Unified Quark Mass Formula from the Casimir Cascade in R12: Boltzmann Suppression, Shannon Saturation, and the Rendered Charmonium Ceiling
Abstract
A single formula mq = C(N, 3) γ1 exp(−Sq) with C(12, 3) = 220 (information budget) and γ1 (Riemann anchor) reproduces all three light quark masses (u, d, s) at 0.1–2.4% accuracy with zero free parameters. The suppression action Sq is a KMS
Boltzmann cascade: Sq = (EQCD+ P2 C barrier2)/Tweak, where EQCD = b0 = 7 (QCD beta coefficient = number of running channels), Tweak = dim(fund, SU(2)) = 2 (weak-sector KMS temperature), and C barrier2 are Casimir invariants accumulated
at each transition. The Casimir selection rule determines barriers: inter-generation transitions (topological, winding change) cost C2(adj, SU(3)) = 3; intra-generation transitions (algebraic, isospin rotation) cost C2(fund, SU(2)) = 3/4. The formula automatically recovers ms/md = exp(C2(8)) = exp(3) (Paper XXXIV) from Sd−Ss = 3 and yields a new identity C2(adj, SU(3)) = (N −Nf )/2 = (12−6)/2 = 3, linking the colour Casimir to the axis–flavour gap. The rendering ceiling Lγ1 = 220γ1 ≈ 3110 MeV coincides with m(J/ψ) = 3097 MeV (0.4%), identifying the J/ψ charmonium ground state as the light–heavy transition point.
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BibTeX
@misc{lim2026unified,
title = {{Unified Quark Mass Formula from the Casimir Cascade in R12: Boltzmann Suppression, Shannon Saturation, and the Rendered Charmonium Ceiling}},
author = {Han-Jun Lim},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23604404},
url = {https://zenodo.org/records/23604404},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Unified Quark Mass Formula from the Casimir Cascade in R12: Boltzmann Suppression, Shannon Saturation, and the Rendered Charmonium Ceiling
AU - Han-Jun Lim
PY - 2026
DA - 2026/10/23
PB - Zenodo
DO - 10.5281/zenodo.23604404
UR - https://zenodo.org/records/23604404
AB - A single formula mq = C(N, 3) γ1 exp(−Sq) with C(12, 3) = 220 (information budget) and γ1 (Riemann anchor) reproduces all three light quark masses (u, d, s) at 0.1–2.4% accuracy with zero free parameters. The suppression action Sq is a KMS Boltzmann cascade: Sq = (EQCD+ P2 C barrier2)/Tweak, where EQCD = b0 = 7 (QCD beta coefficient = number of running channels), Tweak = dim(fund, SU(2)) = 2 (weak-sector KMS temperature), and C barrier2 are Casimir invariants accumulated at each transition. The Casimir selection rule determines barriers: inter-generation transitions (topological, winding change) cost C2(adj, SU(3)) = 3; intra-generation transitions (algebraic, isospin rotation) cost C2(fund, SU(2)) = 3/4. The formula automatically recovers ms/md = exp(C2(8)) = exp(3) (Paper XXXIV) from Sd−Ss = 3 and yields a new identity C2(adj, SU(3)) = (N −Nf )/2 = (12−6)/2 = 3, linking the colour Casimir to the axis–flavour gap. The rendering ceiling Lγ1 = 220γ1 ≈ 3110 MeV coincides with m(J/ψ) = 3097 MeV (0.4%), identifying the J/ψ charmonium ground state as the light–heavy transition point.
ER -