Quantum Self-Verification Geometry (QSVG)

Quantum Self-Verification Geometry (QSVG) Metadata Title: Quantum Self-Verification Geometry (QSVG): A Unified Geometric Framework for Fundamental Physics Authors: Luis Morató de Dalmases Date: March DOI: https://doi.org/10.5281/zenodo.18827384 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. 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 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 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 GeV and Higgs mass of GeV. The Holonomy Condensation Mechanism gives the W boson mass of 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 Hz, proton lifetime of times to the 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 Contents of the Compendium This repository contains the complete formulation of Quantum Self-Verification Geometry (QSVG), organized into four main documents: 1. Quantum Self-Verification Geometry: Physical Theory A general presentation of the theory, including topological foundations, micro-scale demonstrations, gauge structures, electroweak sector, fundamental constants, cosmology, and gravitational waves. This document establishes how the discrete tetrahedral lattice structure gives rise to all observed physical phenomena. 2. QSVG Technical Appendices Detailed mathematical development in seven sectors: Sector I: Geometric and topological foundations: rigorous derivation of the 6.8-degree angular defect from the hyperbolic tessellation, the fractal dimension, and their fundamental relation. Sector II: Quantum graphs and emergent symmetries: how the speed of light emerges from Lieb-Robinson bounds, the Dirac operator on graphs, and the prime-cycle graph connecting to number theory. Sector III: Spectral proof of the Riemann Hypothesis via the CronNet-Holo operator, including numerical verification to high precision. Sector IV: Particle generation: derivation of the periodic table up to element 118, the CKM matrix, and the unified origin of matter, antimatter, and dark matter. Sector V: Cosmology: dark energy as a dynamical cosmological constant, cosmic birefringence from torsion, and dark matter as frozen torsion. Sector VI: Topological unification and gravitational waves: the Conway knot as origin of primordial gravitational waves, emergent GHZ correlations, and black holes as temporal hubs. Sector VII: Experimental validation and summary: comparison with current data from Planck, DESI, JWST, LIGO, and other observatories. 3. The QSVG Fundamental Interactions Atlas Complete derivation of each fundamental force: Electromagnetism: The photon as specific tesseract modes, the fine-structure constant from the Hopf fibration, Maxwell's equations from geometry. Gravity: The graviton as a tesseract mode, Einstein-Cartan equations from the QSVG operator, Newton's constant derived from geometry. Strong Force: Color tesseracts providing SU(3) symmetry, the strong coupling constant matching experiment. Weak Sector and Higgs: Mass as temporal frequency curvature, the Holonomy Condensation Mechanism for gauge boson masses. Unification: The tesseracts as a complete basis for all forces and matter, the grand unification scale of approximately to the GeV. 4. The QSVG Experimental Roadmap and Predictions Falsifiable predictions for near-term experiments: Muonium Hyperfine Splitting: A shift of Hz in the 4.46 GHz transition, testable by the MuSEUM experiment at J-PARC within 3-5 years. Neutrino Masses and Mixing: Mass scale in the milli-eV range, normal hierarchy, with a roadmap for deriving exact mixing angles. Primordial Black Hole Spin: Quantized spin of 0.068, testable by LIGO, Virgo, KAGRA, and future observatories through black hole merger observations. Proton Lifetime: Lifetime of times to the years with specific branching ratios: electron-pion mode at percent, muon-pion at percent, electron-kaon at percent, and neutrino-pion at percent. Testable by Hyper-Kamiokande starting in 2027. Cosmic Birefringence: Scale-dependent polarization rotation following a power law with multipole moment, with amplitude of approximately 0.04 degrees at multipole 100. Directly testable by the LiteBIRD mission scheduled for 2027-2030. Key Achievements The QSVG framework demonstrates that: Spacetime is fundamentally discrete, composed of tetrahedral cells A single geometric constant of 6.8 degrees determines all physics The Riemann Hypothesis is proven as a geometric necessity All fundamental constants are derived, not assumed The periodic table naturally ends at element Dark energy and dark matter have geometric origins Black holes have no singularities, forming Planck stars instead Proton decay is predicted with specific, testable rates and modes Cosmic birefringence follows a precise power law All predictions are falsifiable within the coming decade Acknowledgements The author thanks the members of the CronNet Holo Initiative for discussions that made this work possible, and acknowledges the mathematical contributions that resolved the open questions in the original formulation. Recommended Citation Morató de Dalmases, L. (2026). Quantum Self-Verification Geometry (QSVG): A Unified Geometric Framework for Fundamental Physics. Zenodo. https://doi.org/10.5281/zenodo.18827384