The Quantum Five-Sphere: Particle Masses, Forces, and the Foundations of Quantum Mechanics from Torsional Eigenmodes on S⁵

Two integers determine everything. From d = 3 spatial and D = 4 spacetime dimensions, the angular manifold S⁵ generates the complete particle spectrum, all coupling constants, the mixing matrices, the gravitational constant, the Hubble rate, the baryon asymmetry, and the cosmological constant — spanning 45 orders of magnitude with zero free parameters. Particles are eigenmodes of torsional operators on S⁵. Their masses follow m/mₑ = (2j₁+1) (2j₂+1) ·πᴮ, where (j₁, j₂) label representations of SO (3) ×SO (3) and B is a torsional radius derived from SO (6) branching rules. This reproduces all 17 Standard Model masses with mean error 0. 71%. The fine structure constant follows as 1/α = 4π³+13 (0. 008%), the Weinberg angle as sin²θW = 3/13 (0. 19%), and the strong coupling as αₛ = 2/17 (0. 2%). The CKM and PMNS mixing matrices, including CP-violating phases, are derived from torsional holonomy. At the gravitational scale, the Planck mass is MP = mₑ·π⁴⁵ (1. 5%), the Hubble rate is H₀ = αG·ωₚ·ε¹⁸ = 67. 5 km/s/Mpc (0. 1%), and the cosmological constant hierarchy 10⁻¹²³ decomposes as π⁻¹⁸⁰·ε¹⁶⁸. The S⁵ spectrum is provably closed — no dark matter particles exist — and the phenomena attributed to dark matter arise from gravitational response. The strong CP problem is dissolved (θ = 0 from the parity of S⁵), proton decay is suppressed to ~10⁴⁹ years, and the arrow of time follows from ε-relaxation irreversibility. The foundations of quantum mechanics — quantization, uncertainty, wave–particle duality, measurement — are theorems of S⁵ geometry. This paper is the ultraviolet completion of the companion TOR cosmology paper (Zenodo, 2026), which validates the infrared predictions against supernovae, galaxy rotation curves, and the CMB. Together with the Response Wells paper on black holes and the Eddington number, the three papers constitute a complete theory spanning from quantum measurement to cosmological structure. // v2: Corrected energy scale description in abstract. Minor clarifications to Sections 28 and 31