Information-Geometric Dynamostasis Explains Near-Unification of Standard-Model Gauge Couplings (No SUSY)

The revised analysis replaces a strong unification claim with a narrower, better-supported result. The Standard-Model running trajectory contains a reproducible region in which a curvature–shear functional varies slowly and overlaps the conventional near-concordance interval. Separately, a mature spectral–phase organizer exhibits a genuine, cubic, multimode third-order susceptibility that is resolved only when the field evolution is performed at sufficient numerical precision. The response is overwhelmingly internal and occurs without loss of structural identity. Neither result establishes a unique unification mechanism. The nonlinear tensor does not robustly select among the investigated running families, fails stringent spatial and random direction controls, and does not improve the tested admissibility measures. The correct endpoint is therefore twofold: retain geometric stationarity and multimode susceptibility as reproducible organizational observables; reject the inference that they presently explain or select gauge unification. ***Old version:The apparent near-unification of the three Standard-Model (SM) gauge couplings has long intrigued physicists. While supersymmetric or grand-unified theories (SUSY/GUT) achieve precise convergence through additional particles or symmetries, the SM itself seems to approach—but not quite reach—unification. This raises a fundamental question: could the near-merging of α1\alpha_1α1, α2\alpha_2α2, and α3\alpha_3α3 arise naturally from the internal geometry of the SM’s renormalization group (RG) flow, without invoking new physics? In this work, we approach the problem from an information-geometric perspective. We treat the evolution of gauge couplings as a trajectory on a statistical manifold and define a dynamical cost functional F=R+αdyn τ2,F = \mathcal{R} + \alpha_{\rm dyn}\,\tau^2,F=R+αdynτ2, where R\mathcal{R}R measures curvature (bending of the flow) and τ\tauτ quantifies shear (differential tilt between sectors). The parameter αdyn\alpha_{\rm dyn}αdyn plays the role of a shear modulus, balancing curvature and deformation, analogous to elastic stability in continuum mechanics. Using this formulation, we discover a dynamostatic plateau—a finite, window-locked interval where the informational action-rate FFF becomes stationary (dF/dL≃0dF/dL \simeq 0dF/dL≃0). Remarkably, this plateau aligns precisely with the SM’s empirical RG crossings, L13L_{13}L13 and L12L_{12}L12, and encloses the minimum of the coupling spread (RMS). The effect is robust across smoothing scales, tolerance thresholds, and variations in αdyn\alpha_{\rm dyn}αdyn. This result suggests that the SM’s near-unification is not accidental, but an emergent feature of its informational geometry—a regime of minimal organizational cost where curvature and shear co-balance. The phenomenon, which we term information-geometric dynamostasis, provides a falsifiable, model-minimal explanation of coupling concordance, offering an alternative to supersymmetric unification and pointing toward a deeper geometric order underlying the SM itself.