IndisputableMonolith.Cosmology.BaryonAsymmetryDerivation
Assembles the RS derivation of the baryon-to-photon ratio from Sakharov conditions, Gray-code CP violation, three fermion generations, and the CKM/Jarlskog structure. Records the high-T SM value g_★ = 106.75 as imported bookkeeping (not a free RS number) and the structural form η_B ∼ φ^{-44}. Cosmologists citing the η_B interval or g_★ certificates use this module. Argument is definitional assembly plus positivity/smallness lemmas along the φ-ladder.
claimAt $T > T_{\mathrm{EW}}$, the SM relativistic effective degrees of freedom are $g_\star = 106.75 = 28 + (7/8)\cdot 90$. The RS structural baryon-to-photon ratio is $\eta_B \sim \varphi^{-r}$ on the $\varphi$-ladder (with rung near $44$ after saturation), positive and observationally small, built from ledger Sakharov conditions, Gray-code chirality (CP violation), three generations, and the Jarlskog invariant from $Q_3$.
background
Recognition Science treats baryogenesis as a ledger consequence of the three Sakharov conditions: baryon-number violation, C/CP violation, and departure from thermal equilibrium (module SakharovFromLedger). CP violation is not inserted by hand; it is the chirality of the canonical 3-bit Gray-code cycle on the cube $Q_3$ (GrayCodeChirality), which also feeds the CKM geometry and the Jarlskog invariant $J_{\mathrm{CP}} = \mathrm{Im}(V_{us}V_{cb}V_{ub}^V_{cs}^)$.
Particle content is fixed by the RS three-generation theorem (P-001) together with the $Q_3$-forced gauge structure. The high-temperature relativistic DOF count is then ordinary SM bookkeeping: $g_b = 28$ bosonic modes and $g_f = 90$ fermionic modes with the $7/8$ thermal weight, giving $g_\star = 106.75$ above the electroweak scale (minimal-neutrino convention). That number is imported assembly, not an independent free parameter.
The baryon-to-photon ratio is placed on the $\varphi$-ladder: a structural $\eta_B$ with a definite rung, a saturation exponent, and elementary positivity/smallness statements that later pin the numerical window around $\varphi^{-44}$.
proof idea
Module-level argument, not a single theorem. It wires upstream geometry and ledger facts into named constants and certificates: $g_\star$ is recorded as the standard high-T SM value with a lemma that the DOF count includes three generations; $\eta_B$ is defined structurally on the $\varphi$-ladder; short lemmas prove positivity and smallness; rung and saturation-exponent definitions package the scaling; a completeness flag asserts the derivation chain is fully linked; a certificate bundle (BaryonAsymmetryCert) packages the claims for downstream interval and $g_\star$ modules. No deep new analysis tactic block: assembly, algebraic identities, and inheritance from Gray-code/CKM/Jarlskog/Sakharov imports.
why it matters in Recognition Science
This is the cosmology bridge from RS particle geometry to the observed matter asymmetry. Downstream, EtaBIntervalCert uses the structural $\eta_B$ to prove the interval prediction $\varphi^{-44}\in(5.5\times 10^{-10},7.5\times 10^{-10})$, which contains the Planck 2018 value $(6.10\pm 0.04)\times 10^{-10}$. GStarDerivation reuses the same $g_\star=106.75$ assembly as the high-T DOF fixed by $Q_3$-forced SM content.
In the broader framework it closes the path from T7/T8 discrete structure (eight-tick octave, $D=3$, cube $Q_3$) through Gray-code chirality and three generations to a concrete cosmological observable. Without this module the Sakharov ledger conditions and Jarlskog geometry would not land on a certified $\eta_B$ rung.
scope and limits
- Does not claim g_★ = 106.75 is an independent RS prediction; it is SM bookkeeping with RS-sourced content.
- Does not derive a full Boltzmann transport solution for baryogenesis dynamics.
- Does not replace experimental CKM fits; it supplies the structural Jarlskog/CP origin.
- Does not treat temperature-dependent g_★ thresholds (those live in GStarThresholds/GStarDerivation).
- Does not assert the final numerical η_B interval; that certificate is downstream.