g_star_2MeV

The module supplies the standard instantaneous-threshold step function $g_\star(T)$ over adopted SM content: each species contributes its full relativistic degree count while $T$ exceeds its mass threshold and drops out below it, with a QCD switch at $T_{\mathrm{QCD}}\approx 0.15$ GeV from quark–gluon plasma to pions. All arithmetic is exact over $\mathbb{Q}$.

Here $g_\star(T)$ is the minimal-neutrino convention, valid for $T\gtrsim 1$ MeV. The high-$T$ anchor is the familiar SM value $106.75$ (bosons 28, fermions 90 with the $7/8$ weight). Mass thresholds are imported PDG rationals used only for ordering; particle content matches StandardModel.RelativisticDOF.

The doc-comment for this spot check states the active set at $T=2$ MeV: above neutrino decoupling, with $\pi$ and $\mu$ already gone, leaving $\gamma$, $e$, $\nu$, hence $43/4=10.75$.

Definitional unfolding of $g_\star(T)$ yields a finite rational sum over species still above threshold at $T=1/500$. The active set is fixed by the imported mass cutoffs, so the sum is a concrete rational. native_decide machine-checks the equality to $43/4$ by exact arithmetic; no lemmas beyond the definition are required.

Closes an external-review gap: the repository previously fixed one high-$T$ number and lacked $g_\star(T)$, threshold decoupling, or epoch-dependent content. This theorem is one of the module's textbook spot checks (with the documented monotonic chain $10.75<17.25<61.75<86.25<106.75$ as the universe cools).

It pins the standard BBN-era value under the step model, using SM bookkeeping whose gauge group and generation count are RS-sourced while matter representations and the $7/8$ weight remain imported. No downstream theorems currently depend on it; it stands as a certified evaluation point for cosmology modules that need the post-muon, pre-neutrino-decoupling epoch.