to effectively locate the critical parameters that cause qualitative changes in system stability; 3) Existing methods cannot effectively detect soft failures caused by incentive incompatibility. They usually focus on "hard" failures such as node crashes and double-spending of assets, but cannot quantify "soft" stability problems such as rational nodes manipulating message timing to obtain excess returns, thereby destroying the Nash equilibrium of the system. These problems can also seriously damage the long-term health of the system.

[0014] To address the aforementioned problems in existing technologies, this application proposes a dynamic stability verification method for distributed consensus systems based on complex network dynamics. The main process is as follows: Figure 1 As shown, the main steps include S101 to S105, which are detailed below: Step S101: Model and initialize the system, that is, model the distributed consensus system under test as a time-varying dynamic graph and define the energy feedback function based on the consensus protocol rules, initialize the simulation environment, and load the configuration parameters and initial state of the distributed consensus system under test. The energy feedback function is used to quantify the change of the equity utility value of nodes in the time-varying dynamic graph. Nodes represent consensus participants, and the edges of the time-varying dynamic graph represent communication connections.

[0015] In verifying distributed consensus systems, accurate system modeling is crucial. Existing formal verification methods often abstract the system into a static model, neglecting the dynamic changes in network topology and the real-time interactions of node behavior, making it difficult to cover the complexities of real-world environments. For example, in blockchain systems, connections between nodes may dynamically change due to network latency or node joining / leaving; this time-varying nature significantly impacts the consensus process. This application characterizes the system by introducing a time-varying dynamic graph, where nodes represent consensus participants, such as validators, and edges represent communication connections that evolve over time. The time-varying dynamic graph can be formally represented as follows: ,in, It is a set of nodes. t It refers to discrete time steps, such as time slot indexes. It is a moment t The set of edges represents the connection state. This modeling approach can more realistically reflect the dynamic characteristics of the system, laying the foundation for subsequent perturbation injection and evolution simulation.

[0016] To quantify the impact of node behavior, this application defines an energy feedback function. This function, based on consensus protocol rules, maps node behavior to changes in stake utility value. For example, in Proof-of-Stake (PoS) protocols, the energy feedback function can calculate changes in a node's stake balance due to voting, proposals, or penalties; in Proof-of-Work (PoW) protocols, it can be defined based on computing power share and reward mechanisms. The introduction of the energy feedback function addresses the deficiency of existing testing methods in detecting incentive compatibility issues, as it provides a basis for quantifying soft failures (such as utility deviations). During simulation environment initialization, the configuration parameters of the system under test (e.g., network topology file, protocol parameters) and initial state (e.g., genesis block) are loaded, ensuring the consistency between the verification environment and the real system.

[0017] As an embodiment of this application, system modeling and initialization can be achieved through steps S1011 to S1013, as detailed below: Step S1011: Parse the network topology file of the distributed consensus system under test, and map the node set and dynamic connection relationship into a graph structure.

[0018] In practice, network topology files are typically stored in JSON format, containing node IP addresses, port information, and connection rules. The parsing process involves reading the file, abstracting each node as a vertex of the graph, and constructing edges according to connection rules (such as fully connected, partially connected, or dynamically connected). For example, for a test network containing 100 nodes, the parser would generate a graph object containing a set of nodes. edge set Indicates at timet The connection state in real time can be stored using an adjacency matrix or adjacency list. Dynamic connectivity can be simulated using time-series data, for example, updating the connection graph every 5 seconds to reflect network jitter or node failures. This mapping allows subsequent perturbation injection and evolution simulations to be based on the real topology, avoiding verification distortion caused by model simplification.

[0019] Step S1012: Based on the consensus protocol rules, define an energy feedback function, whereby the energy feedback function maps the behavior of a node to a stake utility value, which includes changes in stake balance and rewards or penalties.

[0020] In this embodiment, the specific definition of the energy feedback function depends on the protocol type. Taking the PoS protocol as an example, the function can be formalized as: in, This represents the utility value of node i at time t. It refers to the equity balance, such as the amount pledged. These are rewards, such as block rewards or voting rewards. This refers to penalties, such as the reduction of stake due to violations. Rewards and penalties are calculated based on protocol rules; for example, rewards might be proportional to a node's voting weight or staked amount. This is achieved through real-time calculations. Changes in this can detect whether node behavior leads to a deviation in utility, thereby identifying incentive incompatibility issues. Furthermore, for the PoW protocol, the energy feedback function is adjusted to adapt to the computing power model. Here, It is the node's computing power share. It's a block reward. This refers to operational costs. Through this calculation formula, the energy feedback function maps node behavior (e.g., voting) to continuous changes in utility values, thus providing a quantitative basis for detecting "incentive incompatibility." In practice, the function parameters (e.g., reward coefficients) must strictly adhere to the rules of the protocol under test to ensure the authenticity of the verification environment.

[0021] Step S1013: Start the simulation environment and deploy the signal injection adapter to take over the node communication port in a non-intrusive manner.

