Matching, Computed Inhomogeneously: The Conjugate Pair (Λ_int, V₄) Across the Bounce, Mode by Mode

Discharges debt D-001-040-48: the inhomogeneous matching computation house paper #15 (One Flaw, Two Residues) stated but did not carry out. Paper #15 tested matching conditions M1-M8 for the conjugate pair (Lambda_int, V4) across the H = 0 bounce in minisuperspace and argued the inhomogeneous case blind from d_mu delta-Lambda = 0. This packet computes it at linear order. Three facts: (i) rho_eff + p_eff = (1+w) rho (1 - 2 rho/rho_A) for arbitrary equation of state w, with the constant density rho_C cancelling identically (symbolic verification; #15 had dust only); (ii) the Henneaux-Teitelboim equation d_mu Lambda = 0 is exact, so delta-Lambda is a single global k = 0 mode with no inhomogeneous component for matching to reach; (iii) the HT term contains e and tau^mu only, no spin connection, so the Cartan channel couples spin perturbations to spin data alone and never to Lambda. The linear matching Jacobian's delta-Lambda column is therefore zero at every wavelength (checked at k = 0, 1, 3, 17, 128), and matched inhomogeneous bounces exist over the unchanged interval rho_C in (-rho_A/4, +inf) (lower edge -2.43e54 g/cm3 at the band top, 4.16e83 times the observed 5.845e-30 g/cm3), with jump residuals exactly zero across a (rho_C, amplitude, k) grid. Paper #15's floor-side verdict is strengthened from argued to computed at linear inhomogeneous order; Two Bounds' Tier-2 kill condition (1) gains its classical linear core. Not claimed: the nonlinear matching, the general superselection theorem, and the quantum caveats (measure, superselection) Two Bounds itself prints. Prior-art search this run (Fiol-Garriga arXiv:0809.1371; Bufalo et al. arXiv:0904.4841; Jirousek review arXiv:2301.01662; EPJC unimodular collapse matching arXiv:2310.16522) located no junction matching of the conjugate pair across an Einstein-Cartan bounce. Graded DERIVED-INDEPENDENT: a new in-frame computation closing a Sharp B debt at its stated order, extending a named predecessor rather than opening a new object.