[12] COS-STAB - Collapsing-Structure Stability Layer: Geometric sector preservation, long-time drift control, and chiral fermion gap protection

COS-STAB provides the stability and verification layer for Collapsing-Structure (COS) dynamics. It consolidates, in a single citable document, the stability requirements that are repeatedly raised in critical assessment of COS-type discrete quantum-gravity frameworks: Geometric sector preservation (staying within the realizable geometric domain), Long-time drift control under Trotterized time stepping and projector-based updates, Chiral fermion gap protection for GW/overlap constructions on dynamically updating graphs. The manuscript specifies an auditable protocol combining: an extended physical projector with an explicit geometric projector, a nonnegative geometric penalty potential (V_geom) supporting soft stabilization, runtime diagnostics tracking sector occupancy (p_geom(t), p_phys(t)) and projection leakage, drift guarantees formulated for a bounded class of quasi-local observables under rTS2 (randomized Strang) time stepping, and a conditional gap lemma and admissibility checklist for monitoring the Wilson-kernel gap during local graph updates. Reproducibility and compliance are operational by design. Pass/fail decisions are computed exclusively from two mandatory run artifacts produced automatically during simulation runs: run_meta.json and metrics.jsonl. The document defines a two-stage gate (Stage 1 “sanity” vs. Stage 2 “paper-grade”) including a required step-size scaling check where applicable. No precomputed numerical result figures or separate result tables are required to evaluate compliance; all decisions are deterministically reproducible from the logs. Intended use. COS-STAB serves as the corpus-level reference for stability requirements that would otherwise be scattered across COS-QD/QF/QHF/SM, and it is designed to be cited by those modules as the normative stability specification.