T_qcd
plain-language theorem explainer
The QCD confinement temperature is fixed at the rational value 3/20 GeV (0.15 GeV). Cosmology code that builds the step-function g_*(T) cites this constant to switch the strong sector from quark–gluon plasma to hadrons. The declaration is a one-line rational literal, not a derived theorem.
Claim. The QCD confinement threshold is the rational temperature $T_{\mathrm{QCD}} = 3/20$ (in GeV). Above this scale the strong sector is treated as quark–gluon plasma; below it, as hadrons.
background
The module implements the standard instantaneous-threshold model of $g_*(T)$, the effective number of relativistic degrees of freedom as a function of temperature. Each Standard Model species contributes its full relativistic count while $T$ exceeds its mass threshold and drops out below it. All arithmetic is exact over $\mathbb{Q}$.
Mass thresholds are imported PDG-rounded rationals used only for ordering against $T$; the module does not re-derive them from the $\varphi$-ladder. The QCD scale is special: it is not a particle mass but the confinement crossover that replaces gluons plus light quarks by pions (and other light hadrons). The real lattice-QCD equation of state is a smooth crossover; this constant encodes the textbook step approximation at $\approx 0.15,\mathrm{GeV}$.
Valid domain of the surrounding $g_*$ construction is $T\gtrsim 1,\mathrm{MeV}$ (above neutrino decoupling). Boltzmann tails, the lattice EOS, and the neutrino reheating factor are out of scope.
proof idea
Pure definition: the rational literal $3/20$ is assigned to the constant. No lemmas, tactics, or computation are involved. The value is the conventional rounded lattice-QCD crossover scale written in GeV.
why it matters
Feeds activeWith, which builds the list of species still relativistic at temperature $T$: when $T_{\mathrm{QCD}} < T$ the quark–gluon-plasma species list is used; otherwise the hadronic list filtered by mass. Without this switch the high-$T$ and low-$T$ strong-sector bookkeeping would be wrong, and the module could not match textbook $g_*$ spot checks or bridge to the fixed high-$T$ value in RelativisticDOF.
In the broader Recognition Science stack this is imported phenomenology, not a forcing-chain output (T0–T8). RS mass modules predict particle masses independently; here the QCD scale is only an ordering threshold so that $g_*(T)$ can be a machine-checked rational function answering the external review demand for temperature-dependent degrees of freedom.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.