Lunar Formation by Triple Phase Transition in the Differentiating Proto-Earth

This document presents a theoretical framework for the origin of the Moon, based on an entirely internal mechanism operating within the Hadean proto-Earth: the Triple Phase Transition (TPT). The starting point is thermodynamic and non-negotiable: the gravitational energy released during terrestrial accretion exceeds the silicate mantle fusion energy by a factor of 155. The proto-Earth is therefore necessarily a rapidly rotating magma sphere (T_rot ≈ 5 h), without a stabilizing satellite, evolving in a permanently out-of-equilibrium Hadean environment. The unique driving force is the progressive segregation of Fe-Ni, which orchestrates three coupled regime transitions — rheological, mechanical, and magnetic. The chaotic wobble of the rotation axis in the co-rotating body frame — defined perpendicular to the instantaneous rotation axis, not to the geographic equator — sustained by continuous Hadean perturbations, generates toroidal flows entering elliptical parametric resonance with the inertial modes of the fluid (Malkus 1968; Kerswell 2002; Lacaze et al. 2004). The resulting growth rate brings the Coherent Magmatic Torus (CMT) to bifurcation velocity in ≈ 32 hours, producing 2 to 3 cohesive ejection episodes in 3 to 4 weeks and a Hadean dynamo delay of 290–360 Myr. Version 4.0 updates: M_TMC internally constrained from the observed radius of the first accretion layer (R₁ ≈ 1,560 km → M_TMC ≈ 2.3 × 10²² kg) τ_Stokes ≈ 257 s fully derived (Appendix E) — resolves the apparent paradox between 3–4 week formation and 40 Myr segregation New prediction P3b: independent observational convergence between Lunar Prospector Fe data and TPT layer 1 stratigraphy SPA references updated: Schultz & Crawford (2011), Wakita et al. (2026, Science Advances), Gowman et al. (2026, JGR Planets) Manuscript submitted to Planetary Science Journal (AAS), #AAS77321, 27 May 2026 The model formulates ten quantitative and falsifiable predictions. The central prediction — seismic interface at d ≈ 200–315 km, impedance contrast |R| ∈ [0.01; 0.04] — is testable by Chang'e 7 (lunar south pole, August 2026) and Artemis III (2028–2029). This deposit registers the theory and its predictions prior to the data from these missions. A interactive WebGL is available to this link : https://orion4622.github.io/moon-formation-triple-phase-transition Preprint also published on EarthArXiv: https://doi.org/10.31223/X5XB6H