cmb_temperature
plain-language theorem explainer
CMB temperature at the present epoch equals recombination temperature divided by one plus recombination redshift. Recognition Science cosmologists cite this when converting the Saha-derived T* and forced z* into the observable T0. The definition is a direct algebraic division with no lemmas or tactics.
Claim. The present CMB temperature satisfies $T_0 = T_* / (1 + z_*)$, where $T_*$ is the temperature at recombination and $z_*$ is the redshift at recombination.
background
The module derives the CMB blackbody temperature from the recombination epoch in Recognition Science. Recombination temperature follows from the Saha equation with the RS eta parameter, while redshift is fixed by the universal forcing chain. Photon temperature redshifts inversely with the scale factor as energy dilutes during expansion. Upstream results on breath periods and simplicial ledger edge lengths supply the structural constraints that determine the recombination epoch.
proof idea
The definition consists of a single division expression. No lemmas are applied and no tactics are used; the body directly encodes the redshift scaling formula.
why it matters
This definition supplies the final conversion step that produces the observable T0 from recombination parameters, feeding rs_cmb_temperature and the Planck spectrum theorem. It realizes the forced redshift scaling within the eight-tick octave and D=3 spatial dimensions. The parent result is the RS prediction of T0 approximately 2.725 K that lies inside the alpha inverse band.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.