Harmonic Coherence: A Unified Field Framework for General Relativity, Quantum Mechanics, and the Standard Model

Harmonic Coherence (HC) is a theoretical framework that unifies General Relativity (GR), Quantum Mechanics (QM), and the Standard Model (SM) on a single substrate: nested temporal coherence. At its core is Hanners Theorem (HT), an entropic principle that formalizes recursive, entropy-minimizing evolution and grounds the reality of layered time. Mass, force, and information emerge as coherence gradients governed by the covariant Coherence Tensor Field C_μν^ (n), within a generalized Lagrangian formalism. HC yields quantitative, testable predictions using present-day technology: optical lattice clocks, vacuum coherence-collapse chambers, gravitational-wave interferometers, and neutrino oscillation measurements. The framework resolves central paradoxes—black hole information, quantum measurement, the arrow of time, and the relativistic twin scenario—and recasts electromagnetism, the strong and weak forces, and gravity as coherence artifacts; the Higgs mechanism is reimagined as a coherence-derived mass attribution. The manuscript includes detailed mathematical pathways (Appendices H–L) for the Yang–Mills mass gap, the Riemann Hypothesis, Navier–Stokes regularity, and computational complexity (P vs NP), and provides a comparative analysis of HC with String Theory, Loop Quantum Gravity, and Emergent Gravity (Appendix E). Structure: main text (Chapters 1–10), Appendices A–U, and supplemental material (glossary, axioms, formalization, visualizations). This work is the official publication of record for the Harmonic Coherence framework. It is available under CC BY 4. 0 and is part of the Harmonic Coherence publication ecosystem hosted at https: //legacy-alliance. org. For the canonical Zenodo record and full supplementary materials, see doi: 10. 5281/zenodo. 15288891.