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Published April 9, 2026 | Version 1.0
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Inverted Hypersphere Cosmology: Subatomic Structure from RP4 Topology

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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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Alternative title (English)
Inverted Hypersphere Cosmology

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Preprint: 10.5281/zenodo.19135785 (DOI)