Spectral Geometry of the Poincaré Homology Sphere: Particle Structure, Gauge Symmetry, and the Proton–Electron Mass Ratio from S³/2I

The Poincaré homology sphere S³/2I — the quotient of the 3-sphere by the binary icosahedral group of order 120 — is shown to encode the structure of the four stable particles, the SU(3) gauge group, and the proton–electron mass ratio within a single geometric framework. The Zoll S³ commitment, made independently for cosmological reasons, produces the following results without additional assumptions: (1) de Rham cohomology H^k(S³) assigns four stable particles to the four form degrees, with Poincaré duality enforcing exact charge equality between proton and electron; (2) ℤ-valued cohomology groups guarantee baryon and lepton number conservation as topological invariants; (3) the proton (0-form) is necessarily…