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

This work proposes a theory of lunar formation grounded in a thermodynamic necessity: Any Earth-mass planet emerges from accretion in a state of near-total silicate mantle melting. Accretion energy exceeds total fusion energy by a factor of 155 — the proto-Earth could only have been a rapidly rotating magma sphere immersed in a Hadean inferno : A raging T-Tauri Sun, a silicate atmosphere at 2 000–4 000 K, incessant planetesimal bombardment, still-active short-lived radionuclides, and a chaotic axial obliquity between 40° and 70°. It is in this context — and nowhere else — that the Triple Phase Transition (TPT) is triggered. Its unique driver is the progressive Fe-Ni segregation, which simultaneously governs three regime changes: (1) A rheological transition — the silicate melt acquires a yield stress (Bingham-Herschel law) and organises a coherent toroidal flow in the intertropical belt |φ| < 30°, the Coherent Magmatic Torus (CMT) (2) A mechanical transition — the CMT crosses the instability threshold and produces two to three episodes of cohesive ejection beyond the Roche radius (3) A magnetic transition — the terrestrial dynamo emerges ≈ 300 Myr after the ejections cease. The central equation of the theory : M^max_ej ≈ 2Ω sin ε · U_crit · M_CMT / g_eff(0) ≈ 2.2–4.0 × 10²² kg per event With N = 2–3 and a capture efficiency f_cap ≈ 0.70, the lunar mass is recovered. Each episode leaves a detectable stratigraphic signature : seismic interface between 200 and 315 km depth, Fe/Si gradient at depth, near-side/far-side crustal dichotomy. An interactive HTML5/WebGL simulation of the TPT dynamics is included in the supplementary files (open in any browser,no installation required). The Chang’e 7 mission (seismometer, South Pole, August 2026) constitutes the nearest validation window. The Artemis III mission (2028–2029) will provide independent geochemical confirmation via direct sampling of SouthPole-Aitken basin ejecta at the lunar South Pole. Epistemic note: this work submits a theory, not certainties. All hypotheses are ranked, all limitations are acknowledged, the validation programme is defined and dated.