Oscillating Hall And AHE Certification: Tz_Center, Disable-L, STLF, And SoZ Under A Fixed G–Σ–P–L Contract

This manuscript introduces an explicit Strong vs Strong-to-Weak classification for runs that already mint inside a fixed G–Σ–P–L corridor, formalizing a distinction that was previously implicit across multiple magnet and Hall/AHE studies. The key idea is that corridor validity and internal robustness are not the same object: some runs survive as a single-lane claim with low stall, low leakage, and wide margins, while others remain corridor-valid only by leaning on nontrivial z-tension, narrow margins, averaging, or additional structure. The Strong-to-Weak tag is computed strictly post-mint from already-logged tokens (yield, Sum-of-Zeros, even residue, quadrature/phase bounds), is bound to a preregistered contract, and is forbidden from moving thresholds or rescuing failures. By writing this stability label directly into the ledger, the work converts narrative judgments about “robust vs fragile” behavior into a replayable, falsifiable, and platform-agnostic object that sits cleanly between SoZ/no-test enforcement and 4S3 promotion. The result is not a new gate but a compression step: it freezes internal stability as a first-class, auditable attribute, preventing ad-hoc reinterpretation in later analyses and enabling consistent cross-run and cross-bench comparisons.