Quantum Gravity and Global Synchrony The Geometric Origin of Fundamental Constants, Gauge Protection, and Coherence

This paper formally establishes the Effective Field Theory (EFT) consistency of the Harmonic Model (HM) program, transitioning from conceptual foundations to a rigorous candidate Grand Unified Theory. We address the critical formal requirements for a higherdimensional framework by explicitly defining the boundary conditions (BCs) and truncationcriteria necessary for a stable 4D limit. Within the Harmonic Field Equation (HFE) framework, 4+ξ + Λ 2 h + δ Ω 2 (x µ , ξ) Ψ(x µ , ξ) = 0, we derive gravity as the effective interaction mediated by the delocalized ξ zero-mode, showing that the weakness of G arises geometrically from fiber-volume suppression. We demonstrate that fundamental constants (c, ~, e) are not arbitrary inputs but emergent elastic and topological parameters of the substrate and the compact manifold K.To ensure particle-physics viability, we present a concrete benchmark model characterized by: (i) Gauge Protection: An exactly massless photon mode protected by internal Killing isometries and compatible Neumann BCs; (ii) Chiral Spectrum: A minimal SU (3) × SU (2) × U (1) embedding where 4D chirality is generated via an S 1 /Z 2 orbifold projection, eliminating mirror fermions at the zero-mode level; (iii) Anomaly Cancellation:A verification that the chiral zero-mode sector satisfies Standard Model anomaly constraints, while the high-energy Kaluza-Klein tower completes the spectrum in a vector-like, anomalyfree manner.Finally, we provide a controlled EFT truncation lemma based on spectral power-counting to preserve unitarity, and establishing quantitative lower bounds on the Kaluza-Klein scale compatible with current collider and sub-millimeter gravity constraints.