Persistence Collapse Transitions and Observable Admissibility in Nonlinear Dynamical Systems: A Preregistered Empirical Benchmark

Detecting the onset of chaos and structural regime change in nonlinear dynamical systems is a central problem in nonlinear dynamics. We introduce a preregistered empirical benchmark for persistence collapse transitions the sharp thresholds at which a trajectory ensemble that has been maintaining a measured quantity within a viability corridor abruptly loses this capacity as a control parameter crosses the critical value. Applied across seven canonical nonlinear systems including the standard map, tent map, Lorenz-63 attractor, Arnold catmap, and baker map, the benchmark produces a principal empirical finding: the observable admissibility constraint. Whether a persistence collapse transition is detectable depends fundamentally on whether the chosen observable tracks the degree of freedom that is structurally constrained in the system. In the standard map, the momentum observable detects a clean transition at K∗ = 1.507, consistent with KAM torus breakdown near the Chirikov critical value, while the position observable detects no transition across the full parameter range K ∈ 0, 2. A Version 6 benchmark extends this to action based observables: the action proxy J = p2/2π finds a transition at K∗ = 1.508 with normalised cliff spread r = 0.0005relative to momentum, demonstrating that the persistence signal generalises across aligned19momentum space observables. A dedicated noise study at fixed ρ = 15 in Lorenz-63 confirms monotone hard persistence decline with noise strength (σ∗ = 0.504), resolving an operating point ambiguity from a prior version. An adversarial null control (iid uniform process) produces a diffusion boundary crossing clearly distinguishable from structured chaotic transitions on both transition width and locked plateau criteria. All results derive from a locked preregistration (300 trajectories per cell, seed 12345, 16760 summary rows, 0 standards failures). The observable admissibility constraint has direct implications for how diagnostic observables are selected in empirical studies of nonlinear regime transitions. Keywords: persistence collapse transition; observable admissibility; standard map; KAM theory; Lorenz system; nonlinear benchmark; preregistration