Harmonic Entanglement Theory
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String tension

The colour flux and \(\sqrt{\sigma}\)

The colour flux bs=Fzτ is a vector one-form on the zτ-face with |bs|2=4. Spread over the edge operator and read through the master equation with the spectral weight squared and the fundamental factor 3/8, it gives \(\sqrt{\sigma}=422.4\) MeV.

The colour flux on the prism

The colour flux is a vector on the colour edges. On the cube every vertex meets one z-edge, so closure forces \(b_{s}=0\) — no confining contour. The prism adds τ, opening the zτ-face, where the flux closes as the field strength Fzτ, an alternating four-cycle with \(|b_{s}|^{2}=4\).

Spectral decomposition over the edge operator

The flux spreads over the edge operator \(M_{1}=L_{1}+I\). Its projections give the propagator weight

\[ G_{b_s}=\frac{7/24}{1}+\frac{1/4}{5}+\frac{1/3}{7}+\frac{1/8}{9}=\frac{127}{315}=0.403175, \]

and the edge Sakharov trace, led by the seventeen zero-modes of the edge kernel, is

\[ \Sigma_E=\operatorname{Tr}M_1^{-1}=\frac{17}{1}+\frac43+\frac65+\frac47+\frac19=\frac{6368}{315}=20.21587, \]

\[ \Pi_{b_s}=\frac{G_{b_s}}{\Sigma_E}=\frac{127}{6368}=0.019943. \]

The master equation

The flux is a vector (p=2) carrying fundamental colour charge threading the octet, Θbs=3/8. Through the master equation with the spectral weight squared,

String tension
\(\sqrt{\sigma}\)=mP Θbs Πbs2 exp(−1/ξ*)=422.4 MeV   within 0.44% of 424.264 MeV (σ=0.18 GeV2)