forty_four_factorization

The module certifies the RS interval prediction for the baryon-to-photon ratio: $\varphi^{-44} \in (5.5, 7.5)\times 10^{-10}$, which contains the Planck 2018 value $\eta_B \approx 6.1\times 10^{-10}$.

The structural story is the "44 connection": the same integer governs both $\eta_B$ (as the rung exponent) and the electromagnetic coupling via $\alpha^{-1} = 44\pi \times \exp(-w_8 \ln\varphi / 44\pi)$. Module text factors that integer as $44 = 4 \times 11 = (\text{flip count on preferred Gray-code axis}) \times (\text{generation torsion gap }|\Delta\tau_{12}|)$.

This declaration isolates the pure arithmetic half of that factorization. Sibling results then identify the factors with flip count and torsion, and bound $\varphi^{\pm 44}$ via the Fibonacci closed form $\varphi^n = F_n\varphi + F_{n-1}$.

One-line tactic proof: norm_num discharges the ground natural-number equality $44 = 4 \cdot 11$ by kernel arithmetic. No lemmas, no hypotheses.

Pins the integer seed of the module's main structural claim: both baryon asymmetry and $\alpha$ are controlled by the same $44 = (\text{chirality})\times(\text{torsion gap})$. Downstream siblings (rung_44_equals_flip_times_torsion, eta_B_interval, the $\varphi^{\pm 44}$ bounds, and the master EtaBCert) treat 44 as given; this theorem makes that factorization a proved fact rather than a comment.

In the broader RS chain it sits next to T6 ($\varphi$ as self-similar fixed point) and the mass/coupling ladder: the exponent $-44$ is the rung that places $\eta_B$ on the $\varphi$-ladder, and the same 44 appears in the $\alpha^{-1}$ band. No used_by edges yet; it is local scaffolding arithmetic for the interval certificate.