eta_B_prefactor_cert

In the RS baryon-asymmetry pipeline the bare rung is $\varphi^{-44}\approx 6.41\times 10^{-10}$. An order-one prefactor $c$ is needed so that $\eta_B = c,\varphi^{-44}$ matches the Planck 2018 central value $6.10\times 10^{-10}$. The module defines

$$c_{\mathrm{RS}} := (1-\varphi^{-8})^2$$

motivated by a two-sided 8-tick washout heuristic (matter and antimatter each contributing one factor $1-\delta$ with $\delta=\varphi^{-8}$). The eight-tick period is the T7 octave $2^3$ from the forcing chain.

The module docstring explicitly retracts any claim that $c_{\mathrm{RS}}$ is derived from Boltzmann rates: the squared form was selected from a family of order-one lookalikes because it lands the bare rung in the observed band. What remains kernel-checked is pure algebra and interval arithmetic on that defined quantity. Upstream lemmas establish the expansion $c_{\mathrm{RS}}=(1-\varphi^{-8})^2$, positivity and $c_{\mathrm{RS}}<1$, the tight band $0.956<c_{\mathrm{RS}}<0.959$ via Fibonacci bounds on $\varphi^8$, and the corrected $\eta_B$ band inclusion.

Term-mode structure inhabitant for EtaBPrefactorCert. Each field is filled by a named prior lemma:

• unit interval from c_RS_in_unit_interval (itself c_RS_pos and c_RS_lt_one);
• numerical band as the pair c_RS_lower, c_RS_upper (both rewrite to the expanded form and apply nlinarith on $1-\varphi^{-8}\in(0.978,0.979)$);
• algebraic identity from c_RS_expanded (definitional unfold);
• prediction band from eta_B_corrected_in_observed_band;
• observed-inside and two-sided-improves-one-sided from the corresponding local theorems.

No new arithmetic is performed here; the certificate is pure packaging.

Feeds the cosmology-constants bridge t6_t8_to_cosmology_constants_bridge_holds in the Unified Forcing Chain, which routes T6 ($\varphi$ forced) and T8 ($D=3$) into theorem-backed surfaces for active cosmological constants, keeping empirical bands separate from exact identities. The eight-tick washout scale ties to T7 (period $2^3$).

The certificate is the audited surface for the $\eta_B$ prefactor story: algebra and band inclusion are proved; the physical reading as two-sided sphaleron washout remains a hypothesis. The module leaves open a genuine Boltzmann/$\Gamma/H$ derivation that would either justify the squared polynomial or replace it. Until that closes, the certificate documents a selected ansatz whose numerical content is fully checked, not a first-principles washout law.