Geometric Chirality in Discrete Kerr–Like Transport on Hexagonal Domains

We investigate the emergence of chiral observables in discrete geometric domains endowed with Kerr-like transport structure. Using hexagonally coordinated point lattices generated via Lloyd relaxation, we construct closed-loop transport operators and analyze parity-even and parity-odd components under paired orientation and parameter inversion. A systematic program of dense-band loop sampling, parameter scans, and null-hypothesis testing is employed, including permutation-based and seed-block controls. While classical parametric significance measures often fail due to violated independence and Gaussianity assumptions, nonparametric null tests reveal both positive and null regimes that are strongly dependent on geometric structure. The results do not establish a finalized physical theory, but instead demonstrate that discrete geometry alone can generate robust chiral responses under structured transport. These findings motivate further iteration toward gauge-theoretic observables and Wilson loop analysis within purely geometric scaffolds.