Complete Rigorous Proof of the Riemann Hypothesis Via Self-Adjoint Dirac Operators and 600-cell Holonomy Based on the QSVG Framework by Lluís Morató de Dalmases

Publication Date:07-03-2026 Title:Complete Proof of the Riemann Hypothesis: Dirac Operators and the Holonomy of the 600-Cell Authors:Lluís Morató de Dalmases (CronNet Holo Initiative) Description:This record contains the complete, rigorous proof of the Riemann Hypothesis (RH) and its generalization (GRH). The proof is based on the construction of a self-adjoint Dirac-type operator whose spectral properties are governed by the intrinsic geometry of the 600-cell ({3,3,5}), a regular 4-dimensional polytope. We present the proof across two complementary documents: The Core Mathematical Proof: It defines the operator D = sum_p (log p) σ_x T_p + T_p^† on the Hilbert space H = ℓ²(N) ⊗ C². Three critical results are proven: Compactness of the Resolvent: A confining potential derived from the 600-cell's angular defect δ₀ ≈ 6.8° guarantees a purely discrete spectrum. Rigorous Trace Formula: A combinatorial analysis of the prime cycle graph links powers of D directly to the von Mangoldt function, Λ(n). Determinant Identity: Through zeta-regularization, we prove that det(1/2 - iD) = K · ξ(1/2 + iD), establishing a bijection between the eigenvalues λ_n of D and the non-trivial zeros ρ_n = 1/2 + iλ_n of ζ(s). The essential self-adjointness of D forces all eigenvalues to be real, proving the Hypothesis. The proof extends naturally to Dirichlet L-functions, establishing the GRH. The Physical Interpretation: This document recasts the mathematical construction as a physical system. The primes form the energy levels of a "Riemann gas" confined by the 600-cell geometry. The Dirac operator becomes the Hamiltonian of a quantum particle on a lattice, and the Riemann Hypothesis is shown to be equivalent to the statement that this system undergoes a stable supersymmetric Bose-Einstein condensation, with the critical line Re(s) = 1/2 emerging from the condensation temperature T_c = 1/(2π). Together, these documents provide a synthesis of number theory, 4-dimensional polytope geometry, and quantum mechanics to resolve one of mathematics' most profound conjectures. Version:v2.0 Language:eng Keywords:Riemann Hypothesis; Generalized Riemann Hypothesis; 600-cell; Dirac operator; zeta function; trace formula; spectral theory; self-adjoint operator; quantum chaos; Bose-Einstein condensation; number theory; prime numbers; Hilbert-Pólya conjecture; 4D polytope; angular defect; holonomy Additional Notes:This deposit includes the core proof, its physical interpretation, and supplementary appendices with geometric data and numerical validation. The work is based on the QSVG Framework by the author. The fundamental coupling constant α_st = (δ₀/(2π)) · ln(2πe) is derived purely from the geometry of the 600-cell and the universal constants π and e. License:Creative Commons Attribution 4.0 International Access Right:Open Access References:Riemann, B. (1859). Über die Anzahl der Primzahlen unter einer gegebenen Größe.Hilbert, D. (1900). Mathematical Problems.Coxeter, H.S.M. (1973). Regular Polytopes. Dover Publications.Connes, A. (1999). Trace formula in noncommutative geometry and the zeros of the Riemann zeta function.Selberg, A. (1956). Harmonic analysis and discontinuous groups.Berry, M.V. (1986). Riemann's zeta function: A model for quantum chaos?Kato, T. (1966). Perturbation Theory for Linear Operators.Odlyzko, A. M. (1992). The 10^20-th zero of the Riemann zeta function...Morató de Dalmases, L. (2026). Complete Proof of the Riemann Hypothesis... [This record]Morató de Dalmases, L. (2026). Physical Proof of the Riemann Hypothesis... [This record]DOI: https://doi.org/10.5281/zenodo.18886876 For the "Files" Tab File 1: Filename: 01_Main_Proof_Riemann_Hypothesis.pdf Title: Complete Proof of the Riemann Hypothesis via Dirac Operators and 600-cell Holonomy File 2: Filename: 02_Physical_Interpretation_RH.pdf Title: Physical Proof of the Riemann Hypothesis: Quantum Interpretation and Bose-Einstein Condensation File 3: Filename: 03_Appendix_Mathematical_Numerics.pdf Title: Appendix: Numerical Comparison of Eigenvalues with Riemann Zeros File 4: Filename: 04_Appendix_Geometric_Data_600-cell.pdf Title: Appendix: Geometric Data of the 600-cell and Derivation of Constants File 5: Filename: 05_Discussion_Fundamental_Breakthrough.pdf Title: Discussion: The Fundamental Breakthrough of Dirac Operators and 600-cell Holonomy