Gauge Robustness and Divergence Triggers: A Unified Necessity Note for the Synkyria Refusal Stack

This note isolates a minimal, gauge-robust kernel that unifies the “refusal necessity” line in finite-capacity systems. Let L(t) denote carried (unassimilated) load and N(t) a bounded support proxy. For any viability/holding gauge in the class |H(t)| ≤ F(N(t))/L(t) with F bounded on bounded sets, if L(t) → ∞ while N(t) remains bounded, then H(t) → 0 (gauge-robust collapse). The note then records two independent trigger mechanisms that force divergence or capacity violation under “no-refusal / no-separation” constraints: (i) thermodynamic/processing overload with zero rejection (TTR trigger), and (ii) adversarial late recognition under finite carried load (LR trigger). Finally, it connects the necessity line to an external-safe operational boundary for certification (REFUSE ⇒ JustRefuse) within the Synkyria Refusal Stack v1.0. Key contributions Kernel (gauge robustness): a one-lemma collapse mechanism that is independent of the specific gauge choice, requiring only bounded-on-bounded regularity of the support function. Triggers (two independent routes): overload-type divergence (TTR) and late-recognition capacity violation (LR) under load-or-discard constraints. Operational boundary (audit-ready link): frames the necessity line as an externally verifiable certification boundary (REFUSE ⇒ JustRefuse), consistent with the archival Refusal Stack packaging. Why it mattersThis kernel makes “refusal necessity” robust to gauge choice: once divergence/capacity-violation regimes are forced by independent triggers, viability collapse is unavoidable without separation/gating mechanisms.