A Zero-Parameter Derivation of Standard Model Parameters, Cosmology, and Planck-Scale Gravity from Torus Knot Topology on T³

The Standard Model of particle physics contains twenty-five empirical parameters (three gauge couplings, six quark masses, three charged lepton masses, three neutrino masses, four CKM mixing parameters, four PMNS mixing parameters, the Higgs mass, and the Higgs vacuum expectation value), none of which are predicted by the theory itself. General relativity introduces two further independent constants, the gravitational coupling and the cosmological constant; the latter represents the most severe theory-observation discrepancy in physics, at one hundred and twenty orders of magnitude. The Unified Quantum Gravity Architectural Framework (UQGAF) previously derived the Standard Model mass spectrum and the gravitational coupling from a single topological structure: coprime torus knots T (P, Q) embedded on a three-torus vacuum manifold T³, together with the manifold constant 2π². We demonstrate here that the remaining independent parameters of the gauge, flavour, lepton, and cosmological sectors are determined by the same structure. The electroweak mixing angle is derived as the ratio of W and Z meridional winding numbers, sin²θW = 3/13, matching experiment to 0. 19%. The strong coupling at the Z-pole is the cross-ratio of light-quark integers, αₛ (MZ) = 484/4117, matching to 0. 37%. The CKM CP-violating phase follows as δ = π/2 − 4αₛ, yielding the Jarlskog invariant to 0. 11%. The three PMNS mixing angles emerge from a single axiom, the neutrino inter-generational ratio n_ν = 5, and lie within 0. 33σ of experiment. Quark confinement is derived as a theorem from the Z₅ symmetry of the three-generation neutrino vacuum. A covariant gravitational action with a constrained aether field and a single scalar reproduces the cosmological constant to 1. 7%, the MOND acceleration scale to 0. 20%, the post-Newtonian parameters γPPN = βPPN = 1 exactly, and the gravitational-wave speed cGW = c exactly. Tree-level collider observables, including Z and W partial widths, the total Z width, and the MW/MZ mass ratio, are reproduced at sub-percent to few-percent precision from the same topological inputs. The framework resolves the cosmological constant hierarchy structurally, through a topological scale suppression of 10⁻¹²², and provides an emergent-spacetime ultraviolet completion below the Planck length that resolves the non-renormalisability of continuum quantum gravity. All predictions are obtained with zero free parameters.