Inverted Hypersphere Cosmology: 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 observation: if the pre-collapse universe is invariant under spatial inversion x ~ -x, the unique free orthogonal involution of S4 forces the underlying manifold to be RP4 = S4/Z2.

From the S4 harmonic spectrum, the Z2 identification selects N = 33 nested toroidal shells through the Fibonacci self-termination condition d(S4, 4) = 55 = F10. This fixes the complete IHC structure with no free parameters. The main results are:

(1) The UV-IR Casimir seesaw gives Omega_Lambda = sqrt(1262/270*pi^2) = 0.6882, agreeing with Planck 2018 (0.6847 ± 0.0073) at 0.48 sigma. A second independent route gives 0.6889; the 0.10% agreement between two structurally independent derivations is a non-trivial internal consistency check.

(2) Against 33 BAO measurements from seven surveys (z = 0.106 to 2.33), the framework achieves chi^2/n = 0.916 versus LambdaCDM's 1.196, with zero parameters fitted to data and Bayesian evidence ln B = +4.76.

(3) The Weinberg angle sin^2(theta_W) = 3*phi^-1/8 = 0.23176 follows from the 24-cell structure. All six quark masses and three charged lepton masses are predicted with RMS deviation 0.24% from PDG.

(4) The proton-to-electron mass ratio mp/me = 4 x 27 x 17 = 1836 (0.008%) and neutron-proton mass difference 1.289 MeV (-0.34%) follow from the same chain spectrum.

(5) The RP4 topology forces theta-bar_QCD = 0 exactly, resolving the strong-CP problem without an axion.

(6) SO(10) is derived from RP4 geometry. The complete breaking chain SO(10) -> SO(5) x SO(5) -> SM is geometrically fixed: k_PS = M(N_co+1) = 253, giving E_PS ~ 1.1 x 10^11 GeV; broken generators = 45 - 12 = 33 = N; and sin^2(theta_W)(M_Z) = sin^2(theta_W)(E_GUT) x phi^-1 exactly from phi^2 = phi + 1 alone.

(7) The electron mass is derived: me/mP = phi^-78 x 33^-4 x e^-alpha (0.001%), where alpha is itself determined geometrically by the k = 8 shell. The only external input is the Planck mass.

(8) Two Wolfenstein CKM parameters are derived: lambda = |V_us| = sqrt(m_d/m_s) = 0.22356 (0.64%); A = beta_coh/6 - 1/6 = B_had + 1/|Z3| = 0.82402 (0.24%), giving |V_cb| = A*lambda^2 = 0.04118 (0.94%). The same cos(pi/23) chain structure that controls the neutron-proton mass difference also fixes |V_cb|.