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

Coherence-based frameworks for identity persistence increasingly appeal to scalar invariants derived from minimal symmetry classes, most commonly SO(2). In such frameworks, identity continuity is defined by bounded drift of a scalar coherence measure, yielding a deterministic criterion for persistence and failure. As these approaches gain visibility, claims of necessity are frequently misread as claims of sufficiency. This paper introduces the Sufficiency Gate, a formal demarcation that separates these notions. An SO(2)-invariant scalar coherence law may be necessary for identity persistence across domains without being sufficient to govern all domain structure. Sufficiency holds if and only if all observables required to adjudicate identity persistence admit reduction to SO(2) phase variables and identity outcomes are fully determined by the scalar invariant and its drift bound alone. The gate renders universality claims fail-closed, preserves ontological minimality, and sharpens falsifiability without introducing new primitives.