[0022] The startup of the simulation environment includes initializing the virtual machine or container cluster, loading node images and protocol clients. The signal injection adapter is a key component, taking over the node's P2P communication ports non-intrusively. For example, the adapter can be deployed as a bypass container for each node, utilizing Linux network namespace isolation and iptables rules to redirect outbound traffic to the adapter's processing logic. Specifically, the adapter listens on sockets or intercepts messages using eBPF technology without modifying the consensus client code. This approach ensures consistency between the verification and production environments and supports testing of multiple client versions, resolving compatibility issues caused by existing intrusive instrumentation. After deployment, the adapter remains in standby mode, awaiting the injection of subsequent perturbation vectors.

[0023] Step S102: Generate a perturbation vector, that is, discretize the continuous spatiotemporal perturbation search space to generate a spatiotemporal topological perturbation vector. The spatiotemporal topological perturbation vector includes a temporal perturbation component and a topological perturbation component. The temporal perturbation component is used to control the timing of message delay, and the topological perturbation component is used to modify the message target or content.

[0024] In distributed system stability verification, efficiently exploring the nearly infinite space of perturbation parameters is a core challenge. Existing technologies, such as random fuzzing, search in continuous time (millisecond-level latency) and topology (arbitrary connection structure) dimensions, resulting in extremely low efficiency and making it difficult to systematically discover critical parameters leading to system instability. This application transforms the infinite problem into a finite problem by discretizing the continuous spatiotemporal perturbation search space. Specifically, the spatiotemporal topology perturbation vector is defined as a structured data object that encapsulates temporal perturbation components (controlling message delay and release timing) and topology perturbation components (controlling the target node and content modification of the message). This discretization lays a solid foundation for subsequent automated and targeted searches, making the originally "needle-in-a-haystack" search feasible and efficient. Specifically, as an embodiment of this application, generating the perturbation vector can be achieved through steps S1021 to S1023, as detailed below: Step S1021: Discretize the time dimension into consensus cycles or time slot units, and discretize the topology dimension into a set of connected components based on node degree to form a discrete spatiotemporal grid.

[0025] The core of discretization is constructing an traversable discrete spatiotemporal grid. For the time dimension, we discretize according to the time division rules of the consensus protocol under test. For example, in PoS protocols such as Ethereum 2.0, time is divided into consensus periods (Epochs) and slots, with one Epoch containing 32 Slots (approximately 6.4 minutes). Therefore, message latency... It is no longer a continuous millisecond value, but is quantized into an offset of an integer number of slots, i.e. ,in, This represents the maximum allowable number of slots for latency. For the topology dimension, it can be discretized based on the node's degree. For example, a degree threshold can be set. Only retain networks with a density greater than 1. The connections between nodes are used as potential perturbation targets, thus significantly reducing the number of connection pairs that need to be considered. Combining these two discretized dimensions forms a structured grid, where each cell represents a specific spatiotemporal perturbation configuration.

[0026] Step S1022: Sample the discrete spatiotemporal grid based on the reduction rule to generate an initial perturbation vector, wherein the reduction rule includes the minimum granularity of time discretization, the topological discretization threshold, and the content perturbation rate limit.

[0027] Even after discretization, the grid size can still be very large. To further improve efficiency, we introduce simplification rules to guide the sampling process. These simplification rules include: 1) Minimum time discretization granularity: For example, set the minimum time granularity to 1 slot to avoid finer-grained searches.

[0028] 2) Topology discretization threshold: For example, setting a degree threshold. =5 means that we only focus on connections related to core nodes with high degrees in the network.

[0029] 3) Content perturbation rate limit: Set an upper limit on the modification of message content (e.g., field mutation), such as a mutation rate not exceeding 15%, to prevent the generation of overly distorted and meaningless test messages.

[0030] Based on these rules, the sampler extracts a representative set of configurations from the discrete spatiotemporal grid to generate an initial perturbation vector. For example, N vectors can be randomly generated, each containing a temporal offset and a target connectivity subset.

[0031] Step S1023: Encode the initial perturbation vector generated in step S1022 so that it can be parsed by the signal injection adapter and used for message matching in step S103.

[0032] The generated perturbation vector needs to be converted into instructions that the signal injection adapter can understand and execute. Therefore, it can be encoded. The encoding format can be JSON or a custom binary protocol. An encoded perturbation vector may contain the following fields: { "vector_id": "P001", "temporal_component": { "delay_slots": 3, "release_condition": "on_competition" }, "topological_component": { "target_modification": {"rewrite_dest_list": ["group_A"]}, "content_mutation": {"mutation_rate": 0.1} } } This structured coding ensures that the intent to disrupt can be accurately and efficiently transmitted and executed.

[0033] Step S103: Perform non-intrusive simulation, that is, intercept node messages at the communication layer through the signal injection adapter and perform message matching. When the intercepted node message matches the characteristics of the spatiotemporal topology perturbation vector generated in step S102, modify the message content or delay message release according to the perturbation components to drive the dynamic evolution of the system.

