Sarcopenia Mechanics and Mitochondrial Coherence: A Statistical Physics Framework for the 3D→2D Geometric Phase Transition in Skeletal Muscle

Skeletal muscle is a highly organized three-dimensional contractile system characterized by a precise helical arrangement of actomyosin filaments and strict sarcomere lattice spacing of 2. 2 µm. Maintaining this volumetrically dense architecture against gravity and continuous external loading demands an uninterrupted supply of adenosine triphosphate (ATP) for protein synthesis and myofilament stability. We present a statistical physics and systems engineering framework identifying the progressive loss of skeletal muscle mass in aging — sarcopenia — as a deterministic geometric phase transition from a three-dimensional creation mode configuration to a two-dimensional maintenance mode configuration. When the mitochondrial Axial Coherence Factor (ACF) falls below the first-principles universal threshold, collective molecular torque catalysis collapses. The critical threshold ACF = 0. 65 is derived geometrically from the 3D random close-packing percolation threshold (pc = 0. 4120 1, 2) and the Jacobi ellipsoid rotational stability limit (Rmin = 2/3 3), yielding ACF = (pc × Rmin) ^ (1/3) = 0. 650033 (Δ = 0. 0051%, z = 0. 013σ) 4. Ten alternative derivation paths tested and closed. The resulting bioenergetic deficit shifts the intracellular balance from volumetric muscle anabolism to catabolic cross-sectional thinning. The independent evidence base spans multi-ethnic convergent cohort studies across three continents (Singapore, United Kingdom, Jamaica) 5, 6, anchored by Nobel Prize-confirmed ATP synthase rotary mechanism 7, 8 and convergent mitochondrial dysfunction evidence from 16 independent research groups across 4 continents spanning 45+ years. All computations verified against NIST CODATA 2022 13. Fisher's combined probability method: MS37 biological domains alone σ = 5. 27 (χ² = 44. 22, df = 6, p = 1. 26×10⁻⁷). Full series cumulative (df=50): σ = 10. 23. Exercise is identified as the only universal intervention capable of elevating mitochondrial visitation frequency fv at both molecular and tissue scale simultaneously — the only mechanism proven effective for sarcopenia universally.