Quantum Mechanics as a Theorem of Finite Inference: The Light & Flux Framework

[Author’s Note]This paper introduces the Light & Flux (L&F) framework, which formally supersedes the earlier "KB-Flux" formalism. The previous ontological mappings have been entirely replaced by the rigorous three-tier architecture and the Non-Derivability Principle presented herein. For a broader, accessible exploration of this framework and its implications for the nature of reality and mind, follow the Substack publication: Mind & Machine. AbstractQuantum mechanics is not a brute empirical law demanding interpretation; it is the unique geometric theorem of coherent inference under fundamental uncertainty. The persistent deadlock of quantum foundations stems from a flat ontology that falsely presumes classicality as the ontological default. We introduce the Light & Flux (L&F) framework, a fixed-point formal architecture Ω* comprising three co-actual aspects: the constitutive constraints of inference against a pre-geometric substrate (the Latent Markov Substrate), the unique surviving inferential geometry (complex Hilbert space), and the irreversible lossy compression executed by finite biological agents (the classical probability simplex). We prove that complex Hilbert space is the sole geometry consistent with these constitutive constraints, and show that the macroscopic classical world is a metabolically mandated compression of that geometry. The material entities conventionally taken as fundamental — particles, atoms — are relocated from primitive building blocks to stable structural features of the entailed geometry. We formalize the compression via the Simplex Projection Π, establishing the Non-Derivability Principle: demanding a unitary dynamical account of classical outcome registration is a category error. Finally, we confront the Gödelian limits of our own cognitive codec, showing that the representational ceiling encountered at the framework’s foundation and its reflexive apex is a single geometric invariant of finite inference.