[0034] Traditional testing methods typically require modifying the consensus client's source code for instrumentation if message flow intervention is needed. This not only introduces the risk of inconsistency with the production environment but also makes it difficult to adapt to multiple client versions. The non-intrusive architecture employed in this application overcomes this deficiency. The signal injection adapter, as an independent middleware, runs on the operating system's network stack or virtualization layer. It controls the message flow by intercepting and redirecting network traffic without touching the core business logic of the node under test. This allows the application to precisely manipulate the timing and content of messages based on perturbation components (including temporal and topological perturbation components) in a real or near-realistic operating environment, thereby driving the system to evolve dynamically. This evolution is not a one-time stimulus-response but a continuous interactive process spanning multiple consensus cycles, effectively simulating long-term game behavior between nodes and revealing stability issues that only emerge in high-round interactions. As an embodiment of this application, non-intrusive simulation can be performed through steps S1031 to S1033, detailed below: Step S1031: The signal is injected into the outbound message of the monitoring node of the adapter and matched with the features of the spatiotemporal topology disturbance vector generated in step S102.

[0035] The adapter continuously listens for outbound packets on the taken-over port. For each message to be sent, the adapter parses its key metadata, such as message type (e.g., block proposal, vote proof), source node ID, target node ID (or broadcast identifier), timestamp, and specific content fields (e.g., block height, view number). The adapter then matches this metadata with features of the spatiotemporal topology perturbation vector encoded in step S102. The matching logic can be exact matching (e.g., message type equals block and block height is within a specific range) or fuzzy matching (e.g., the target node set intersects with the topology subset defined in the perturbation vector). This ensures that only messages meeting the preset perturbation conditions are intervened, guaranteeing the targeted and controllable nature of the perturbation behavior.

[0036] Step S1032: When a message is successfully matched, intercept the message and modify the message target or content according to the topology perturbation component.

[0037] Once a match is found, the adapter immediately intercepts the message and does not send it. Next, it performs modification operations based on the topology perturbation component. Specifically, modifications to the target or content can be performed based on preset rules of the topology perturbation component, rather than random operations. The rule design must reflect the perturbation intent, such as constructing partitions or simulating attacks. In practice, the rule base contains the logic for target modification rules and content modification rules as shown in the following examples: 1) Target modification rules: 1.1) Conditions: The message type is either a block broadcast or a vote, and the perturbation vector specifies "partition construction"; 1.2) Action: Rewrite the message target node list. For example, if the original message is broadcast across the entire network, modify it to be sent only to a specific group (such as a set of core nodes with a degree greater than 5). The rule can be expressed as: ,in, It is a degree threshold (e.g., =5), This is the preset partition.

[0038] 2) Content modification rules: 2.1) Conditions: The perturbation vector allows content variation, and the message is a transaction or block body.

[0039] 2.2) Action: According to the preset variation rate (For example, ≤15%) Randomly flip field bits. The rules include: selecting a random subset of consecutive fields in the message body (e.g., transaction hash); performing a bit flipping operation on this subset with a flipping probability of . Ensure the syntax of the mutated message is valid (e.g., the hash length remains unchanged) to avoid triggering low-level protocol errors. Through these rules, the implementation of the topology perturbation component is transformed from an abstract description into executable logic, ensuring the perturbation's specificity while avoiding the injection of unnecessary noise.

[0040] For example, if the perturbation vector specifies partitioning, the adapter might rewrite the target node list of the message, changing the original broadcast message to be sent only to a specific group of nodes (e.g., only to group A), thus artificially creating network partitions. Alternatively, if the perturbation vector allows content mutation, the adapter might randomly flip or tamper with certain bits in specific fields of the message body, with the mutation rate limited by a preset percentage (e.g., no more than 15%), to simulate tampering behavior by erroneous or malicious nodes in network transmission. These operations directly alter the message propagation path or semantics, laying the foundation for observing the system's behavior under non-ideal communication conditions.

[0041] Step S1033: Based on the timing perturbation component, release the successfully matched message after a specified delay.

[0042] After content modification is complete (or when no modification is needed), the timing of message transmission is determined based on the timing perturbation components. The adapter places the message into a delay queue, the duration of which is determined by the timing components in the perturbation vector, such as delay... Each time slot (Slot) is used for perturbation strategies, such as tiered attacks. To implement more complex perturbation strategies, the adapter may need to calculate the optimal delay offset. This can be achieved by predicting the proposer or network state within several future time slots, with the goal of ensuring that delayed messages disrupt the consensus process at the most critical moments. For example, intentionally delaying the broadcast of a block so that it and competing blocks generated by honest nodes are received by a majority of nodes in the network simultaneously, thereby maximizing the fork probability. In some scenarios, the adapter may also periodically switch delay strategies in critical time slots to maintain a competitive state and prevent rapid system convergence. Finally, when the delay condition is met, the adapter removes the message from the queue and injects it into the network.

[0043] Step S104: Detect stability, that is, collect the system state update data after the driving evolution in step S103 in real time, and calculate the divergence index, wherein the divergence index is used to quantify the degree of deviation of the system state from the synchronous steady state.

