The Central Theorem: From Foam to the Standard Model

We state and assemble the framework's central claim: the continuum limit of the torsion-weighted face Laplacian action S = 2 Σ ψ†L_Tψ on the BCC lattice of truncated octahedra is the Standard Model coupled to general relativity, with gauge group SU(3)×SU(2)×U(1), three fermion generations, one Higgs doublet, and all parameters determined by the seven cell integers {V, E, F, |O_h|, C_A, Δ, d} = {24, 36, 14, 48, 3, 17, 3}. The argument proceeds in five steps: gauge kinetic terms from the 24 triangles and 42 four-cycles of the face graph; the Dirac equation from T₁u Wilson fermions; Yukawa couplings from the torsion cross-block T₂₁ = 2U; spontaneous symmetry breaking forced by the A₂u T_hex charge −1; and uniqueness of the continuum limit from asymptotic freedom with irrelevant O_h artefacts. Symanzik-style matching gives corrections scaling as (E/M_P)² ~ 10⁻³⁵, numerically negligible. Status is declared precisely: the individual step-lemmas are theorem-strength and cite their proofs; the composite five-step statement is a proof-sketch pending external audit. Changes in version 2.0: torsion operator citations are corrected per Paper #57 v2.0 (the A₂u charge −1 belongs to T_hex, the hexagonal-subgraph operator, not to the inter-type operator T, which annihilates A₂u; Sections 4.2 and 5.1 updated, no numerical results change), and the status field is clarified: the composite five-step statement is a proof-sketch pending external audit, while the individual step-lemmas remain theorem-strength. Corrections are machine-verified in verify_FtF_audit_2026-07.py in the repository.