Holographic Fiber Theory: Topological Weaving Rule for the Standard Model
Year: 2026
Type: preprint
Abstract: Holographic Fiber Theory (HFT) is a topology-driven framework that derives the parameters of the Standard Model from a single classical degree of freedom --- a tensioned $S^1$ thread on the Hopf bundle $S^3\xrightarrow{S^1}S^2$, projected as a tension field on the $S^2$ base mesh --- constrained by the Bekenstein bound and Călugăreanu's link--twist--writhe identity. The framework yields the cosmological dark-matter-to-baryon ratio $\Omega_c/\Omega_b \approx 5.42$ with no parameter adjusted to match this observation, agreeing with the Planck 2018 measurement of $5.357$ to $\sim\!1\%$. The result follows directly from the partition of the topological action budget between visible and dark sectors; the derivation is given in Section~6. The framework has zero free theory parameters. The integers that recur throughout the derivation ($N_{\text{Nyquist}}=128$, $\sum Q_f^2=8$, $E(\text{dodec})=30$) are forced by the Hopf structure, from which the Standard Model itself emerges: $U(1)$ from the $S^1$ fiber, $SU(2)$ from the $T^1S^2$ tangent rotation, and $SU(3)$ from the trivalent coordination of the Planck mesh. Other quantities derived without further fitting include the fine-structure constant ($\alpha^{-1} = 137.036$, as a curvature-corrected Wyler volume ratio on a bounded symmetric domain), the Weinberg angle ($\sin^2\theta_W = 30/128 \approx 0.234$, the chiral-locking tilt of the dodecahedral mesh), and the electroweak and Higgs mass scales. Electroweak Symmetry Breaking is realised as a first-order topological phase transition in which $Tw\!\to\!Wr$ chiral locking populates a hierarchy of anti-chiral topological-knot excitations $W^{(1,2,3)}$, identified respectively with cold dark matter, dynamic dark energy, and the cosmological-constant stator.
Authors: Hsieh, C.Y., Claude 4.6 Sonnet, Gemini 3.1 Pro
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7155502648
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