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 Oncogenesis[07:32, 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.