Paper 3 of the Interior Observer Cosmological Framework. Derives the two-phase Vaidya-to-Oppenheimer-Snyder interior structure from Israel junction conditions with zero free parameters: metric continuity, extrinsic curvature continuity, and the equation-of-state acceleration ratio äᵣad/ädust = 2. The junction geometry motivates τVaidya = rₛ/c and the geometric identity τᵣad/τₘax = 2/π. The total interior lifecycle is 181. 66 Gyr; the observable universe has completed 81. 6%. The Continuity Theorem proves the IO transfer function is an analytic law valid at every interior epoch. The cosmological invariant TCMB × RU = ħcγ/ (4πkB) is an algebraic identity. The observer coordinate τₒbs is the irreducible minimum input all physical theories require — the framework is not fine-tuned. Two errors in Paper 1 are identified and corrected: (1) Ωₖ normalization used a = rₛ instead of a = RU, corrected from −0. 057 to −0. 130; (2) DESI observable identification (DV/rd compared against DM/rd data at z ≥ 0. 510). Both independently verified by Gemini. Core predictions (TCMB = 2. 663 K, ρ_Λ, a₀ = 1. 345 × 10⁻¹⁰ m/s², γ derivation) are completely unaffected. With H₀ as a single fitted parameter, the IO geometric expansion history achieves χ² = 7. 57 (AIC = 9. 57) versus ΛCDM χ² = 8. 83 (AIC = 14. 83) — statistically preferred with five fewer parameters. The IO matter-radiation equality zₑq = 1758 is a new zero-parameter prediction testable against Matter Power Spectrum data from Euclid and DESI. v1. 4 correction: The Ωb sensitivity analysis in §7. 4 used Ωᵣ (total radiation including neutrinos) instead of Ω_γ (photons only) in the baryon loading formula Rb, making Rb 41% too small and shifting the χ² minimum from fb ≈ 0. 25 to fb ≈ 0. 41. Corrected results: zero-parameter minimum is χ² = 14. 05 at Ωb/Ωₘ = 0. 25, with Ωb = 0. 049 — consistent with ΛCDM's fractional baryon density. The 1-parameter fit (H₀ = 62. 3, χ² = 7. 57) is unaffected. See Paper 4 Appendix A for the full diagnosis. v1. 5 correction: The two-phase Vaidya-to-Oppenheimer-Snyder model used the Vaidya null dust metric for the radiation-dominated phase. Paper 5 demonstrates through independent symbolic tensor analysis (Wolfram/ChatGPT 5. 3) that Vaidya null dust is anisotropic radial streaming, fundamentally incompatible with the isotropic thermal bath required for CMB acoustic oscillations and Big Bang nucleosynthesis. The radiation phase is correctly modeled as a continuous mixed-fluid closed FRW interior containing both radiation (p = ρ/3) and dust (p = 0), which naturally transitions through matter-radiation equality without a sharp junction. The Israel junction conditions analysis, the Continuity Theorem, the cosmological invariant, the dust-phase Friedmann equation, and the DESI BAO fit (χ² = 7. 57) are all unaffected by this correction — they use only the dust-phase geometry. See Paper 5 for the full analysis. Companion to Paper 1 (DOI: 10. 5281/zenodo. 18854813), Paper 2 (DOI: 10. 5281/zenodo. 18868612), Paper 4 (DOI: 10. 5281/zenodo. 18883069), and Paper 5 (DOI: 10. 5281/zenodo. 18889865).
Fife et al. (Fri,) studied this question.