Geometric Foundations of Quantum Theory and Gravity
Published May 31, 2026 | Version v19
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Holographic Fiber Theory: Topological Weaving Rule for the Standard Model

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Holographic Fiber Theory (HFT) models the vacuum as a discrete, trivalent cell complex carrying Hopf-bundle topology $S^3 \xrightarrow{S^1} S^2$. Its continuum limit bridges to QFT: the path integral as a finite Markov-chain transition product, a baryon as energy trapped in a $B_3$-braided topological knot, and exactly three fermion generations fixed by the topological weaving rule.

A symmetry-breaking event locks chirality on the substrate's $B_2$-braided edges, rigidifying the substrate and fixing the gauge sector by coupling the strands together; the $U(1)$, $SU(2)$, and $SU(3)$ factors emerge from the substrate's cohomology channels. At the IR limit ($\mu = 0$) these couplings are fixed dimensionless ratios, with $\alpha^{-1} \approx 137.036$ (8 ppb) and $\sin^2\theta_W \approx 0.2386$ (5 ppm).

The Higgs VEV emerges as the substrate's saturation tension, and down-scaling from it forward-derives the Standard-Model mass spectrum. The lightest Majorana neutrino mass, $m_{\nu_1} \approx 1.8$ meV, is a near-term falsifiable target.

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Dates

Created
2026-04-24
v1 submitted
Updated
2026-05-31
v19 updated; Reframe Title

References

  • H. K. Urbantke, "The Hopf fibration—seven times in physics," Journal of Geometry and Physics, vol. 46, pp. 125–150, 2003.
  • G. 't Hooft, "Dimensional reduction in quantum gravity," in Salamfestschrift, World Scientific, 1993; arXiv:gr-qc/9310026.
  • L. Susskind, "The world as a hologram," Journal of Mathematical Physics, vol. 36, no. 11, pp. 6377–6396, 1995.
  • G. Călugăreanu, "Sur les classes d'isotopie des nœuds tridimensionnels et leurs invariants," Czechoslovak Mathematical Journal, vol. 11, no. 4, pp. 588–625, 1961.
  • J. H. White, "Self-linking and the Gauss integral in higher dimensions," American Journal of Mathematics, vol. 91, no. 3, pp. 693–728, 1969.
  • 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.
  • S. Weinberg, "A model of leptons," Physical Review Letters, vol. 19, no. 21, pp. 1264–1266, 1967.
  • E. Witten, "Quantum field theory and the Jones polynomial," Communications in Mathematical Physics, vol. 121, no. 3, pp. 351–399, 1989.
  • H. Nyquist, "Certain topics in telegraph transmission theory," Transactions of the American Institute of Electrical Engineers, vol. 47, no. 2, pp. 617–644, 1928.
  • C. E. Shannon, "A mathematical theory of communication," Bell System Technical Journal, vol. 27, no. 3, pp. 379–423, 1948.
  • T. H. R. Skyrme, "A unified field theory of mesons and baryons," Nuclear Physics, vol. 31, pp. 556–569, 1962.
  • Planck Collaboration, "Planck 2018 results. VI. Cosmological parameters," Astronomy & Astrophysics, vol. 641, p. A6, 2020. DOI: 10.1051/0004-6361/201833910.
  • 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.
  • G. Spencer-Brown, Laws of Form, Allen & Unwin, London, 1969.
  • D. J. Fixsen, "The temperature of the cosmic microwave background," Astrophysical Journal, vol. 707, no. 2, pp. 916–920, 2009.
  • 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.
  • I. M. H. Etherington, "On the definition of distance in general relativity," Philosophical Magazine, vol. 15, no. 100, pp. 761–773, 1933.
  • I. Labbé et al., "A population of red candidate massive galaxies ∼ 600 Myr after the Big Bang," Nature, vol. 616, pp. 266–269, 2023.
  • 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.
  • 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.
  • 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.
  • S. Navas et al. (Particle Data Group), "Review of Particle Physics," Physical Review D, vol. 110, p. 030001, 2024.
  • 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.
  • J. Erler and M. J. Ramsey-Musolf, "Weak mixing angle at low energies," Physical Review D, vol. 72, no. 7, p. 073003, 2005.
  • 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.
  • P. W. Higgs, "Broken symmetries and the masses of gauge bosons," Physical Review Letters, vol. 13, no. 16, pp. 508–509, 1964.
  • S. Coleman, "Fate of the false vacuum: Semiclassical theory," Physical Review D, vol. 15, no. 10, pp. 2929–2936, 1977.
  • P. A. M. Dirac, "The quantum theory of the electron," Proceedings of the Royal Society A, vol. 117, no. 778, pp. 610–624, 1928.
  • W. Pauli, "The connection between spin and statistics," Physical Review, vol. 58, no. 8, pp. 716– 722, 1940.
  • J. Schwinger, "On quantum-electrodynamics and the magnetic moment of the electron," Physical Review, vol. 73, no. 4, pp. 416–417, 1948.
  • R. P. Feynman, "Space-time approach to non-relativistic quantum mechanics," Reviews of Modern Physics, vol. 20, no. 2, pp. 367–387, 1948.
  • G. C. Wick, "Properties of Bethe-Salpeter wave functions," Physical Review, vol. 96, no. 4, pp. 1124–1134, 1954.
  • M. Born, "Zur Quantenmechanik der Stoßvorgänge," Zeitschrift für Physik, vol. 37, no. 12, pp. 863–867, 1926.
  • Y. Koide, "Fermion–boson two-body model of quarks and leptons and Cabibbo mixing," Lettere al Nuovo Cimento, vol. 34, no. 8, pp. 201–205, 1982.