The Interior Observer Cosmological Framework - Paper 29 - The Galaxy/Quasar Baryon Acoustic Oscillation Readout Kernel, Sound Speed Baryon Selector, and Forecast Predictions for Euclid and Roman

This paper of the Interior Observer Cosmological Framework derives the galaxy/quasar Baryon Acoustic Oscillation (BAO) readout kernel on the DESI Data Release 2 galaxy-and-quasar combined observable definition, from two founding premises: (P1) the observable universe exists inside a Schwarzschild black hole, and (P2) the physics inside the horizon is the same as outside. The kernel RWᵍal = exp−η D_⊥ − (η/2) D_∥ with η = Kgauge/x = 0. 0361 is forced uniquely by five structural theorems. A second uniqueness result, the Sound-Speed Baryon Selector Theorem, fixes the baryon density entering the pre-recombination sound speed to the geometric bare-frame value ωb = 0. 02100, yielding sound horizon rd = 144. 01 Mpc. On combined cosmic chronometer + DESI Data Release 2 BAO data (48 points), the framework gives χ² = 42. 44 versus Planck 2018 ΛCDM χ² = 46. 40, with zero parameters fit to either dataset. Approximately thirteen pre-registered falsifiable predictions are listed across three observational domains: Euclid Data Release 1 and Roman High-Latitude Spectroscopic Survey late-time BAO; Cosmic Dawn (reionization midpoint z₅0, IO = 10. 19, optical depth τIO = 0. 074, 21cm brightness temperature T₂1 = −191 mK at z = 17) ; and cosmic microwave background amplitude and curvature (Nₑff = 3. 044, Ωₖ = −0. 046). Near-term decisive tests are expected 2026–2028 from Euclid Data Release 1, the Simons Observatory Large Aperture Telescope, and Hydrogen Epoch of Reionization Array Phase II. A reproducibility bundle accompanies this paper with all numerical predictions reproducible from public inputs (SHA256: c342f4897cff8b69db6fd79b7514d86e6779e8fdcd5dcab7b9dfe76d54716168). https: //dfife. github. io/index. html v2. 0 (May 2026): Paper reframed from corrigendum/audit format into a positive prediction paper. New body: full prose derivation of the galaxy/quasar BAO readout kernel (§2), sound speed baryon selector theorem (§3), DESI Data Release 2 + cosmic chronometer data confrontation (§4), Euclid Data Release 1 forecast suite (§5, six predictions: transverse and radial Alcock-Paczynski parameters, tomographic consistency, matter density, growth rate, dark-energy equation of state), Roman High-Latitude Spectroscopic Survey forecast (§6), reionization and 21cm predictions (§7), cosmic microwave background amplitude and curvature tests (§8). Radial-to-transverse claim corrected: exponent ratio is exactly 1: 2; multiplier-excess ratio is 0. 4955 (not 1/2). Reproducibility bundle built and attached: SHA256 c342f4897cff8b69db6fd79b7514d86e6779e8fdcd5dcab7b9dfe76d54716168. References expanded from 11 to 24 entries. Physicist-grade revision pass: Kgauge and x defined inline in the abstract, Premise P1 motivation paragraph added, §2. 1 Hille-Yosida hypotheses motivated from the DESI/Euclid pipeline, §3 derivation made self-contained with substantive upstream paper statements, Δχ² interpretation added, framework slang replaced with standard physics terminology, body status sentences integrated into prose. See https: //github. com/dfife/ioframework-public/tree/main for claim naming convention. v1. 2 (April 2026): Rebuild audit. Schur branch retired: √ (1+γ²) vacuum ansatz identified as hidden fitted parameter, K_Λ shifted from 49. 85 to 48. 50. Paper 10 legacy branch (H₀ = 67. 58) confirmed as sole survivor. Title, abstract, and conclusion rewritten. All branch-dependent values updated to Paper 10 legacy branch. Data confrontation (§4) recomputed on Paper 10 legacy branch. Scorecard updated: Aₛ = 2. 007 (C1b killed), H₀ = 67. 58. Assembly gap closure simplified. Open Problems updated. Appendix replaced with Paper 28 v1. 3 clean chain + Paper 29 theorem-grade steps only. Appendices B, C, D removed (not theorem-grade). Author block corrected. Terminology: Schur definitive → conditional Schur, Rosetta → gauge partition. v1. 1 (April 2026): Validation corrections applied. BAO Ωₘ Jacobian investigation added. Full Appendix A inherited from Paper 28 v1. 0 (Steps 1–443) with Paper 29 results appended (Steps 444–460).