[0044] Traditional testing methods primarily focus on "hard failures" such as node crashes and protocol violations. However, deep stability issues in consensus systems often manifest as subtle deviations in system state synchronization or gradual imbalances in incentive mechanisms. These "soft failures" are difficult to capture using traditional metrics. This application achieves a quantitative assessment of system stability by real-time collection of state update data during the evolution process (e.g., the generation and propagation of new blocks and voting proofs) and calculating a divergence index based on a predefined energy feedback function. This index not only focuses on whether the state is consistent but also on whether the system remains on a healthy, incentive-compatible evolutionary trajectory, providing a key criterion for identifying stability risks emerging under long-term game dynamics. As an embodiment of this application, real-time collection of system state update data after the driving evolution in step S103 and calculation of the divergence index can be achieved through steps S1041 to S1043, as detailed below: Step S1041: Collect block and voting messages, and calculate the Euclidean distance between the system state and the ideal state.

[0045] The detector continuously monitors network traffic, collecting block and attestation messages. These messages reflect each node's perception of the current system state. To quantify the degree of state synchronization, the Euclidean distance between the system state and the ideal state can be calculated. The ideal state typically refers to a globally consistent state (e.g., the same highest block hash) that all nodes should reach in a undisturbed, fully synchronized environment. This can be achieved by converting the longest chain of block hashes agreed upon by each node into a feature vector, or by directly using key state variables such as block height and finality checkpoints. Suppose the system has... N Each node, in time t ,node i The state vector is The ideal state vector is Then the Euclidean distance of the system state It can be calculated as: This Euclidean distance The larger the value, the more serious the state divergence between nodes and the worse the synchronization.

[0046] Step S1042: Calculate the node utility deviation based on the energy feedback function.

[0047] The core of detecting stimulus incompatibility soft failures is to periodically calculate the equity utility value of each node based on the energy feedback function defined in step S101. Then, the node utility deviation is calculated, focusing on the payoff fairness between controlled nodes (the nodes that exert the perturbation) and honest nodes. For the set of controlled nodes... A and honest node setH This allows us to define the deviation between the actual share of profit and the theoretical fair share. Let the theoretical equity weight of the controlled node be... (For example, 30%), which occurs within a certain time window. T The percentage of actual benefits (e.g., block rewards) obtained within the block is Then the degree of utility deviation It can be defined as: like A consistently high value indicates that the controlled nodes have gained excess returns, and there may be a risk of incentive incompatibility in the system. Furthermore, the overall utility trend across the network can be calculated; a sustained decline may trigger "global utility dissipation."

[0048] Step S1043: Output a comprehensive divergence index by weighted fusion of Euclidean distance and node utility deviation.

[0049] A single metric may not fully reflect the stability of a system. For example, a large state distance might only indicate a temporary network partition, while utility deviation reveals deeper mechanistic flaws. Therefore, we obtain a comprehensive divergence index D by weightedly fusing the Euclidean distance and node utility deviation. An example of the fusion formula is shown below: in, It is the normalization factor for the state distance. and It is a weighting coefficient, and The weights can be dynamically adjusted based on the detection scenario. For example, when a bifurcation is detected, the weights are automatically increased. The weighting emphasizes state synchronization; when a deviation in utility is detected to exceed a threshold, the weighting is increased. The weighting emphasizes incentive compatibility. This fusion strategy enables the divergence metric to respond sensitively to different types of stability anomalies, providing accurate feedback signals for subsequent optimization iterations.

[0050] Step S105: Closed-loop optimization iteration, that is, using the divergence index calculated in step S104 as a feedback signal, adaptively adjusting the spatiotemporal topological perturbation vector in step S102, and repeating steps S103 to S104 until the divergence index converges or a stability anomaly is detected.

[0051] Considering that a single test verification cannot exhaustively cover complex perturbation scenarios and cannot automatically discover the optimal perturbation strategy, this application transforms the verification process into an optimization problem by constructing a closed-loop feedback loop. The divergence index calculated in step S104 is used as a feedback signal (i.e., reward) to drive the optimization algorithm to adaptively adjust the perturbation generation strategy parameters in step S102. This process repeats steps S103 and S104, forming a loop of "applying perturbation - observing response - adjusting strategy." Through this iteration, the system can autonomously explore the perturbation space, approaching the critical parameters that best expose system vulnerabilities, until the divergence index converges (i.e., it is difficult to find a more effective perturbation) or a stability anomaly is clearly detected. This method greatly improves the automation and depth of verification, enabling the discovery of complex attack patterns that are difficult to pre-set manually. Specifically, as an embodiment of this application, the closed-loop optimization iteration can be implemented through steps S1051 to S1053, as detailed below: Step S1051: Input the divergence index as a reward signal into the adaptive optimization algorithm.

