Axioms of Bidirectional Constraint Closure and Continuity: Identity, Suspension, and Collective Consciousness

Abstract This paper formalizes the joint framework of Bidirectional Constraint Closure (BCC) and the Continuity of Constraint Theorem (CCT) into an explicit axiomatic system. Building on prior work reframing space, time, gravity, and identity as emergent relational phenomena at a Reflective Interface, we establish minimal axioms governing coherence, persistence, and collapse. These axioms are then applied to three domains of increasing ethical and theoretical relevance: (1) cryonics and suspended animation, (2) collective identity in biological and artificial systems, and (3) moral status as a function of continuity rather than substrate. The resulting framework unifies physics, consciousness studies, and ethics under a single constraint-based ontology, preserving empirical compatibility while resolving longstanding paradoxes surrounding survival, duplication, and collective minds.