Unified Geometrization of Standard Model Parameters: A Holographic Fiber Theory (HFT) Framework

Holographic Fiber Theory (HFT) is a parameter-free topological derivation of the Standard Model's free constants and the leading dark-sector ratios from a single substrate --- the Hopf bundle $S^3\xrightarrow{S^1}S^2$ realised as two-strand framed fibers discretized as a trivalent mesh on its $S^2$ base with $B_3$ vertex braiding. A single global $\mathbb{Z}_2$ symmetry-breaking event --- the chirality lock --- converts the loose pre-EWSB substrate into the post-EWSB vacuum $\mathcal{V}$.

The locked mesh's topology forward-derives three geometric coupling constants: $\sin^2\theta_W = 30/128$, $\alpha^{-1} = 137$, and the vacuum angle $\theta_v = 1/32$. The first two fix the dark-to-baryonic ratio via writhon excitations crystallised at EWSB, giving $\Omega_c/\Omega_b \approx 5.35$.

The vacuum angle $\theta_v$ functions as the framework's mass-generating coupling constant, from which the SM mass spectrum follows. HFT predicts $M_Z = 91.14$~GeV and $M_p = 937.7$~MeV, matching observation to $0.05\%$ and $0.06\%$ respectively; Table 1 lists the leading-order results across the spectrum.