The Triadic Knot: Zero-Parameter Derivation of the CKM Matrix, Quark Confinement, and Fractional Charge from Torus Knot Topology on S³

We derive confinement, color charge, fractional electric charge, the CKM mixing hierarchy, the restriction to exactly two matter sectors, and the within-generation quark mass ratios from the topology of T (3, q) torus knots on S³ via the Hopf fibration, with zero free parameters. Companion paper to the PMNS derivation (doi: 10. 5281/zenodo. 19010631). The CKM matrix elements are derived from the Cantor sieve transition probability: |Vᵤs| = 2/9 (1. 4%), |Vcb| = 10/243 (0. 9%), |Vᵤb| ≈ 0. 00381 (0. 2%). The CP-violating phase δCKM = 3π/8 = 67. 5° (0. 45σ). Within-generation quark mass ratios follow from triadic activation of R = Ψ × I × P ≠ 0. Twenty predictions from two empirical inputs at 0. 1–8% accuracy. Keywords: CKM matrix, quark confinement, torus knots, Hopf fibration, S³ topology, PMNS matrix, Cantor set, Hausdorff dimension, Wolfenstein parameters, CP violation, color charge, fractional charge, three generations, CAT'S Theory, triadic invariant, Pattern Intent Presence, zero free parameters, Chern-Simons, 369 invariant, XOR