Harmonic Coherence Comprehensive Mathematical Reconciliation and Unified Theoretical Summary

Canonical supplemental reference for the Harmonic Coherence (HC) and Hanners Theorem (HT) submission suite. This document is not submitted to a journal; it is hosted for stable citation and referee access. It provides the unified exposition, definitions, and consolidated equation toolkit (Appendix G) cited in HC/HT submissions (FoP, HT, Yang–Mills, Navier–Stokes, Riemann, BSD, Hodge, P vs NP, Beal’s Conjecture). Contents: Introduction and mathematical foundations (Ch 1–2); quantum–gravitational coupling and Schrödinger formulation (Ch 3–4); cross-disciplinary reconciliation and Universal Translation Protocol (Ch 5–6); proofs, validation, applications, experimental predictions, conclusion (Ch 7–10); Appendix G — consolidated mathematical toolkit (equations G.1–G.6). The full abstract is provided in the file abstract.txt. Author: Michael Hanners. Manuscript completed May 2025. CC BY 4.0. Part of the Harmonic Coherence publication ecosystem.