Series Paper — SS-Line
Strong Sector Series
SS-4: String Tension from the 600-Cell Face-Mode Multiplicity
The QCD string tension comes out to 926.5 MeV/fm — 1.8% of the Cornell fit — from the discrete ZBW polygon
σ to 1.8% of Cornell fit
Abstract: SS-4 identifies the source of the factor of ~3.8 discrepancy between SS-2's heuristic string tension and the charmonium Cornell fit: the ZBW orbit in CPP is not a continuous circle but a discrete lattice polygon traversing z=12 nearest-neighbour vertices on the 600-cell. Replacing the continuum circumference factor 2 pi with the discrete vertex count z gives one power of z, and the mode multiplicity around the closed orbit contributes a second power, yielding sigma = M_0 z^2 / (phi l_edge) = 926.5 MeV/fm, in agreement with the Cornell fit to 1.82%. The self-consistent confinement radius 0.158 fm matches the C14 closure value to 1.6%. The factorisation admits a clean physical reading as one DP energy quantum per lattice edge, with a face-mode multiplicity of z^2 and a golden-ratio propagation efficiency. The rigorous derivation of the z^2 multiplicity from 600-cell gauge traces remains as the open step.
- σ = 926.5 MeV/fm vs Cornell ~910 MeV/fm (1.8%)
- r_conf = 0.158 fm matches C14 closure to 1.6%
- z/π correction factor physically identified as discrete-vs-continuum