SFVdSB/Deriving_Lambda-_Star_and_Closing_Lane-B_from_Bounce_Microphysics: Deriving Lambda_star and Closing Lane-B from Bounce Microphysics

This note documents the first full ``internal-consistency closure'' pass that links a corridor two-field SFV/dSB bounce solution (golden run $\sim$1078) to a deterministic Lane-B cosmology table $\alpha(z)$ used in BAO distance tests. The main deliverables are: (i) a derived (not hand-inserted) energy scale $\Lambda_\star$ that maps the rescaled bounce potential to physical units; (ii) a model-driven onset redshift $z_c$ obtained from the first-principles crossing condition $m_{\rm eff}=3H(z_c)$; (iii) a reproducible pipeline that exports an $\alpha(z)$ table and evaluates DESI BAO full-covariance likelihoods; and (iv) an explicit demonstration that BAO fits performed with an inverse-distance-ladder normalization are insensitive to the SFV sound speed $c_s$ once the overall ruler $r_d$ is allowed to float. We also document a CMB-theory spectral consistency check (Best vs.\ $\Lambda$CDM) and clarify why naive relative-difference metrics for the TE spectrum are ill-conditioned near zero-crossings.