Inverted Hypersphere Cosmology - 15 part Monograph

This monograph collects the complete fifteen-paper Inverted Hypersphere Cosmology as of the current version date.

Figures are not included in this version

(IHC) series into a single volume, organised for logical flow from foundational 

axiom to experimental predictions.

The entire framework derives from one axiom: the pre-geometric state is a 

non-preferential void — no direction, scale, or configuration is preferred. 

This single requirement uniquely selects real projective four-space 

(RP⁴ = S⁴/ℤ₂) as the topology of the universe, with no additional assumptions 

and zero free parameters.

From this axiom alone, the following are derived in full:

COSMOLOGICAL SECTOR

• Dark energy density: Ω_Λ = 0.6889 (Planck 2018: 0.6847 ± 0.0073)

• BAO sound horizon: r_s = 153.2 Mpc (CAMB/Planck: 147.78 Mpc)

• Cosmological constant problem resolved via geometric seesaw: 

  ρ_Λ² = ½ ρ_UV |ρ_IR|

• H₀ tension addressed through RP⁴ shell-crossing at z = 0.754

• DESI DR2 dynamical dark energy signal predicted as topological shell 

  crossing, not phantom crossing

• Friedmann equations derived from RP⁴ topology (not assumed as input)

STANDARD MODEL MASS SPECTRUM

• Charged lepton masses (e, μ, τ) to < 0.06% with zero free parameters

• Proton/electron mass ratio: 4 × 27 × 17 = 1836 (0.008% from observed)

• Neutron–proton mass difference: 1.289 MeV (0.34% from observed)

• Complete quark mass spectrum from φᵏ shell hierarchy

• QCD confinement scale: Λ_QCD = 305 MeV (8% from PDG)

• Strong-CP problem resolved: RP⁴ topology forces θ_QCD = 0 exactly

GAUGE STRUCTURE

• Gauge group SO(10) derived as a mathematical consequence of RP⁴ topology

• Three fermion generations from ℤ₃ triality of SO(8)

• Weinberg angle: sin²θ_W = 3φ⁻¹/8 = 0.23176 (PDG: 0.23122)

• Fine structure constant: α⁻¹ = 137.036 (error 3.5 × 10⁻⁸)

• Base-24 arithmetic identified as the natural language of IHC

The monograph is structured in five parts:

  Part I — Foundations (Prequel, GR derivation, Companion Proofs)

  Part II — Cosmological Structure (Papers I–III, DESI)

  Part III — Gauge Structure and Unification (GUT, Base-24)

  Part IV — Standard Model Mass Spectrum (Papers IV–VII)

  Part V — Synthesis (Complete Lagrangian, Unified)

All 15 papers are included at full length with a unified bibliography 

(112 entries). The complete Lagrangian and a unified single-paper summary 

are included as the final two chapters.