Holographic Fiber Theory: Topological Weaving Rule for the Standard Model

Holographic Fiber Theory (HFT) models the vacuum as a discrete, trivalent cell complex carrying Hopf-bundle topology S³ S¹ S². Its continuum limit bridges to QFT: the path integral as a finite Markov-chain transition product, a baryon as energy trapped in a B₃-braided knot, and gauge invariance as the interconversion of topological strains. A symmetry-breaking event locks chirality on the substrate's B₂-braided edges, rigidifying the substrate and fixing the gauge sector by coupling the strands together, its factors emerging from the substrate's cohomology channels and the braid-reconnection operators on them. At the IR limit (μ = 0) these couplings are fixed dimensionless ratios, with α⁻¹ ≈ 137.036 (8 ppb) and sin²θW ≈ 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 summed Majorana neutrino mass, ∑ m_ν ≈ 61.2 meV (with mν₁ ≈ 1.77 meV), is a near-term falsifiable target.