Minimum Bell-Setting Complexity for Qubit POVM–PVM Separation Integrity Manifest

This unreviewed preprint establishes a minimum-setting classification for fixed-qubit POVM–PVM separation in bipartite Bell experiments. For every two-input-per-party architecture with arbitrary finite, input-dependent output alphabets, the shared-randomness convex hull of qubit POVM behaviors equals the shared-randomness convex hull of fixed-qubit PVM behaviors. The paper also gives an explicit rational 3×2 Bell functional with an exact qubit-POVM strategy whose value exceeds a global analytic qubit-PVM upper bound. Consequently, 3×2, up to exchanging the parties, is the minimum input architecture for such a linear Bell-functional separation.

The equality concerns convexified behavior sets. It does not assert equality of the raw nonconvex strategy images, same-state simulation, or operator-level projective simulability of individual POVMs.

Generative-AI systems were used substantively throughout the mathematical exploration, derivation, adversarial proof analysis, software development, literature support, and manuscript preparation. The human author accepts responsibility for all claims, citations, and released artifacts. At the time of this version’s initial release, the manuscript had not undergone independent expert peer review.

Source release: https://github.com/AlecKriebel/Math/releases/tag/qubit-povm-pvm-minimum-settings-v1.1.0