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Inverted Hypersphere Cosmology: Subatomic Structure from RP4 Topology

Authors: Peacock, Samuel; Hall, Lauren;

Inverted Hypersphere Cosmology: Subatomic Structure from RP4 Topology

Abstract

We extend the Inverted Hypersphere Cosmology (IHC) series into the subatomic sector, deriving five results with zero free parameters beyond the IHC mass axiom m(k) = m_e × phi^k. First, the proton-to-electron mass ratio is derived as m_p/m_e = Z2^2 × Z3^3 × k_tau = 4 × 27 × 17 = 1836, matching the observed value to 0.008%. All three factors are independently derived from RP4 topology: Z2^2 = 4 from the spatial and colour-phase antipodal boundary conditions, where the colour-phase factor follows from the chain reflection j → 23−j swapping colour classes R and B and sending epsilon^{RGB} → −epsilon^{RGB}; Z3^3 = 27 from SO(8) triality; and k_tau = 17 as the unique odd Class-B shell in the lepton spectral bracket [k_mu, k_4th] = [11, 23], confirmed as the fixed point of the spectral involution k → 34−k. The leading-order QED correction Delta = 8*alpha*phi^2 = 0.15284 m_e is derived from the 8 Class-G self-dual modes of the 22-site co-rotating chain (0.11% from observed). Second, the strong-CP problem is resolved topologically: on RP4 = S4/Z2 the antipodal map reverses orientation, forcing the Pontryagin index Q = integral(Tr(F wedge F)) = 0 for all gauge field configurations. This predicts theta_QCD = 0 exactly, d_n = 0, and the absence of the axion without any new fields. Third, the Z3 triality of SO(8) accommodates three quark colours; quark masses follow the same phi^k hierarchy as leptons with the up quark at k=3 to 0.2% and isospin doublet spacings Delta_k in {2, 5, 7} — all Fibonacci-related integers. Fourth, the QCD confinement scale is derived as Lambda_QCD = Z3 × m_e × phi^M = 305 MeV (8% from PDG), where M=11 is the Hopf factor. Fifth, the CMB temperature parity ratio R_TT = [(6pi−1)/(6pi+1)]^2 = 0.8086 is derived from RP4 antipodal geometry with Z3 suppression, agreeing with Planck 2018 at 0.05 sigma. The integer 23 = N_co + 1 is the common origin of the cosmological constant (via beta_coh = 6cos(pi/23)), the proton mass (via the colour-phase reflection j → 23−j), and the fourth-generation lepton prediction (k_4th = 23).

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