IndisputableMonolith.Cosmology.NeutrinoDilution
Neutrino dilution after electron-positron annihilation is packaged as entropy accounting for a relativistic plasma. The module defines radiation entropy density from bosonic and fermionic degrees of freedom, then derives the classic factors $(T_\nu/T_\gamma)^3=4/11$ and $g_{*s}=43/11$ under comoving entropy conservation. Cosmologists on the $\eta_B$ or CMB entropy chain would cite it. The argument is algebraic: equate total entropy before and after annihilation and solve for the temperature ratio and effective $g_{*s}$.
claimFor a relativistic plasma with $g_B$ bosonic and $g_F$ fermionic internal degrees of freedom at temperature $T$, the entropy density is assembled as $s=\sum(g/2\pi^2)\,T^3\int\sigma$ from the radiation entropy-functional integrals. Under conservation of comoving entropy through $e^+e^-$ annihilation, $(T_\nu/T_\gamma)^3=4/11$, and today's effective entropy degrees of freedom satisfy $g_{*s}=43/11$.
background
In standard early-universe cosmology, neutrinos decouple before electron-positron annihilation. Photons are reheated by the annihilation entropy dump; neutrinos are not. The temperature ratio and the effective entropy count $g_{*s}$ then follow from equating comoving entropy before and after the dump.
This module sits between two closed pieces of the Recognition Science entropy chain. RadiationEntropyRelation supplies the statistical-mechanics identity $s=(4/3)\rho/T$ for a massless quantum gas, built from entropy-functional integrals (status: theorem, zero sorry). EntropyPerPhoton supplies the photon-side arithmetic that uses $g_{*s}=43/11$ as a model input for the entropy-per-photon ratio. NeutrinoDilution defines the plasma entropy density from those integrals and packages the dilution algebra that produces the $4/11$ and $43/11$ factors.
Local objects include radiation entropy for a mixed Bose-Fermi plasma, the pre-annihilation $g$ identification, the dilution map from entropy conservation, total entropy today, and the recovery of $g_{*s}$ from that conservation statement.
proof idea
Definition-plus-algebra module, not a deep analysis proof. Radiation entropy density is assembled species-by-species from the RadiationEntropyRelation integrals: each bosonic or fermionic multiplet contributes $(g/2\pi^2)T^3\int\sigma$. Equality lemmas identify the pre-annihilation plasma with the standard $g$-before count.
Dilution is obtained by imposing conservation of comoving entropy $s a^3$ across $e^+e^-$ annihilation, which yields $(T_\nu/T_\gamma)^3=4/11$ as an algebraic identity (and the cubed form of the dilution factor). Total entropy today is rewritten as the usual $g_{*s}$ expression, and $g_{*s}=43/11$ is recovered from the same conservation statement. The MODEL hypotheses (adiabatic expansion, sector coupling) are left for the downstream FRW module to discharge.
why it matters in Recognition Science
EntropyConservationFRW imports this module and discharges the two MODEL hypotheses NeutrinoDilution was stated over. Downstream doc-comment: there, $(T_\nu/T_\gamma)^3=4/11$ and $g_{*s}=43/11$ were derived from adiabatic expansion (comoving entropy $s\cdot a^3$ of the coupled sector conserved), and that module closes those hypotheses via the FRW continuity equation (theorem, zero sorry).
In the broader Recognition Science $\eta_B$ chain, EntropyPerPhoton needs $g_{*s}=43/11$ as a model input for the entropy-per-photon ratio built from $\zeta(3)$, $\pi^4$, and Standard Model content. This module is where that $g_{*s}$ factor is justified from plasma entropy accounting rather than inserted by hand. It does not touch the forcing chain T0-T8 or the J-cost; it is cosmology scaffolding for the baryogenesis lane.
scope and limits
- Does not derive adiabatic expansion from the FRW continuity equation (that is EntropyConservationFRW).
- Does not compute numerical $\zeta(3)$ or $\pi^4$ factors for entropy per photon.
- Does not treat massive neutrinos or non-instantaneous decoupling.
- Does not prove photon reheating microphysics beyond entropy bookkeeping.
- Does not address baryon-asymmetry dynamics, only the dilution factors they consume.