The Riemann Xi Theta Mixture: Missing Information, the Healing Law, and a Sharp Finite-Resolution Theorem

Abstract

This Zenodo record archives the canonical materials for Aaron Woffinden's 2026 preprint The Riemann Xi Theta Mixture: Missing Information, the Healing Law, and a Sharp Finite-Resolution Theorem, affiliated with the Institute of Unitive Cross-Domain Morphology. The record contains the manuscript PDF, a LaTeX source archive, a supplementary code archive, and this README. The supplementary code (Python 3 / mpmath) reproduces the machine-certification table of Section 12: the Turán coefficient margin, the exact pair-angle law, the orientation-inversion disk formula, Pick-orientation samples, and the Platt–Trudgian horizon M(H) = 4,712,664,392,501. The paper studies the Stieltjes reformulation of the Riemann Hypothesis through Riemann's positive theta-kernel representation. Two unconditional structural results are proved: an exact missing-information identity (the Healing Law) — the aggregate's first Stieltjes curvature equals posterior mean fibre curvature minus the Fisher information of a posterior tilt of the theta source, with an explicit two-fibre counterexample showing positive mixing does not preserve the zero class — and a sharp finite-resolution theorem: an exact pair-angle cosine law under which derivative order acts as angular magnification, forcing 4,712,664,392,502 unconditional alternating-derivative signs from the verified zero spectrum, with a matching optimality theorem. An unconditional half-line positivity corollary closes the converse of the associated Pick criterion. All displayed identities were independently machine-verified against high-precision zeta evaluations. The paper proves no case of the Riemann Hypothesis and asserts no new conjecture; its scope section states explicitly what is proved, certified, and not claimed.