Geometric Foundations of Quantum Theory and Gravity

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Published May 16, 2026 | Version v16
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Unified Geometrization of Standard Model Parameters: A Holographic Fiber Theory (HFT) Framework

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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 carrying a trivalent weaving rule 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 $\theta_v$ enters as a geometric pre-stress correction in the Higgs vev calculation, with the downstream SM mass cascade inheriting this $\theta_v$ dependence. 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.

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References

  • [1] Planck Collaboration, "Planck 2018 results. VI. Cosmological parameters," Astronomy & Astrophysics, vol. 641, p. A6, 2020. DOI: 10.1051/0004-6361/201833910.
  • [2] H. K. Urbantke, "The Hopf fibration—seven times in physics," Journal of Geometry and Physics, vol. 46, pp. 125–150, 2003.
  • [3] E. Witten, "Quantum field theory and the Jones polynomial," Communications in Mathematical Physics, vol. 121, no. 3, pp. 351–399, 1989.
  • [4] L. Susskind, "The world as a hologram," Journal of Mathematical Physics, vol. 36, no. 11, pp. 6377–6396, 1995.
  • [5] G. 't Hooft, "Dimensional reduction in quantum gravity," in Salamfestschrift, World Scientific, 1993; arXiv:gr-qc/9310026.
  • [6] P. W. Higgs, "Broken symmetries and the masses of gauge bosons," Physical Review Letters, vol. 13, no. 16, pp. 508–509, 1964.
  • [7] F. Englert and R. Brout, "Broken symmetry and the mass of gauge vector mesons," Physical Review Letters, vol. 13, no. 9, pp. 321–323, 1964.
  • [8] S. Weinberg, "A model of leptons," Physical Review Letters, vol. 19, no. 21, pp. 1264–1266, 1967.
  • [9] S. Coleman, "Fate of the false vacuum: Semiclassical theory," Physical Review D, vol. 15, no. 10, pp. 2929–2936, 1977.
  • [10] R. D. Peccei and H. R. Quinn, "CP conservation in the presence of pseudoparticles," Physical Review Letters, vol. 38, no. 25, pp. 1440–1443, 1977.
  • [11] H. Nyquist, "Certain topics in telegraph transmission theory," Transactions of the American Institute of Electrical Engineers, vol. 47, no. 2, pp. 617–644, 1928.
  • [12] C. E. Shannon, "A mathematical theory of communication," Bell System Technical Journal, vol. 27, no. 3, pp. 379–423, 1948.
  • [13] A. D. Sakharov, "Violation of CP invariance, C asymmetry, and baryon asymmetry of the universe," JETP Letters, vol. 5, pp. 24–27, 1967.
  • [14] G. Călugăreanu, "Sur les classes d'isotopie des nœuds tridimensionnels et leurs invariants," Czechoslovak Mathematical Journal, vol. 11, no. 4, pp. 588–625, 1961.
  • [15] J. H. White, "Self-linking and the Gauss integral in higher dimensions," American Journal of Mathematics, vol. 91, no. 3, pp. 693–728, 1969.
  • [16] F. B. Fuller, "The writhing number of a space curve," Proceedings of the National Academy of Sciences USA, vol. 68, no. 4, pp. 815–819, 1971.
  • [17] S. Navas et al. (Particle Data Group), "Review of Particle Physics," Physical Review D, vol. 110, p. 030001, 2024.
  • [18] G. S. Bali, "QCD forces and heavy quark bound states," Physics Reports, vol. 343, no. 1, pp. 1–136, 2001. DOI: 10.1016/S0370-1573(00)00079-X.
  • [19] G. Spencer-Brown, Laws of Form, Allen & Unwin, London, 1969.
  • [20] T. H. R. Skyrme, "A unified field theory of mesons and baryons," Nuclear Physics, vol. 31, pp. 556–569, 1962.
  • [21] R. C. Tolman, "On the estimation of distances in a curved universe with a non-static line element," Proceedings of the National Academy of Sciences USA, vol. 16, no. 7, pp. 511–520, 1930.
  • [22] I. M. H. Etherington, "On the definition of distance in general relativity," Philosophical Magazine, vol. 15, no. 100, pp. 761–773, 1933.
  • [23] A. H. Guth, "Inflationary universe: A possible solution to the horizon and flatness problems," Physical Review D, vol. 23, no. 2, pp. 347–356, 1981.
  • [24] D. J. Fixsen, "The temperature of the cosmic microwave background," Astrophysical Journal, vol. 707, no. 2, pp. 916–920, 2009.
  • [25] D. Clowe et al., "A direct empirical proof of the existence of dark matter," Astrophysical Journal Letters, vol. 648, no. 2, pp. L109–L113, 2006.
  • [26] A. G. Riess et al., "A comprehensive measurement of the local value of the Hubble constant with 1 km s−1 Mpc−1 uncertainty from the Hubble Space Telescope and the SH0ES team," Astrophysical Journal Letters, vol. 934, no. 1, p. L7, 2022.
  • [27] I. Labbé et al., "A population of red candidate massive galaxies ∼ 600 Myr after the Big Bang," Nature, vol. 616, pp. 266–269, 2023.
  • [28] G. Agazie et al. (NANOGrav Collaboration), "The NANOGrav 15 yr data set: Evidence for a gravitational-wave background," Astrophysical Journal Letters, vol. 951, no. 1, p. L8, 2023.
  • [29] R. Abbott et al. (LIGO Scientific, Virgo, KAGRA Collaborations), "Upper limits on the isotropic gravitational-wave background from Advanced LIGO and Advanced Virgo's third observing run," Physical Review D, vol. 104, no. 2, p. 022004, 2021.
  • [30] P. A. R. Ade et al. (BICEP/Keck Collaboration), "Improved constraints on primordial gravitational waves using Planck, WMAP, and BICEP/Keck observations through the 2018 observing season," Physical Review Letters, vol. 127, no. 15, p. 151301, 2021.