Quantum Self-Verification Geometry (QSVG): A Unified Geometric Framework for Fundamental Physics

Authors: Luis Morató de Dalmases
Date: March 2026
DOI: https://doi.org/10.5281/zenodo.18924002
Keywords: quantum gravity, discrete spacetime, Riemann hypothesis, fine-structure constant, dark energy, cosmic birefringence, proton decay
License: CC BY 4.0

Abstract

Quantum Self-Verification Geometry (QSVG) is a first-principles framework in which spacetime is modeled as a discrete tetrahedral lattice in hyperbolic space, characterized by the Coxeter group {3,3,5} (the 600-cell). The theory is built upon a single fundamental geometric constant: the angular defect of 6.8 degrees, which arises uniquely from the condition that four tetrahedra meet at each edge while forming a hypercubic structure.

This compendium presents the complete mathematical derivation of all fundamental physics from this geometric foundation:

• Mathematical Foundations: The angular defect connects to the fractal dimension of the Coxeter group, unified by a precise mathematical relation. The CronNet scale of approximately 0.001 eV emerges from the spectral gap of the self-verification operator.

• Riemann Hypothesis: The CronNet-Holo operator has a spectral determinant that equals the completed Riemann zeta function, proving that all non-trivial zeros of the Riemann zeta function lie on the critical line. Numerical verification on the prime-cycle graph matches the first 1,000 zeros to within one millionth.

• Fundamental Constants: The fine-structure constant emerges from the Hopf fibration of the Coxeter group, matching the experimental value to within four ten-millionths. Newton's constant yields the observed value.

• Particle Physics: The 16 tesseracts of the Coxeter group provide a complete basis for all forces and matter. The strong coupling matches the experimental value. The CKM matrix hierarchy follows from tesseract overlaps with simple integer coefficients. The Jarlskog invariant matches experiment.

• Electroweak Sector: The Higgs field emerges as chronion density with a vacuum expectation value of 227 GeV and a Higgs mass of 123 GeV. The Holonomy Condensation Mechanism gives the W boson mass of 76 GeV, with predicted high-energy coupling deviations following a power law.

• Cosmology: Dark energy arises from the 36-degree icosahedral phase with instanton suppression, yielding the observed cosmological constant. Cosmic birefringence follows a precise power law with multipole moment.

• Gravitational Waves: The tensor-to-scalar ratio is predicted and testable by LiteBIRD in 2027. Primordial black holes have quantized spin.

• Experimental Roadmap: The framework makes falsifiable predictions including muonium hyperfine splitting of 35 Hz, a proton lifetime of 9×10³⁴ years with specific branching ratios, and scale-dependent cosmic birefringence.

All derivations proceed from first principles with no free parameters beyond the fundamental angular defect of 6.8 degrees. The theory unifies quantum gravity, particle physics, cosmology, and number theory into a single coherent geometric framework, with all predictions testable within the coming decade.

Description

Complete Contents of the Compendium

This repository contains the complete formulation of Quantum Self-Verification Geometry (QSVG), organized into six main parts with a thematic numbering system designed for clarity. All original files are listed with their new identifiers.

PART 0: THE CORE FOUNDATIONS

The essential documents that define the theory.

1. 0.1. Quantum Self-Verification Geometry (QSVG) Physical Theory.pdf                                                                              QSVG Physical Theory: The Architecture of Spacetime. A general presentation of the theory, including topological foundations, gauge structures, the electroweak sector, fundamental constants, cosmology, and gravitational waves. Establishes how the discrete tetrahedral lattice gives rise to all observed physical phenomena.
2. 0.2 QSVG Technical Appendices.pdf.                                                                                                                                      QSVG Technical Appendices: The Mathematical Core. Detailed mathematical development across seven sectors, including geometric foundations, quantum graphs, the spectral proof of the Riemann Hypothesis, particle generation, cosmology, topological unification, and experimental validation.
3. 0.3 The QSVG Fundamental Interactions Atlas.pdf.                                                                                                               The QSVG Fundamental Interactions Atlas: The Unification of Forces. Complete derivation of each fundamental force from geometry: electromagnetism (from Hopf fibrations), gravity (from the QSVG operator), the strong force (from color tesseracts), and the weak sector (from the Holonomy Condensation Mechanism).
4. 0.4 The QSVG Experimental Roadmap and Predictions.pdf.                                                                                                The QSVG Experimental Roadmap: The Path to Validation. A detailed guide to all falsifiable predictions, including muonium hyperfine splitting, primordial black hole spin, proton decay modes, cosmic birefringence, and a timeline for near-term experiments (2027-2030).
5. 0.5 Complete Derivatives Appendix.pdf.                                                                                                                                 Complete Derivatives Appendix: The Calculus of Geometry. Step-by-step calculus, Hessian matrices, and critical point analysis for the U(1) and SU(2)xU(1) potentials, providing the mathematical backbone for the electroweak symmetry breaking mechanism.

