Emergent Directional Drift in a Reversible Geometric Network

This paper presents a numerical study of transport on a reversible discrete geometric network constructed from a relaxed hexagonal lattice with a Kerr-like signed transport rule. Despite the absence of explicit dissipation or stochastic forcing, the system exhibits a robust, gate-dependent directional drift in loop-level observables. The effect persists across extensive sampling and survives structure-preserving bootstrap, holdout, and permutation null tests designed to account for strong geometric correlations. Pair-breaking and rank-matched controls further indicate that the observed directionality arises at the ensemble level from constrained geometry and signed transport, rather than from fragile loop-by-loop correspondence. The results establish a reproducible example in which effective directionality emerges from reversible geometric transport alone, providing a concrete empirical target for further analytic and universality studies.