Trajectory-Dependent Temporal Asymmetry in Radius-Conditioned Lagrangian Dynamics

Trajectory-Dependent Temporal Asymmetry in Radius-Conditioned Lagrangian Dynamics reports a preregistered, falsification-oriented analysis of temporal structure in radius-conditioned Lagrangian dynamics. A nine-offset temporal kernel revealed a pronounced asymmetric profile: correlations remained positive across preceding records, peaked near the contemporaneous state, and transitioned through zero to increasingly negative correlations at later offsets. The frozen primary asymmetry statistic was A = 0.2072243756. A hierarchy of permutation nulls was used to determine which preserved structures could reproduce this asymmetry. Global identity permutation (N1) eliminated the effect, while preserving initial-radius strata (N2) or coarse spatial locality (N3) recovered less than 1% of the observed asymmetry. Preserving four-record temporal blocks (N4) recovered approximately 12.3% on average, but the observed asymmetry remained outside all 999 N4 permutations (Monte Carlo p = 0.001). These results indicate that the measured temporal asymmetry is strongly dependent on trajectory identity and temporally ordered history and cannot be reproduced by the tested snapshot, radius-stratified, coarse-spatial, or short-block structures alone. The results do not by themselves establish fundamental non-Markovianity, violation of the Navier–Stokes equations, retrocausality, direct particle-to-particle causation, or a new physical law. They instead identify a robust trajectory-dependent temporal structure and define progressively stronger falsification tests for determining its physical origin. The accompanying supplement contains the analysis code, frozen Gate-9 results, permutation-null outputs, audit information, and supporting materials required to reproduce and inspect the reported analysis.