Inverted Hypersphere Cosmology. Unified paper: Cosmological and Standard Model Parameters from a Single Topological Constraint

The cosmological constant problem, the fermion mass hierarchy, and the strong-CP problem are three of the deepest unsolved puzzles in theoretical physics. We present a framework that addresses all three from one geometric starting point: the CPT-invariant de Sitter vacuum is the unique self-consistent ground state with no external reference frame, and the Z2 CPT identification forces the underlying manifold to be RP4 = S4/Z2 — a theorem of QFT on curved spacetime.

The 55 spectrally stable modes at harmonic degree l=4 distribute equally across the 5 embedding directions of R5 — the same non-preferential principle that forces RP4 — giving M=55/5=11, N=3M=33 nested toroidal shells. This fixes the complete IHC structure with no free parameters. The main results are: (1) Ω_Λ = 0.6882 from the UV–IR Casimir seesaw, confirmed to 0.10% by an independent chain eigenspectrum route; (2) against 33 BAO measurements from seven surveys, χ²/n = 0.916 versus ΛCDM's 1.196, with Bayesian evidence ln B = +4.76; (3) the Weinberg angle sin²θ_W = 3φ⁻¹/8 from the 24-cell; all six quark masses and three charged lepton masses with RMS deviation 0.24% from PDG; (4) the proton-to-electron mass ratio 1836 (0.008%) and neutron–proton mass difference 1.289 MeV; (5) θ_QCD = 0 exactly, resolving the strong-CP problem without an axion; (6) w_Λ = −1 exactly and Ω_K = 0 exactly, ruling out dynamical dark energy; (7) the electron mass m_e/m_P = φ⁻⁷⁸ × 33⁻⁴ × e⁻ᵅ to 0.001%, where α is itself determined by the k=8 shell.

The complete logical inventory distinguishes starting points (CPT theorem), theorems (8, including N=33 from non-preferential collapse), identifications (2), derived results (14), and falsifiable predictions (5).