Operational Dissolution of the Measurement Problem in Quantum Mechanics: Born Rule, EPR Paradox, and Bell Inequalities

The quantum measurement problem has resisted resolution for nearly a century, fragmenting into three seemingly independent challenges: the Born rule's probabilistic interpretation, the EPR paradox of simultaneous reality, and Bell inequality violations challenging local realism. This fragmentation has obscured a common structural origin. This work demonstrates that all three problems arise from a single theoretical defect: the misapplication of commutative probability theory to non-commutative operational structures. Within the framework of Cognitional Mechanics (CM), grounded in two axioms—non-commutativity ([Ô_A, Ô_B] ≠ 0) and finite operational resolution (Level of Detail)—these problems dissolve simultaneously through structural reconstruction. The Born rule emerges as the unique projection measure compatible with resource conservation and tensor-product linearity under non-commutative constraints, repositioning probability as an epistemic consequence of finite resolution rather than ontological randomness. EPR correlations are resolved as constraint propagation across shared operational stacks, eliminating the apparent conflict between quantum completeness and local realism without invoking non-local signaling. Bell inequality violations follow from the logical impossibility of factorization: non-commutativity structurally excludes the simultaneous eigenstates required by the factorization condition, rendering the measure space for joint distributions undefined rather than merely violated. The framework derives from Tier 1 axiomatic necessity within Cognitional Mechanics. Mathematical formalisms—Hilbert spaces, operator algebras, measure theory—serve as Tier 3 projection tools expressing this structure, not as foundational requirements for its validity. This paper builds on Operational Quantum Mechanics I (DOI: 10.5281/zenodo.18649525), which resolved Schrödinger's cat through operational stack management, and forms a symmetrical counterpart to Universal Relativity (DOI: 10.5281/zenodo.18645324) within the CM framework.