Rotational Coherence Collapse at the Mitochondrial Scale: A Statistical Physics Framework for the Warburg Phase Transition in Cellular Oncogenesis

07: 18, 17/05/2026 Pai: Rotational Coherence Collapse at the Mitochondrial Scale: A Statistical Physics Framework for the Warburg Phase Transition in Cellular Oncogenesis07: 32, 17/05/2026 Pai: We present a statistical physics framework describing the transition of mitochondrial rotary motors from a coherent high-energy state to an incoherent low-energy state, and identify the geometric threshold governing this transition. The ATP synthase — a rotary molecular motor operating at 100–150 revolutions per second (RPS) 1, 2 — is modelled as an active biological oscillator whose coherence is parametrised by the Axial Coherence Factor (ACF). The critical threshold ACF = 0. 65 is derived from first principles by the present work by combining two independent physical constants: the three-dimensional random close-packing percolation threshold (pc = 0. 4120 3, 4) and the Jacobi ellipsoid rotational stability limit (Rmin = 2/3 5), yielding ACF = (pc × Rmin) ^ (1/3) = 0. 650033 (deviation 0. 0051% from the empirically identified value; z = 0. 013σ) 6. Below this threshold, the system undergoes a deterministic phase transition: rotational coherence collapses, oxidative phosphorylation fails, and the cell activates compensatory aerobic glycolysis — the Warburg effect 7. The cell membrane potential simultaneously depolarises from −70 mV (coherent, creation mode) to −15 to −30 mV (collapsed, maintenance mode) 8, 9, providing a directly measurable macroscopic correlate of the microscopic phase transition. This framework positions cancer as a physical phase transition in a dissipative active matter system rather than a stochastic accumulation of genetic errors. Statistical validation using Fisher's method (df-corrected, df = 38) across 19 independent empirical domains yields χ² = 172. 59, p = 4. 61×10⁻¹⁹, σ = 8. 84. Critically, the three biological physics domains alone — excluding all prior theoretical series — yield σ = 5. 16 (χ² = 42. 83, df = 6, p = 1. 26×10⁻⁷), confirming that the empirical evidence independently crosses the 5σ discovery threshold. Three falsifiable predictions are presented for experimental validation.