Entanglement Harmonics: The Standard Model Mass Spectrum as Defect Modes of the FCC Tensor Network

We derive the bare masses of the proton, tau lepton, neutral kaon, muon, and Higgs boson as entanglement defect modes of the FCC tensor network, classied by the di- mensionality of the disruption. Every particle is a specic way of breaking the entan- glement structure of the vacuum triad τ = (4,4,4)the unique decomposition of the FCC coordination shell (K = 12) into three orthogonal 4-bond sheets. Using Triadic Orthogonal Calculus (TOC), the defect modes stratify into a natural hierarchy: 0D vertex-pinned disruptions (baryons), 1D edge-propagating disruptions (heavy lep- tons), internal void disruptions (light leptons), 2D face-radiated disruptions (dark matter), and bulk saturation (Higgs). The proton (|τ |+1)|τ |2 −dim(τ )|τ |= 1836 me (0.008%), the tau 2|τ |·|τ |2 = 3456 me (0.6%), the kaon |τ |3/2 + |τ |2 −dim(τ )|τ |= 972 me (0.2%), and the muon |τ |3/(2τi) −|τ |= 204 me (1.3%) all emerge with zero free parameters. The Higgs (|τ |5 ≈127 GeV, 1.5%) is the maximum entanglement capacity before the network ruptures. The lattice Laplacian provides a natural UV cuto at |τ |+ τi = 16. The mass spectrum is not a set of arbitrary inputs but a tower of entanglement harmonics on a single discrete structure.