A broken-phase six-direction support mechanism for $α_s/α_{\mathrm{em}}=16$ from a common visible Yang--Mills coupling
Tejinder P. Singh
Abstract
We isolate a simple broken-phase mechanism that yields \[ \frac{α_s}{α_{\mathrm{em}}}=16 \] at the symmetry-breaking scale in the octonionic $E_8\times ωE_8$ framework, starting from a single visible Yang--Mills coupling $g$ before symmetry breaking. The first ingredient is the standard visible charge-trace factor \begin{equation} \frac{α_s}{α_{\mathrm{em}}^{(0)}}=\frac{8}{3}, \end{equation} coming from one generation of quark and lepton charges. The second ingredient is an effective broken-phase support model on the six real octonionic directions entering the three ladder operators. We make this second step more explicit by projecting the visible $q_B^\dagger q_B$ block onto the six real ladder directions and showing that it separates naturally into a trace-like abelian direction and traceless color directions. If the unbroken visible electromagnetic mode is the democratic trace vector on this six-dimensional support space, while color modes and the relevant visible matter mode are localized on one effective support sector, then the electromagnetic coupling is diluted by an additional factor $6$ and one obtains \begin{equation} \frac{α_s}{α_{\mathrm{em}}}=\frac{8}{3}\times 6=16, \qquad e=\frac{g}{4}. \end{equation} The note is intentionally conservative about what has and has not been shown. It does not claim a first-principles derivation of the localization dynamics. Rather, it identifies the precise broken-phase support hypothesis under which a common pre-breaking coupling produces the ratio $16$.