[0052] The starting point of the optimization loop is to feed the evaluation results back to the decision-making system, which can include divergence indicators. D As a reward signal, the goal is to find the one that maximizes D Perturbation strategy parameters (For example, parameters that control delay time and target selection). Therefore, rewards R You can set it directly. D ,Right now R=D This reward signal is fed into an adaptive optimization algorithm, which is responsible for updating the strategy based on historical reward data.

[0053] Step S1052: Update the parameters of the perturbation vector generation strategy of the adaptive optimization algorithm.

[0054] The optimization algorithm updates the parameters of its perturbation vector generation strategy based on the received reward signal. For the reinforcement learning policy gradient method, its update rule can be expressed as: in, It's the learning rate. It is policy gradient estimation, and the goal is to maximize the expected cumulative reward. For genetic algorithms, selection, crossover, and mutation operations are performed on the parameter population. For particle swarm optimization, the positions and velocities of the particles are updated. After the parameters are updated, the new perturbation generation strategy produces a new perturbation vector for the next round of simulation testing.

[0055] Step S1053: Repeat steps S103 and S104 until the policy converges or the abnormality persists.

[0056] This is a cyclical decision-making process. After parameter updates, steps S103 (non-intrusive simulation) and S104 (stability detection) are repeated. Each iteration generates a new divergence index, which is used for the next parameter update. There are two loop termination conditions: first, policy convergence, meaning that multiple iterations fail to significantly improve the reward signal, indicating that a locally optimal perturbation policy may have been found; second, a stability anomaly is detected and persists, for example, the divergence index consistently exceeds a certain safety threshold, indicating that the system indeed has stability defects under this type of perturbation. Once either condition is met, the loop stops, and a final verification report is output, including the specific perturbation parameters causing the anomaly and details of the system's performance.

[0057] From the above appendix Figure 1 The example of a dynamic stability verification method for a distributed consensus system based on complex network dynamics demonstrates that, on the one hand, by employing a combination of non-intrusive simulation execution and closed-loop optimization iteration, the method can continuously drive the dynamic evolution of the system over a long timescale without interfering with its normal operation. By repeatedly injecting perturbations and observing the system response, this method can simulate the long-term effects of multi-round games between nodes in the real world, effectively revealing stability issues that only manifest in long-term interactions, overcoming the limitation of existing technologies that can only verify instantaneous or short-term behavior. On the other hand, thanks to the discretization of the continuous spatiotemporal search space in the generation of perturbation vectors, the originally infinite search range is reduced to a finite, structured discrete grid, providing a feasible search basis for subsequent optimization algorithms. This approach enables a systematic and targeted exploration of critical perturbation parameters that may lead to system instability, avoiding the blindness of traditional random testing and thus improving verification efficiency and the ability to discover boundary scenarios. Thirdly, an energy feedback function is introduced during system modeling and initialization, and used as the core basis for calculating the divergence index in stability testing. This allows the method described in this application to quantify changes in node equity utility values, effectively identifying whether the system has deviated from the incentive-compatible equilibrium state. Whether a node gains excess returns or the entire network experiences utility dissipation, these can be sensitively captured through the divergence index, solving the problem that traditional methods cannot quantify and evaluate soft failures. In summary, the technical solution of this application, through closed-loop dynamic verification and an energy feedback mechanism, can automatically discover deep-seated stability risks and incentive compatibility issues in the system.

[0058] Please see Figure 2As shown, in one embodiment, a dynamic stability verification device for a distributed consensus system based on complex network dynamics is provided. This device may include an initialization module 201, a generation module 202, a simulation module 203, a calculation module 204, and an iteration module 205, as detailed below: Initialization module 201 is used to model the distributed consensus system under test as a time-varying dynamic graph and define an energy feedback function based on the consensus protocol rules, initialize the simulation environment, and load the configuration parameters and initial state of the distributed consensus system under test. The energy feedback function is used to quantify the change in the equity utility value of nodes in the time-varying dynamic graph. Nodes represent consensus participants, and the edges of the time-varying dynamic graph represent communication connections. The generation module 202 is used to discretize the continuous spatiotemporal perturbation search space and generate a spatiotemporal topological perturbation vector. The spatiotemporal topological perturbation vector includes a temporal perturbation component and a topological perturbation component. The temporal perturbation component is used to control the timing of message delay, and the topological perturbation component is used to modify the message target or content. The simulation module 203 is used to intercept node messages at the communication layer through the signal injection adapter for message matching. When the intercepted node message matches the characteristics of the generated spatiotemporal topology disturbance vector, the message content is modified or the message release is delayed according to the disturbance component to drive the dynamic evolution of the system. The calculation module 204 is used to collect system state update data after the dynamic evolution of the driving system in real time and calculate the divergence index, which is used to quantify the degree of deviation of the system state from the synchronous steady state. The iteration module 205 is used to adaptively adjust the spatiotemporal topological perturbation vector with the divergence index as a feedback signal, and repeatedly execute the functions or actions of the simulation module and the calculation module until the divergence index converges or a stability anomaly is detected.

