GEC as a Principle of Mathematical Reality: A Philosophical–Physical Essay Extending the Strictly Physical Axiomatic Framework

The original article The Global Entropic Consistency Principle (GEC): A Strictly Physical Axiomatic Framework formulated GEC as a physical principle governingclosed quantum systems through global entropic invariance and compensatory informational flux. This essay argues that the same axioms that define GEC physically alsopossess a deeper mathematical–ontological status: they express necessary conditions for any reality that is mathematically representable. Under this interpretation, GEC acquires a dual character. It remains a physical principle describing the informational dynamics of closed quantum systems, yet simultaneously functions as a meta-principle of mathematical reality, constraining the structure of any world that can be mathematically formulated. The three axioms ofGEC—distinguishability, boundedness (derived from the existence of a horizon with finite entropy at a given moment), and global–local consistency—are therefore not onlyphysical requirements but also mathematical necessities. The essay thus positions GEC as a bridge between ontology and epistemology: a principle that governs both what can exist and what can be known.