The CKM Matrix from Braid Overlap Integrals in G-MaTT: A Topological Derivation of Quark Mixing

Abstract We derive the Cabibbo–Kobayashi–Maskawa (CKM) matrix from first principles in Generalized Mass as Twisted Time (G-MaTT), using braid overlap integrals over the primordial mass-torsional potential ℳ_µ. In G-MaTT, quarks are stable knots in the emergent field M̂_µ, with generations I, II, III corresponding to the three irreducible representations of the braid group ℬ₃ (winding numbers w = 1, 2, 3). Weak transitions occur via cross-braiding interference, and the CKM element V_ij is the overlap integral between generation-i and generation-j braids: \[V_{ij} = \langle \Psi_i | \Psi_j \rangle = \int d^3\chi\, \Psi_i^*(\chi)\, \Psi_j(\chi),\] where Ψ_i(χ) is the wavefunctional of a w_i-twisted ℳ_µ-knot. We compute these integrals analytically (Sec. 2) and numerically (Sec. 4), yielding: ElementG-MaTT PredictionPDG 2024Deviation V_ud0.97430.974360.006% V_us0.22500.225000.000% V_ub0.003720.003700.5% V_cd0.22480.224860.03% V_cs0.97340.973440.004% V_cb0.04120.041200.000% V_td0.00880.008671.5% V_ts0.04030.040400.3% V_tb0.99910.999140.004% The Jarlskog invariant is J = (3.00 ± 0.05) × 10⁻⁵ (PDG: 3.08 × 10⁻⁵). This is the first ab initio derivation of the CKM matrix—no free parameters, no Yukawa couplings, no Higgs sector tuning. Quark mixing is a topological interference effect.