Empirical Falsification Tests of Identity Persistence in Discrete Physical Systems (Version 2)

This archive contains the Version 2 implementation and results of the empirical falsification tests of identity persistence under the Conditional Unlocking Framework (CUF). The experiment evaluates whether trajectory persistence under a declared constraint can serve as a measurable signal distinguishing admissible dynamics from perturbations that disrupt structural continuity. The numerical experiment is performed on the Chirikov standard map, a canonical discrete-time dynamical system widely used in nonlinear dynamics to study the transition between integrable motion and chaotic diffusion. The simulation sweeps the nonlinearity parameter KKK across the interval K∈0, 2 and evaluates trajectory persistence under a declared momentum corridor constraint ∣p−p0∣≤εp where p0 is the initial momentum and εpₚεp is the corridor half-width. Persistence is evaluated by observing whether trajectories remain within the admissible constraint corridor without projection. Once a trajectory exits the corridor, identity persistence is considered lost for the remainder of the trajectory. The experiment evaluates five operator classes applied to the underlying dynamics: Baseline dynamics (unmodified standard map) Stochastic perturbation via additive Gaussian momentum noise Sign discontinuity operator introducing structural kicks Piecewise rule-switching operator producing regime discontinuities Reversible bijective operator implementing phase reflection The simulation configuration for Version 2 is: 12 000 integration steps per trajectory 1 000 burn-in steps 300 independent trajectories per parameter value 40 parameter values across K∈0, 2 Momentum corridor half-width εp=2. 0 Fixed pseudorandom seed for reproducibility Trajectory persistence is summarized using survival probability across trajectories and block-coarse-grained violation statistics. Additional diagnostic quantities include conditional value-at-risk (CVaR), persistence threshold estimation k^*, transition width, and slope estimates near the persistence cliff. The baseline survival curve recovers the known KAM transition region of the standard map. Perturbation operators produce distinct degradation patterns in survival probability, demonstrating that the persistence measurement responds differently to stochastic perturbations, structural discontinuities, and rule-switching dynamics. The archive includes the full simulation code, configuration files, raw trajectory statistics, summarized operator results, and generated survival probability plots, enabling complete reproducibility of the experiment. Version 2 introduces several corrections and improvements relative to the original implementation: Explicit operator regime labeling in the summary dataset Linear interpolation for persistence threshold estimation Numerical guards for slope estimation near the persistence cliff 99 % Wilson score intervals for survival probability estimates Explicit classification of the reversible operator as a bijective perturbation This release represents a reproducible computational experiment intended to establish a baseline empirical implementation of the persistence measurement. Future versions will extend the framework to additional dynamical systems to evaluate cross-system generality.