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

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.