Phase-Dependent Resonance Coupling in Earth's Layered Seismicity: An Annex to the Earth-Moon Framework

This annex applies the Unified Harmonic Shells (UHS) framework to the solid Earth interior, deriving a deterministic model for planetary layer architecture and deep-focus seismicity from first principles.

Using the curvature-frequency duality of the Φ-operator (f = c/r), a single spatial invariant Λ = 6,960 km is calibrated to the Core-Mantle Boundary. From this single constant, the complete interior shell ladder is derived: the lithospheric base (n = 11/10), the upper/lower mantle transition at 660 km (n = 11/9), the mid-lower mantle transition (n = 4), the F-zone crystallization envelope (n = 6), and the Innermost Inner Core boundary (n = 8). All boundaries are computed without parameter fitting.

Deep-focus seismicity at 41 km (Hawaiian lithospheric flexure) and 250 km (Calabrian slab rupture, June 2, 2026) is mapped to rational phase nodes 11/10 and 8/7 respectively. The failure mechanism is derived from the quadratic strain-rate dependence of the Φ-operator and a phase reset condition at rational nodes, resolving the classical brittle-failure paradox at high lithostatic pressure without ad hoc mechanisms.

Two observed values enter the model: mean Earth radius Rₑ = 6,371 km and CMB radius r_CMB = 3,480 km. No parameters are fitted.

Part of the Harmonic Structures in Natural Systems series. SemanticShift.net.