Infinity as Collapse_ A Deterministic Reframing of the Infinite under CODES

Full CODES Framework Abstract Infinity has long been treated as a fundamental property of mathematics, physics, and philosophy. From Cantor’s transfinite sets and Hilbert’s paradoxes, to black hole singularities, cosmological expansion, and Turing’s noncomputability, the infinite has been both indispensable and paradoxical. This paper introduces a deterministic reframing: infinity is not ontological, but the symbolic trace of coherence collapse. Within the CODES framework (Chirality of Dynamic Emergent Systems), infinity corresponds to breakdown conditions in the Phase Alignment Score (PAS_n). PAS_n → 0: collapse through decoherence (singularities). PAS_n → ∞: collapse through unbounded oscillatory divergence (divergences, runaway recursion). Across domains: Mathematics: Cantor’s uncountable sets and Hilbert’s Hotel are reframed as unresolved phase loops, not higher cardinalities. Computation: Turing’s undecidability and infinite loops are drift states prevented by ELF and PAS_lock. Physics: Black holes, cosmological infinities, and QFT divergences are collapse conditions, not physical infinities. Philosophy: Aristotle’s rejection of actual infinity is validated; Hegel’s dialectical “infinity” is reframed as unanchored recursion; Continental invocations of the void become symbolic drift. The paper includes diagnostic and blueprint tables showing how every STEM domain transitions pre- vs post-CODES. Infinity is eliminated as a primitive; what remains is lawful recursion within PAS thresholds and deterministic collapse at their breach.