Dual-Field Interference as a Common Biomechanical Origin of Cell Division, Differentiation, and Aging

This work develops a biophysical theory in which a bioelectric field V(x,t) and a cortical stress field sigma(x,t) are weakly and reciprocally coupled. Because the mechanical sector includes an inertial-viscoelastic element, the coupled system supports two underdamped normal modes whose interference defines a measurable slow cadence f_slow = (omega+,r - omega-,r) / (2 pi). Sampling the dynamics at the neutral moment (the recurring near-symmetric crossing between the two sectors) produces an even circle map (mod pi) for the slow phase, with effective forcing Omega and coupling K2. Both Omega and K2 can be computed a priori from directly measurable electrical and mechanical properties of the tissue (membrane time constant tau_m, cortical stiffness kappa, viscosity eta, effective areal inertia rho_eff, diffusion constants D_V and D_sigma, and weak electromechanical gains gamma, beta_R, beta_I), without arbitrary integer fitting. Helical quantization then appears as a mode-locking problem: the canonical B-DNA rotation number n ~ 10.5 corresponds to the high-order lock rho_pi = 2/21, whose center in this even (mod pi) convention is Omega2/21 = pi * (2/21) ~ 0.2992 rad. We define a functional order parameter Lambda as the cross-spectral coherence CVsigma(f_slow) between V and sigma at f_slow. We hypothesize that high Lambda inside the 2/21 tongue is associated with more stable spindle orientation and cortical anchoring during division, constraining chromatin torsion and supporting controlled proliferation and differentiation. Drifting out of that tongue suggests two generic failure modes: (i) persistent unlocking with low Lambda and elevated spindle-angle dispersion (dysregulated proliferation and abnormal division geometry), and (ii) over-locked, low-plasticity states with a rigid slow cadence (aging-like overlock/drift). The model yields three preregisterable and falsifiable predictions. (P1) Homeostatic epithelia exhibit a shared narrow slow-band cadence in both V and sigma, together with a coherence peak Lambda = CVsigma(f_slow). (P2) The point (Omega, K2), obtained from those directly measurable properties together with neutral-moment stroboscopy, lies inside the 2/21 Arnold tongue while avoiding broad low-order tongues. (P3) A weak, frequency-specific electrical or mechanical drive at f_slow is predicted to increase Lambda and reduce spindle-angle dispersion, whereas a matched off-resonant control should not. This study provides analytical bounds, a numerical sandbox, and preregistered analysis code, enabling direct experimental falsification using combined optical electrophysiology and mechanical readouts.