gauge_generators

In the high-temperature plasma above the electroweak phase transition every Standard Model species is relativistic and unsuppressed. The effective relativistic degrees of freedom $g_\star$ then split as $g_b + (7/8)g_f$. The bosonic half begins with the gauge sector: the unbroken group is $\mathrm{SU}(3)\times\mathrm{SU}(2)\times\mathrm{U}(1)$, whose adjoint dimensions are $8$, $3$, and $1$.

This module replaces the hand-entered constant $g_\star = 106.75$ used in baryon-asymmetry work by an explicit helicity count forced by the $Q_3$ chord-cube particle content. Gauge generators are the first integer in that count; each massless gauge boson later multiplies by two transverse polarisations, and the Higgs complex doublet adds four real scalars, giving the textbook $g_b = 28$.

The only named dependency is a foundation class on infinite-order circle windings; it does not enter the arithmetic of this definition and is incidental to the import graph.

Pure definitional abbreviation: the natural number is written as the sum $8 + 3 + 1$. No lemmas, tactics, or rewriting are required. Downstream equalities unfold this name and discharge the resulting numeral arithmetic by decide or native_decide.

Without a fixed generator count the bosonic side of $g_\star$ cannot be derived. The definition is multiplied by two polarisations to form total gauge degrees of freedom, then added to the four Higgs scalars; the theorem that the bosonic total equals 28 unfolds exactly these names. The closing identity $g_\star = 427/4$ likewise unfolds the generator count before evaluating the rational expression $28 + (7/8)\cdot 90$.

In the Recognition framework this pins the high-$T$ effective DOF that baryogenesis and early-universe thermodynamics inherit, converting a previously hard-coded $106.75$ into an exact rational forced by SM gauge structure. It does not itself invoke the T0–T8 forcing chain, but it supplies the particle-content input those cosmological bridges consume.