The Axiom of Absolute Boundary: Boundaries and Metabolic Failure in Self-Referential Systems

This paper is a natural extension of the Theory of Energy Primitive (four axioms: existence is difference; difference necessarily differentiates; differentiation drives interaction; interaction tends toward dynamic stability). It proposes a fifth axiom – the Axiom of Absolute Boundary: any self-referential system contains a boundary that cannot be eliminated from within; this boundary manifests as a residual difference that the system cannot metabolize. This axiom is not intended to challenge or replace classical results such as Gödel’s incompleteness theorems, the second law of thermodynamics, or the uncertainty principle. Instead, it reveals a structural isomorphism between those results and the present principle, offering a cross‑disciplinary meta‑theoretical perspective. Through a coin self‑reference model, an interpretation of entropy as boundary clarity, and an analysis of paradoxes, the explanatory power of the axiom is illustrated. The paper also discusses the Collatz conjecture as an example, showing that a novel perspective may not rely on existing mathematical foundations – a situation that places such perspectives in an awkward position within mainstream academic evaluation. As a theoretical construction by an independent researcher, this work aims at self‑consistency and heuristic value, not at formal proof.