Integer-Labeled Saturation in a Monotonic Geometric Drift: Null-Tested Evidence from a Relaxed Hexagonal Loop Ensemble

This work analyzes a large ensemble (79,200 realizations) of relaxed hexagonal loop geometries exhibiting a monotonic, gate-dependent drift in loop orientation. A specific set of structural integers �, previously observed to reproduce particle-scale ratios, is examined under a comprehensive sequence of null tests (v11–v28c) to determine whether these integers correspond to identifiable geometric features within the drift landscape. A wide range of hypotheses are systematically rejected, including alignment with local extrema, curvature maxima, slope transitions, state boundaries, prime-matched coincidences, and arbitrary bin placement. The surviving signal is a statistically significant clustering of the integers toward the global saturation endpoint of the monotonic drift, corresponding to the deepest region of the geometric response. To provide dimensional context, the drift endpoint is anchored to a Planck-scale volumetric pressure proxy, allowing the integers to be interpreted as cumulative depth milestones rather than discrete geometric attractors. The results indicate that the integers label progressive immersion into a global geometric “cliff” regime, rather than isolated resonances or local trapping points. All analyses are reproducible from the provided per-loop dataset and portable scripts. The work makes no claims regarding fundamental particles or forces, and is presented as a structural and statistical characterization of an emergent geometric phenomenon.