Locality-Bounded Continuity: A Minimal Architecture for Distributed Function Under Scale and Adversarial Load (v4.1)

Locality-Bounded Continuity v4.1 defines a minimal, substrate-independent architecture for maintaining functional continuity in distributed systems under scale and adversarial load. The paper proves that continuity is preserved if and only if all state transitions, verification, propagation, and history retention are locality-bounded. A completeness set of five required operations is established, and the removal of any single element is shown to produce endogenous cascade failure.This version introduces a fully reproducible deterministic implementation — the Unified Bloom Engine — demonstrating that multiple functional regimes emerge from a single locality-bounded continuity law while conserving state and containing adversarial input. The executable Colab allows independent verification of conservation behavior, relay propagation, fail-closed ejection, retention structure formation, and finite non-singular expansion.The result reframes scalability, reliability, and adversarial robustness as topological properties rather than synchronization or consensus problems.