The Ontic Coherence Theorem and the Coherent-Observership Bridge: Non-Emergent Order and the Logical Necessity of G (With Adversarial Validation Under Physical Admissibility Constraints)

We prove a conditional representation theorem—the Ontic Coherence Theorem (OCT)—which states that if a universe satisfies Ontic Coherence (no perpetual harm under any physically admissible policy, finite harm-typal space, and no re-injury), then there necessarily exists a non-contingent structural closure operator that realizes this property. We then establish the Coherent-Observership Bridge (COA), deriving from a physically motivated axiom: the existence of a non-zero-measure set of observer worldlines with unbounded proper time, bounded harm, and persistent render stability. Through the causal-admissibility analysis (“Secure Enclave” refutation), we demonstrate that indefinite stable observership implies global coherence, yielding the qualified synthesis: (L0 > 0) & COA =⇒ C(S) =⇒ G.