The Torsional Manifold: A Parameter-Free Unification of Particle Physics and Cosmology from the Geometry of S⁵

A complete derivation of the Standard Model particle spectrum, coupling constants, mixing matrices, and cosmological parameters from two integers (d=3, D=4) and three constants (π, e, mₑ). The Theory of Relational Reality (TOR) proposes that all physics emerges from torsional relaxation on a five-dimensional sphere S⁵ = S^ (d+D−2), governed by a single fractal iteration law. From this seed, the monograph derives: all 17 Standard Model particle masses (0. 028% mean error after aging corrections) ; the fine structure constant 1/α = 4π³+13 (0. 0002%), the Weinberg angle sin²θW = 3/13 (0. 002%), and the strong coupling αs = 2/17 (0. 006%) ; the complete CKM matrix (1. 3% mean) and PMNS matrix (1. 9% mean) from torsional overlap integrals; three neutrino masses; the Higgs vacuum expectation value (1. 0%), self-coupling (2. 3%), and a geometric resolution of the hierarchy problem; Z and W boson widths at one loop (0. 07% and 0. 18%) ; the Hubble constant H₀ = 67. 5 km/s/Mpc (0. 1%) ; the cosmic energy budget Ωm = 1/3, ΩΛ = 2/3 from Ricci curvatures; the baryon fraction Ωb = e⁻³; the CMB temperature and TT power spectrum peaks; and galaxy rotation curves for 153 SPARC galaxies with zero free parameters. Colour confinement is derived as a geometric selection rule (only modes complete across d=3 spatial dimensions freeze), the arrow of time as the direction of torsional relaxation, dark matter absence as gravitationalmemory on S⁵, and electroweak symmetry breaking as torsional freezing of the internal SO (3). Empirical validation against Pantheon+ supernovae (Δχ² = −6. 2 vs ΛCDM), five weak lensing surveys (S₈ tension resolved), and Planck CMB data is presented. The framework spans 31 orders of magnitude of mass with zero free parameters. // V 2. 0 - No content change, fixed cropped tables.