Holographic Fiber Theory: A Topological Substrate 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 topological knot, and exactly three fermion generations fixed by the topological weaving rule. A symmetry-breaking event --- the chirality lock --- rigidifies the topological substrate and fixes the gauge sector by coupling the strands at each vertex and edge; the $U(1)$, $SU(2)$, and $SU(3)$ factors emerge from the substrate's cohomology channels. 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 lightest Majorana neutrino mass, mν₁ ≈ 1.8 meV, is a near-term falsifiable target.