Geometric Foundations of Quantum Theory and Gravity

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Published July 7, 2026 | Version v22
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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 an informationally discrete, trivalent cell complex carrying Hopf-bundle topology $S^3 \xrightarrow{S^1} S^2$. Its continuum limit reproduces the structures of quantum field theory from the substrate's four cohomology channels, which pair into a tension field and a phase field by Poincaré duality.

A symmetry-breaking event locks chirality on the two-strand braided edges, rigidifying the mesh and fixing the gauge sector: the abelian factor is the fiber's phase holonomy, and the non-abelian factors are the braid-reconnection operators on the two fields. The dynamics is a set of entropy-driven transition rules on finitely many states per cell; read as a signed-measure Markov chain, it reproduces the Tsirelson bound of quantum correlations from local, real-valued weights, and coarse-grains to the path-integral measure.

The Standard-Model mass spectrum emerges as energy topologically trapped in the tension field, gravity its free spin-2 mode. The summed Majorana neutrino mass, $\sum m_\nu \approx 61.2$ meV (with $m_{\nu_1} \approx 1.77$ meV), is a near-term falsifiable target.

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2026-04-24
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