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.