What question did this study set out to answer?

The aim is to present a cohesive framework for Inverted Hypersphere Cosmology derived from a single axiom.

May 2, 2026Open Access

Inverted Hypersphere Cosmology - 15 part Monograph

Key Points

The aim is to present a cohesive framework for Inverted Hypersphere Cosmology derived from a single axiom.
Collection of 15 papers organized logically from foundational concepts to experimental predictions.
Derivation of various cosmological and physical constructs based on projective four-space topology.
Inclusion of a complete Lagrangian and unified bibliography.
Cosmological constants and mass spectra are calculated with high precision, showing minimal error.
New signals for dark energy are predicted, changing approaches to cosmological tension problems.
Gauge group structure and particle masses derived from geometric principles demonstrate robustness.

Abstract

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: rₛ = 153. 2 Mpc (CAMB/Planck: 147. 78 Mpc) • Cosmological constant problem resolved via geometric seesaw: ρ_Λ² = ½ ρUV |ρIR| • 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: ΛQCD = 305 MeV (8% from PDG) • Strong-CP problem resolved: RP⁴ topology forces θQCD = 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: sin²θW = 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.

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