PART I: GEOMETRIC FOUNDATIONS

The basis of everything: where the 6.8° number comes from and how spin behaves.

I.1. Annex 0 - Derivation of the Effective Angular Defect from the 600-cell.pdf.                                                                          Derivation of the Angular Defect δ₀ ≈ 6.8° from the 600-cell. A rigorous demonstration of how the condition that four tetrahedra meet at each edge in a hypercubic structure forces an angular defect of 6.8 degrees, the fundamental constant from which all physics emerges.

I.2. Annex 1 - Geometric Structure of Spin Riemann Zeros, Quaternion Groups, and Prime-Number Phases.pdf.                    Geometric Structure of Spin: Riemann Zeros, Quaternion Groups, and Prime-Number Phases. Explores how spin emerges as a geometric phase when traversing the lattice, connecting quaternion groups with the structure of prime numbers and the zeros of the Riemann zeta function.

I.3. Annex 2 - Spin Correlation Derivation Static approximation of the {3,3,5} lattice and the hadronization scale.pdf.  Spin Correlation Derivation: Static Approximation of the {3,3,5} Lattice and the Hadronization Scale. Derivation of the spin correlation function along the lattice, which determines the hadronization scale (~200 MeV) and the statistical behavior of accumulated geometric phases.

PART II: THE BRIDGE TO NUMBER THEORY

The heart of the Riemann Hypothesis proof.

II.1. Annex18 Holonomy-600-cell-Gauss-Sum-L-functions.pdf.                                                                                                     Holonomy, Gauss Sums, and Dirichlet L-functions: The Arithmetic of the 600-cell. Demonstrates that the holonomy of a cycle of length p in the 600-cell can be expressed as a Gauss sum, connecting it to Dirichlet L-functions and establishing the bridge between geometry and prime numbers.

II.2. Annex19 Geometric-Harmonization_600-Cell-RiemannZ.pdf.                                                                                          Geometric Harmonization: The Golden Ratio and the Riemann Zeros. Harmonizes the geometric parameters of the 600-cell (defect, fractal dimension) using the golden ratio (φ⁻²), converting the approximation θ_p ≈ log p / p into an exact identity that proves the Riemann Hypothesis.

PART III: PHENOMENOLOGY AND PREDICTIONS

How the geometry manifests in experiments and materials.

III.1. Annex 3 - QSVG-Lattice and the STAR Experiment Proof of the transfer tensor Jij and the topological spin superconductor vacuum.pdf.                                                                                                                                                              QSVG-Lattice and the STAR Experiment: Proof of the Transfer Tensor J_ij. Proof of the existence of the transfer tensor J_ij in the lattice, predicting a topological spin superconductor vacuum with potential signatures in STAR experiment data.

III.2. Annex 4 - Complete Geometric Derivation of the 12.8 THz Universal Synchronization Frequency.pdf.                    Complete Geometric Derivation of the 12.8 THz Universal Synchronization Frequency. Derivation of the 12.8 THz universal synchronization frequency from the geometry of the 600-cell, a direct signature of the "chronion" mass scale.

III.3. Annex 5 - Experimental Proposal for 12.8 THz Pulsed EPR protocol using CaF2-Mn2p to detect chronion mass scales.pdf.                                                                                                                                                                                  Experimental Proposal for 12.8 THz: Pulsed EPR Protocol using CaF₂:Mn²⁺.A detailed experimental protocol to detect the 12.8 THz frequency using pulsed electron paramagnetic resonance in CaF₂ crystals doped with Mn²⁺.

III.4. Annex 9 - Triple Convergence Alignment of ETH Zurich-MIT experimental data with {3,3,5} geometric parameters.pdf.                                                                                                                                                                                  Triple Convergence: Alignment of ETH Zurich/MIT Experimental Data with {3,3,5} Parameters. Analysis of experimental data from ETH Zurich and MIT that converges with the geometric parameters of the 600-cell, providing an initial empirical validation of the theory.

III.5. Annex 10 - Emergent Lorentz Invariance Corrected photon dispersion relations and astrophysical constraints (GRB-TeV astronomy).pdf.                                                                                                                                                                            Emergent Lorentz Invariance: Corrected Photon Dispersion Relations. Demonstrates how Lorentz invariance emerges at large scales despite spacetime discretization, with subtle corrections to photon dispersion that could be detectable in TeV astronomy.

III.6. Annex 14 - Geometric Correspondence Mapping the 600-Cell to Kagome Lattice Motifs for quantum materials.pdf. Geometric Correspondence: Mapping the 600-Cell to Kagome Lattice Motifs. Establishes a correspondence between the 600-cell geometry and Kagome lattice motifs, opening the door to realizing the theory in laboratory quantum materials.

PART IV: ENGINEERING AND PROPULSION

Practical applications: force generation and thermodynamics.