BU01 Single-Universe Boundary Axiomatics

This paper introduces Single-Universe Boundary Axiomatics, a minimal formal framework for re-grounding physical intelligibility in the global uniqueness of boundary conditions. Its central claim is that universe-level unity is not a metaphysical slogan, but a structural condition: a universe is single if and only if its physical boundary condition is globally unique and invariant across the entire domain of existence. This principle is formalized as S \equiv B_U, where B_U denotes global boundary consistency over the total admissible domain U, and B_0 denotes the unique fixed boundary set. On this basis, the framework derives three consequences: global law admissibility L_U, global constant admissibility C_U, and single-valued measurement settlement R_{\text{single}}. The paper is intentionally minimal. It uses only a small symbol set and four axioms to establish a strict separation between local effective validity and universe-level ontological license. Local models, regional approximations, statistical descriptions, and scale-dependent effective theories may remain valid within bounded contexts, yet none of them automatically acquires the right to rewrite the total structure of the universe. This distinction yields a sharp criterion for theory sorting. Any framework that permits drifting boundary conditions, independent causal bubbles, branching result-spaces, or observer-conditioned global reality fails global boundary consistency and therefore loses full universe-level standing. The aim is not to eliminate useful local theory, but to restore hierarchy: projection-level success does not imply total-structure truth. In this sense, Single-Universe Boundary Axiomatics functions as a compression and cleanup framework for disordered backward-facing theoretical proliferation. It provides a rigorous basis for distinguishing globally admissible physics from explanatory overextension, ontological inflation, and paper-level universe splitting.