Geometric Mass Generation in the 59-Dimensional Framework: QCD Casimir Derivation of Baryon Masses, Singularity Prevention, and Testable Predictions at the LHC

The Standard Model treats elementary particle masses asfree parameters with no underlying explanation. This paperpresents a 59-dimensional geometric framework as a candidatefor deriving these masses from first principles. CENTRAL PROVED RESULT: For the nine lightest baryons, the geometric index n isderived from QCD Casimir operators without using anybaryon mass as input: n = −7 + (αs/2) (CF + CA·S − Jdiquark) with CF = 4/3, CA = 3, TF = 1/2 (exact SU (3) values), S = strangeness, J = diquark spin, αs = 0. 1179 (PDG 2022). Agreement with PDG 2022 measurements: - Proton: 942. 3 MeV predicted vs 938. 3 MeV measured (+0. 43%) - Neutron: 942. 3 MeV predicted vs 939. 6 MeV measured (+0. 29%) - Lambda: 1124. 5 MeV predicted vs 1115. 7 MeV measured (+0. 79%) - Sigma: 1192. 8 MeV predicted vs 1189-1197 MeV measured (±0. 39%) - Xi: 1342. 1 MeV predicted vs 1314-1321 MeV measured (+1. 5-2. 1%) - Omega: 1699. 0 MeV predicted vs 1672. 5 MeV measured (+1. 59%) SINGULARITY PREVENTION (proved): The No-Vacuum Principle S + Sᵀ = I implies Re (λ) = 1/2for all eigenvalues, which guarantees |det (g) | > 0 always. Gravitational singularities are algebraically impossibleunder this constraint. Proved rigorously in Paper V. BASE MASS COINCIDENCE (computed): mbase = K·exp (−52) = 1019. 31 MeVphi meson (PDG 2022) = 1019. 461 MeVDiscrepancy: 0. 015% — not engineered into the formula. TESTABLE PREDICTION (closest to current experiment): A baryon resonance at n = −7. 50 → m = 1680. 6 MeV. Four experimental groups (GRAAL, CBELSA/TAPS, LNS, Crystal Ball/TAPS) report evidence for N* (1685) at ~1685 MeV. Discrepancy from prediction: 4. 4 MeV = 0. 26%. FAILURES (reported explicitly): The formula fails for mesons (dynamical chiral symmetrybreaking), excited baryons (ground states only), andheavy baryons (charm/bottom — HQET corrections needed). HONEST COMPARISON WITH STANDARD MODEL: The SM treats all masses as inputs. The 59D frameworkderives baryon indices from group theory (no baryon massused). The SM covers the full particle spectrum; the 59Dframework currently covers only light baryons precisely. DARK MATTER ESTIMATE (partial — not derived): dim (so (29) ) /dim (so (59) ) = 406/1711 = 23. 7%Measured: 26. 8% (Planck 2018). Gap: 11. 5% — reported honestly. Synthesis of: DOI 10. 5281/zenodo. 20045130, 10. 5281/zenodo. 20088148, 10. 5281/zenodo. 20089209, 10. 5281/zenodo. 20089959, 10. 5281/zenodo. 20090894, 10. 5281/zenodo. 20091189, 10. 5281/zenodo. 20091557. Declaration: This work was developed in collaborationwith Claude (Anthropic, Claude Sonnet 4. 6) used fornumerical verification, figure construction, andsystematic testing of all predictions. All scientific ideas and responsibility rest with the author.