Purification as the Structural Seed of Quantum Theory: Minimal Axioms Beyond Finite Accessibility

Arc V — Gravity & Quantum Theory Paper 7 Title Purification as the Structural Seed of Quantum Theory:Minimal Axioms Beyond Finite Accessibility Zenodo DOI 10.5281/zenodo.18226009 Description This paper presents a full axiomatic reconstruction of quantum theory starting from finite accessibility augmented by a single additional structural principle: purification. Building on the identification of the quantum gap in Paper V.6, it demonstrates that purification is not merely sufficient but structurally generative—acting as the seed from which the full architecture of quantum mechanics emerges. The analysis shows that when purification is imposed on an accessibility-limited operational framework, core quantum features arise necessarily rather than by assumption. These include superposition, entanglement, reversible dynamics, and the tensor-product structure of composite systems. No geometric ontology, wavefunction realism, or microscopic state postulates are introduced. The paper carefully distinguishes purification from interpretational assumptions. It is treated not as a metaphysical claim about reality, but as a constraint on admissible descriptions: all apparent irreversibility must be explainable as loss of access to a larger, pure structure. From this requirement alone, the mathematical formalism of quantum mechanics is shown to follow. By identifying purification as the minimal axiom beyond finite accessibility, the paper sharply limits the space of possible quantum theories. Any alternative framework lacking purification is shown to fail to reproduce essential quantum phenomena, while any stronger assumption introduces surplus structure. Keywords quantum reconstruction; purification axiom; entanglement; superposition; operational quantum mechanics; axiomatic foundations Notes Arc V — Gravity & Quantum Theory (axiomatic quantum reconstruction) Purification elevated from repair mechanism to generative principle Quantum structure derived without geometry or microstates Strong separation between operational axioms and interpretation Direct precursor to non-geometric formulations of quantum mechanics