CAT'S Theory — Zero-Parameter Derivation of the PMNS Matrix from Torus Knot Topology on S³

We derive all four independent parameters of the Pontecorvo–Maki–Nakagawa–Sakata (PMNS) neutrino mixing matrix from the topology of torus knots on S³ via the Hopf fibration, with zero free parameters. Charged leptons are identified with T(2,q) torus knots (q ∈ {3,5,7}); neutrinos with their mirror knots T(2,q)*. The resulting predictions — sin²θ₁₂ = 7/22, sin²θ₂₃ = 35/62, sin²θ₁₃ = 1/45, δ_CP = 9π/8 = 202.5° — all fall within 1σ of current global fits, with δ_CP within 0.2σ of the PDG central value. The charged-lepton mass formula m(2,q)/mₑ = [(q²−4)/5]^(26/7) reproduces the muon mass to 0.13% and the tau mass to 0.72% with zero free parameters. The mass scaling exponent n = 26/7 is derived independently via four convergent routes: the spectral zeta function of the Dirac operator on S³, triadic dimensional counting, bosonic string critical dimension, and the QCD β-function coefficients for SU(3) with six flavors. These four routes are four projections of the same geometric object. Falsifiable predictions include normal neutrino mass ordering and a gravitational wave signature at 8.37 Hz (T(2,7) tau ŕ) within the projected sensitivity of the Einstx̌x̌ein Telescope.