Infinity as the Resolution Horizon of Generative Granularity

Abstract

We propose that every infinity encountered in mathematics or physics is the resolution horizon of a generative system equipped with a strict generation rank μ. Six theorems are proved in ZFC for systems of granularity at most ω₁. A weak holographic quotient theorem (Theorem 2.2′) is rigorously established with a complete proof (Appendix A2). A stronger version remains a conjecture (Conjecture 2.2). An explicit information-theoretic mapping links the physical entropy bound to the generative rank (Postulate 2.4). The Swampland functor F : Swampland-EFT → Gen exhibits the bound as a categorical limit. Six concrete, falsifiable predictions for dark energy and dark matter are derived and will be tested by 2040.

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