[0059] From the above appendix Figure 2As demonstrated by the example of a dynamic stability verification device for a distributed consensus system based on complex network dynamics, on the one hand, by employing a combination of non-intrusive simulation execution and closed-loop optimization iteration, this method can continuously drive the dynamic evolution of the system under test over long timescales without interfering with its normal operation. By repeatedly injecting disturbances and observing the system response, this method can simulate the long-term effects of multi-round games between nodes in the real world, thereby effectively revealing stability issues that only manifest in long-term interactions, overcoming the limitation of existing technologies that can only verify instantaneous or short-term behavior. On the other hand, thanks to the discretization of the continuous spatiotemporal search space in the generation of the disturbance vector, the originally infinite search range is reduced to a finite, structured discrete grid, which provides a feasible search basis for subsequent optimization algorithms. This approach enables a systematic and targeted exploration of critical perturbation parameters that may lead to system instability, avoiding the blindness of traditional random testing and thus improving verification efficiency and the ability to discover boundary scenarios. Thirdly, an energy feedback function is introduced during system modeling and initialization, and used as the core basis for calculating the divergence index in stability testing. This allows the method described in this application to quantify changes in node equity utility values, effectively identifying whether the system has deviated from the incentive-compatible equilibrium state. Whether a node gains excess returns or the entire network experiences utility dissipation, these can be sensitively captured through the divergence index, solving the problem that traditional methods cannot quantify and evaluate soft failures. In summary, the technical solution of this application, through closed-loop dynamic verification and an energy feedback mechanism, can automatically discover deep-seated stability risks and incentive compatibility issues in the system.

[0060] Optionally, the above Figure 2 The example initialization module 201 may include a parsing unit, a definition unit, and a startup unit, wherein: The parsing unit is used to parse the network topology file of the distributed consensus system under test, mapping the node set and dynamic connection relationship into a graph structure. The definition unit is used to define the energy feedback function based on the consensus protocol rules. The energy feedback function maps the behavior of a node to a stake utility value, which includes changes in stake balance and rewards or penalties. The startup unit is used to start the simulation environment and deploy the signal injection adapter to take over the node communication port in a non-intrusive manner.

[0061] Optionally, the above Figure 2 The example generation module 202 may include a discretization unit, a perturbation vector generation unit, and an encoding unit, wherein: Discretization units are used to discretize the time dimension into consensus cycles or time slots, and the topology dimension into connection subsets based on node degree, forming a discrete spatiotemporal grid. The perturbation vector generation unit is used to sample the discrete spatiotemporal grid based on simplification rules to generate an initial perturbation vector. The simplification rules include the minimum granularity of temporal discretization, the topological discretization threshold, and the content perturbation rate limit. The encoding unit is used to encode the generated initial perturbation vector so that it can be parsed by the signal injection adapter and used for message matching.

[0062] Optionally, the reduction rules in the above example include: when discretizing time, the minimum granularity is set to 1 time slot; when discretizing topology, only node connections with a degree greater than a preset threshold are retained; and the content perturbation rate is limited to a preset ratio.

[0063] Optionally, the above Figure 2 The example simulation module 203 may include a matching unit, a modification unit, and a release unit, wherein: The matching unit is used to inject outbound messages from the signal injection adapter monitoring node and match the messages with the features of the generated spatiotemporal topology perturbation vector. The modification unit is used to intercept the successfully matched message when the message match is successful, and modify the message target or content according to the topology perturbation component; The release unit is used to release successfully matched messages after a specified delay, based on the timing perturbation components.

[0064] Optionally, the modification unit in the above example may include a rewrite unit and a change unit, wherein: The rewrite unit is used to rewrite the target node list of a block or voting message to construct a partition based on the topology perturbation component. The transformation unit is used to perform field mutations on the message content based on topological perturbation components, wherein the field mutation rate is limited by a preset ratio. Optionally, the above Figure 2 The example computing module 204 may include a first computing unit, a second computing unit, and a fusion unit, wherein: The first computing unit is used to collect block and voting messages and calculate the Euclidean distance between the system state and the ideal state. The second computing unit is used to calculate the node utility deviation based on the energy feedback function; The fusion unit is used to output a comprehensive divergence index by weighted fusion of the Euclidean distance and the node utility deviation.

[0065] In one embodiment, a computer device is provided, the internal structure of which can be shown as follows: Figure 3As shown, the computer device includes a processor, memory, network interface, and database connected via a system bus. The processor provides computational and control capabilities. The memory includes non-volatile and / or volatile storage media and internal memory. The non-volatile storage media stores the operating system, computer programs, and database. The internal memory provides an environment for the operation of the operating system and computer programs stored in the non-volatile storage media. The network interface is used to communicate with external clients via a network connection. When the computer program is executed by the processor, it implements the functions or steps of a dynamic stability verification method for a distributed consensus system based on complex network dynamics.

