IndisputableMonolith.Cosmology.Track4ACert
Master certificate for Track 4.A cosmology: five clauses that force the η_B rung −44 from D=3 (three convergent routes), state Ω_Λ = 11/16 − α/π with band (0.683, 0.686), and record 2σ consistency with Planck 2018. Cosmologists citing RS predictions for η_B and dark energy would reference it. The module aggregates inhabited proofs from three upstream derivation modules into one certificate structure.
claimA Track 4.A certificate asserting five clauses: (i) the integer $-44$ is forced as the $\eta_B$ $\varphi$-rung from $D=3$ by three independent routes; (ii) $\Omega_\Lambda = 11/16 - \alpha/\pi$; (iii) $\Omega_\Lambda \in (0.683, 0.686)$; (iv) the prediction is consistent with Planck 2018 $0.6889 \pm 0.0056$ at $2\sigma$; (v) the gap-from-dimension identity $1 - D^2(D+2)$ equals $-44$ at $D=3$.
background
Recognition Science cosmology ties dimensionless observables to the forcing chain, especially T8, which fixes $D=3$ spatial dimensions. The baryon-to-photon ratio $\eta_B$ lives on a $\varphi$-ladder whose integer rung offset must be $-44$. Upstream EtaBExactRungDerivation closes that integer from $D=3$ alone by three structurally distinct routes (gap-from-dimension, chirality $\times$ torsion, fermionic DOF) that are required to agree.
Dark energy enters as a phase-saturation fraction on the $D=3$ ledger. Upstream OmegaLambdaDerivation and CosmologicalConstantDerivation supply the core claim $\Omega_\Lambda = 11/16 - \alpha/\pi$: the seed $11/16$ is structural; $\alpha/\pi$ is the sole electromagnetic correction, using measured CODATA $\alpha$. The present module is the aggregation layer that packages those closures into a single Track 4.A certificate.
proof idea
Certificate aggregation module, not a primary derivation. It imports the three upstream cosmology modules and assembles their proved clauses into one inhabited Track4ACert structure with five named fields: etaB_rung_forced, omegaLambda_formula, omegaLambda_band, planck_2sigma, and etaB_dimension_route. An inhabited instance and a headline theorem witness that all five hold simultaneously. No new analytic work occurs here beyond packaging and the explicit gap-from-dimension witness $1-D^2(D+2)=-44$ at $D=3$.
why it matters in Recognition Science
Track 4.A closes two open-frontier cosmology items: the integer $-44$ pinning $\eta_B$ from $D=3$ alone, and the $\Omega_\Lambda$ formula with a tight observational band inside $(0.683,0.686)$. That band sits against Planck 2018 at $2\sigma$, addressing C-010 (what determines $\Lambda$) at the level of the density fraction rather than the absolute scale.
Downstream, Gravity.MasterTheorem (Track 7.A) imports this module as part of the seven-track closure gate for the master gravity statement. The certificate is the cosmology end of the chain T8 ($D=3$) $\to$ rung and ledger structure $\to$ $\eta_B$ and $\Omega_\Lambda$, and is required before the conditional master gravity theorem can load.
scope and limits
- Does not derive α from first principles; uses measured CODATA α as one external input.
- Does not claim 1σ Planck agreement; only 2σ consistency with 0.6889 ± 0.0056.
- Does not re-prove the three η_B routes; packages upstream derivation modules.
- Does not fix the absolute scale Λ, only the density fraction Ω_Λ.
- Does not address Ω_m, H_0 tension, or growth observables beyond the Ω_Λ band.