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

We propose a theory of lunar formation via Triple Phase Transition (TPT) in the differentiating Hadean proto-Earth — requiring no external impactor, no synestia, and no free parameter. The starting point is thermodynamic and non-negotiable: gravitational accretion energy exceeds mantle fusion energy by a factor of 155. The proto-Earth is therefore a fully molten, rapidly rotating magma sphere (T_rot ≈ 3.5 h), without a stabilising satellite, in a permanently out-of-equilibrium Hadean environment. A single driver — progressive Fe-Ni segregation — orchestrates three coupled transitions. (1) Rheological: the silicate melt acquires a yield stress (Bingham-Herschel, τ_y ∈ [10², 10⁴] Pa) and organises a Coherent Magmatic Torus (CMT) in the oblique intertropical band |φ| < 30° of the co-rotating frame. (2) Mechanical: elliptical parametric resonance drives the CMT to bifurcation, producing N ≈ 7 ± 2 hypersonic ejection episodes (Ma ≈ 12.5) and layer-by-layer construction of a Proto-Accretion Orbital body. (3) Magnetic: the terrestrial dynamo ignites 290–360 Myr after ejection, consistent with Jack Hills zircon palaeomagnetic constraints — with no free parameter. The central prediction — seismic interfaces in the 200–530 km window of the lunar mantle, impedance contrast |R| ∈ [0.01, 0.04] — is directly testable by Chang'e 7 (south pole, August 2026). Geochemical predictions (Fe/Si depth gradient, Hf-W chronometry at 4.467 Ga) are testable by Artemis III (2028–2029) via South Pole-Aitken basin mantle samples. This deposit pre-registers ten quantitative falsifiable predictions prior to these mission data. All hypotheses are explicit and ranked. Limitations are acknowledged. Falsification conditions are defined.