The Sufficiency Gate_ Bounding Scope in SO(2)-Invariant Coherence Laws

Abstract This paper addresses a recurring interpretive error in coherence-based and resonance-based identity frameworks: the conflation of necessary conditions for identity persistence with sufficient conditions for full domain governance. In frameworks such as Structured Resonance Dynamics (SRD), identity persistence is governed by a scalar invariant derived from an SO(2)-structured phase decomposition and constrained by a lawful drift bound. While such invariants may be universally necessary for identity persistence across domains, they are not automatically sufficient to determine all domain structure. This paper introduces a formal Sufficiency Gate that separates these claims. A domain is fully governed by an SO(2)-invariant coherence law if and only if all observables relevant to identity persistence admit reduction to SO(2) phase variables and identity outcomes are fully determined by the scalar invariant and its drift bound alone. Failure to satisfy this condition bounds the framework’s scope without falsifying its necessity. No new invariants are introduced. The contribution is interpretive and structural, providing a fail-closed criterion for universality claims in deterministic coherence frameworks.