[0066] In one embodiment, a computer device is provided, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor, when executing the computer program, performs the following steps: The distributed consensus system under test is modeled as a time-varying dynamic graph and an energy feedback function is defined based on the consensus protocol rules. The simulation environment is initialized and the configuration parameters and initial state of the distributed consensus system under test are loaded. The energy feedback function is used to quantify the change in the equity utility value of nodes in the time-varying dynamic graph. Nodes represent consensus participants and the edges of the time-varying dynamic graph represent communication connections. The continuous spatiotemporal perturbation search space is discretized to generate a spatiotemporal topological perturbation vector. The spatiotemporal topological perturbation vector includes a temporal perturbation component and a topological perturbation component. The temporal perturbation component is used to control the timing of message delay, and the topological perturbation component is used to modify the message target or content. The system intercepts node messages at the communication layer through a signal injection adapter and performs message matching. When the intercepted node message matches the characteristics of the generated spatiotemporal topology perturbation vector, the message content is modified or the message release is delayed based on the perturbation components to drive the dynamic evolution of the system. Real-time acquisition of system state update data after dynamic evolution of the driving system, and calculation of the divergence index, which is used to quantify the degree of deviation of the system state from the synchronous steady state. Using the divergence index as a feedback signal, the spatiotemporal topological perturbation vector is adaptively adjusted, and the functions or actions of the simulation module and the calculation module are repeatedly executed until the divergence index converges or a stability anomaly is detected.

[0067] The aforementioned computer program, through closed-loop dynamic verification and energy feedback mechanisms, can automatically detect deep-seated stability risks and stimulus compatibility issues in the system.

[0068] In one embodiment, a computer-readable storage medium is provided that stores a computer program, which, when executed by a processor, performs the following steps: The distributed consensus system under test is modeled as a time-varying dynamic graph and an energy feedback function is defined based on the consensus protocol rules. The simulation environment is initialized and the configuration parameters and initial state of the distributed consensus system under test are loaded. The energy feedback function is used to quantify the change in the equity utility value of nodes in the time-varying dynamic graph. Nodes represent consensus participants and edges of the time-varying dynamic graph represent communication connections. The continuous spatiotemporal perturbation search space is discretized to generate a spatiotemporal topological perturbation vector. The spatiotemporal topological perturbation vector includes a temporal perturbation component and a topological perturbation component. The temporal perturbation component is used to control the timing of message delay, and the topological perturbation component is used to modify the message target or content. The system intercepts node messages at the communication layer through a signal injection adapter and performs message matching. When the intercepted node message matches the characteristics of the generated spatiotemporal topology perturbation vector, the message content is modified or the message release is delayed based on the perturbation components to drive the dynamic evolution of the system. Real-time acquisition of system state update data after dynamic evolution of the driving system, and calculation of the divergence index, which is used to quantify the degree of deviation of the system state from the synchronous steady state. Using the divergence index as a feedback signal, the spatiotemporal topological perturbation vector is adaptively adjusted, and the functions or actions of the simulation module and the calculation module are repeatedly executed until the divergence index converges or a stability anomaly is detected.

[0069] The aforementioned computer program, through closed-loop dynamic verification and energy feedback mechanisms, can automatically detect deep-seated stability risks and stimulus compatibility issues in the system.

[0070] The steps described above, implemented when the computer program is executed by the processor, significantly improve computational efficiency, stability, and resource utilization through coordinate pre-calculation, atomic-free kernel design, and circular buffer optimization.

[0071] It should be noted that the functions or steps that can be implemented by the computer-readable storage medium or computer device described above can be referred to the relevant descriptions on the server side and client side in the foregoing method embodiments. To avoid repetition, they will not be described one by one here.

[0072] Those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium. When executed, the computer program can include the processes of the embodiments of the above methods. Any references to memory, storage, databases, or other media used in the embodiments provided in this application can include non-volatile and / or volatile memory. Non-volatile memory may include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM), or flash memory. Volatile memory may include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in a variety of forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), dual data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous link DRAM (SLDRAM), RAMbus direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and memory bus dynamic RAM (RDRAM), etc.

[0073] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the above-described division of functional units and modules is used as an example. In practical applications, the above functions can be assigned to different functional units and modules as needed, that is, the internal structure of the device can be divided into different functional units or modules to complete all or part of the functions described above.

[0074] The above-described embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention, and should all be included within the protection scope of the present invention.

Claims

1. A method for verifying dynamic stability of a distributed consensus system based on complex network dynamics, characterized in that, The method includes the following steps: S101: Model and initialize the system, that is, model the distributed consensus system under test as a time-varying dynamic graph and define an energy feedback function based on the consensus protocol rules, initialize the simulation environment, load the configuration parameters and initial state of the distributed consensus system under test, the energy feedback function is used to quantify the change of the equity utility value of the nodes in the time-varying dynamic graph, the nodes represent consensus participants, and the edges of the time-varying dynamic graph represent communication connections. S102: Generate a perturbation vector, that is, discretize the continuous spatiotemporal perturbation search space to generate a spatiotemporal topological perturbation vector. The spatiotemporal topological perturbation vector includes a temporal perturbation component and a topological perturbation component. The temporal perturbation component is used to control the timing of message delay, and the topological perturbation component is used to modify the message target or content. S103: Perform non-intrusive simulation, that is, intercept node messages at the communication layer through the signal injection adapter for message matching. When the intercepted node message matches the characteristics of the spatiotemporal topology disturbance vector generated in step S102, modify the message content or delay message release according to the disturbance component to drive the dynamic evolution of the system. S104: Detect stability, that is, collect the system state update data after the driving evolution in step S103 in real time, and calculate the divergence index. The divergence index is used to quantify the degree of deviation of the system state from the synchronous steady state. S105: Closed-loop optimization iteration, that is, using the divergence index calculated in step S104 as a feedback signal, adaptively adjusting the spatiotemporal topological perturbation vector in step S102, and repeating steps S103 to S104 until the divergence index converges or a stability anomaly is detected.

2. The method of claim 1, wherein the method is characterized by, The system modeling and initialization process includes: The network topology file of the distributed consensus system under test is parsed, and the node set and dynamic connection relationship are mapped into a graph structure. Based on the consensus protocol rules, the energy feedback function is defined, which maps the behavior of the node to a stake utility value, which includes changes in stake balance and rewards or penalties. Start the simulation environment and deploy the signal injection adapter to take over the node communication port in a non-intrusive manner.

3. The dynamic stability verification method for a distributed consensus system based on complex network dynamics as described in claim 1, characterized in that, The generated perturbation vector includes: The time dimension is discretized into consensus cycles or time slot units, and the topology dimension is discretized into connection subsets based on node degree, forming a discrete spatiotemporal grid. The discrete spatiotemporal grid is sampled based on simplification rules to generate an initial perturbation vector. The reduction rules include the minimum granularity of time discretization, the topological discretization threshold, and the content perturbation rate limit. The generated initial perturbation vector is encoded so that it can be parsed by the signal injection adapter and used for message matching.

4. The dynamic stability verification method for a distributed consensus system based on complex network dynamics as described in claim 3, characterized in that, The reduction rules include: When discretizing time, the minimum granularity is set to 1 time slot; During topology discretization, only node connections with a degree greater than a preset threshold are retained; The content disturbance rate is limited to a preset percentage.

5. The dynamic stability verification method for a distributed consensus system based on complex network dynamics as described in claim 1, characterized in that, The non-intrusive simulation includes: The signal injection adapter monitors the outbound messages of the node and matches the messages with the features of the spatiotemporal topology disturbance vector generated in step S102; When a message is successfully matched, the matched message is intercepted, and the message target or content is modified according to the topology perturbation component. Based on the timing perturbation component, the successfully matched message is released after a specified time slot delay.

6. The dynamic stability verification method for a distributed consensus system based on complex network dynamics as described in claim 5, characterized in that, The modification of message target or content based on topology perturbation components includes: Based on the topology perturbation components, the target node list of blocks or voting messages is rewritten to construct partitions; Based on the topology perturbation component, the message content is subjected to field mutation, wherein the field mutation rate is limited by a preset ratio.

7. The dynamic stability verification method for a distributed consensus system based on complex network dynamics as described in claim 1, characterized in that, The detection stability includes: Collect block and voting messages, and calculate the Euclidean distance between the system state and the ideal state; Calculate the nodal utility deviation based on the energy feedback function; By weighted fusion of the Euclidean distance and node utility deviation, a comprehensive divergence index is output.

8. A dynamic stability verification device for a distributed consensus system based on complex network dynamics, characterized in that, The device includes: The initialization module is used to model the distributed consensus system under test as a time-varying dynamic graph and define an energy feedback function based on the consensus protocol rules, initialize the simulation environment, load the configuration parameters and initial state of the distributed consensus system under test, and the energy feedback function is used to quantify the change of the equity utility value of the nodes in the time-varying dynamic graph, where the nodes represent consensus participants and the edges of the time-varying dynamic graph represent communication connections. The generation module is used to discretize the continuous spatiotemporal perturbation search space and generate a spatiotemporal topological perturbation vector. The spatiotemporal topological perturbation vector includes a temporal perturbation component and a topological perturbation component. The temporal perturbation component is used to control the timing of message delay, and the topological perturbation component is used to modify the message target or content. The simulation module is used to intercept node messages at the communication layer through a signal injection adapter for message matching. When the intercepted node message matches the characteristics of the generated spatiotemporal topology perturbation vector, the message content is modified or the message release is delayed based on the perturbation components to drive the dynamic evolution of the system. The calculation module is used to collect system state update data after the dynamic evolution of the driving system in real time and calculate the divergence index, which is used to quantify the degree of deviation of the system state from the synchronous steady state. The iterative module is used to adaptively adjust the spatiotemporal topological perturbation vector using the divergence index as a feedback signal, and repeatedly execute the functions or actions of the simulation module and the calculation module until the divergence index converges or a stability anomaly is detected.

9. An apparatus comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the steps of the method as described in any one of claims 1 to 7.

10. A storage medium storing a computer program, characterized in that, When the computer program is executed by a processor, it implements the steps of the method as described in any one of claims 1 to 7.

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