The Interior Observer Cosmological Framework: Paper 4: Evidence for a Black Hole Interior - Four Horizon Connections, the Light-Element Abundances, and Early-Galaxy Timing

Paper 4 of the Interior Observer (IO) cosmological framework, which proposes that the observable universe exists inside a Schwarzschild black hole with the same physics inside the horizon as outside. Where Paper 3 established that the framework's only per-epoch input is the observer coordinate, this paper presents the observational case on the active projection branch (H0 = 67.58 km/s/Mpc, Omega_m = 0.349, Omega_k = -0.046, Omega_Lambda = 0.697, zero continuously fitted cosmological parameters). The case rests on four horizon connections, each tying a measured or observer-normalized quantity to the horizon within the fixed upstream stack: the interior CMB-temperature scale (2.663 K) and its FIRAS-normalized readout; the dark-energy density, overdetermined by a torsion route (5.82e-27 kg/m^3, 2.4%) and the active Friedmann route (5.98e-27 kg/m^3, 0.3%); the MOND acceleration scale a0 = c^2/r_s (12%); and the amplification factor sqrt(r_s/l_P) from the Carlip-Virasoro horizon algebra. These span roughly forty orders of magnitude with no quantity fitted to cosmological data. Confrontation with observation, with claims scoped honestly. The light-element abundances all land within one observational sigma with zero fitted cosmological parameters through the rate-dressing mechanism of Papers 22 and 24 (D/H -0.66 sigma, Y_p +0.68 sigma, Li-7 +0.52 sigma), conditionally resolving the forty-year cosmological lithium problem. Early-galaxy timing turns on two clocks: the projected optical age tracks LambdaCDM to within about 5 percent, while the interior formation clock (Paper 28) gives roughly 46 percent more matter-era assembly time, the account of JWST's over-evolved galaxies. The dark-energy equation of state is a constant w = -1 with a small curvature signature (apparent w0 ~ -1.03, Paper 35). The OS dust supplies the cold-dark-matter scaffolding role, identifying dark matter with the interior geometry at the scaffold level. The first acoustic-peak position matches Planck (l_1 = 220); the framework's one quantified tension is the finer acoustic scale theta* = 0.5994 deg against Planck's 0.5970 deg +/- 0.00026 deg, a 9.2 sigma residual (Paper 20), which sets up the early-time physics taken up in Paper 5. Reproducibility bundle paper4-v2.0 (SHA256 ed3a62190bfb6293d66d15c786437830b3a5f3d0c0b287689967d3556087ec7a, validator 27/27 PASS) at https://github.com/dfife/io-framework-public/releases/tag/paper4-v2.0. https://dfife.github.io/index.html v2.0 (May 2026): Storytelling rebuild onto the active projection branch (Papers 10 and 29: H₀ = 67.58 km/s/Mpc, Ωₘ = 0.349, Ωₖ = −0.046, Ω_Λ = 0.697, zero continuously fitted cosmological parameters). The v1.3 dead-branch values (H₀ = 58.41, Ωₘ = 0.197, Ω_Λ = 0.933, Ωₖ = −0.130) and the single-fitted-parameter DESI exercise are dropped; the empirical confrontation is sourced to Papers 29, 30, 34, and 35. The light-element-abundance section is rewritten: the v1.3 “BBN failure” (ω_b 24% low, Vaidya thermal history) is superseded by the rate-dressing result of Papers 22 and 24, which places D/H, Y_p, and Li-7 within one observational sigma and conditionally resolves the lithium problem. The CMB-peak section is rewritten: the v1.3 “ℓ₁ ≈ 180, 18% failure” is superseded by Paper 12 (ℓ₁ = 220) and Paper 20 (acoustic scale θ* = 0.5994° against Planck θ* = 0.5970° ± 0.00026°, a 9.2σ residual; rounded display 0.599° against 0.597°), now the single quantified acoustic tension. The Vaidya radiation phase is replaced by the continuous mixed-fluid interior of Paper 5. Early-galaxy timing is recomputed and reframed around the two-clock distinction (Paper 28): the projected optical age tracks ΛCDM to within 5%, while the interior formation clock (Paper 28 master clock t_bare) that governs matter assembly gives about 46% more time through the matter era; the curvature signature is small and cited to Paper 35; and the growth amplitude S8 is sourced from Paper 32. Title updated to match content. Code and data availability and an Active Theorem and Definition Ledger added. Premises-led abstract; hyphens only. Reproducibility bundle: paper4-v2.0 published (release tag paper4-v2.0, SHA256 ed3a62190bfb6293d66d15c786437830b3a5f3d0c0b287689967d3556087ec7a, commit 62e8fde, validator 27/27 PASS) at https://github.com/dfife/io-framework-public/releases/tag/paper4-v2.0. See https://github.com/dfife/io-framework-public/tree/main for claim-naming convention. v1.3 (March 2026): Cycloid parameterization correction. The OS cycloid in §1.1 has been corrected from a(η) = (r_s/2)(1+cos η) to a(η) = (r_s/2)(1−cos η) (expanding phase); η_s updated from 1.249 to 1.893. §5.4 (Vaidya Phase Duration) removed: τ_Vaidya = 70.66 Gyr and τ_total = 181.66 Gyr were computed under the contracting convention and are incompatible with the expanding-phase chronology. Paper 5 supersedes with mixed-fluid FRW. All four horizon connections, JWST predictions, DESI BAO results, and quantitative tensions are invariant. Title page reformatted to series standard. See Paper 21 v1.1 for the full audit. v1.2 correction (Paper 12, DOI: 10.5281/zenodo.18936508): Baryon sector annotations per Paper 12 (Baryon Dictionary Principle). Paper 12 derived f_b = 2γ/x = 0.313, superseding the BAO-optimized f_b = 0.254 used in this paper. Under the BDP: Ω_b = 0.062, ω_b = 0.021 (vs. 0.050 and 0.017 at f_b = 0.254). The "24% below ΛCDM" ω_b tension described in §5.2 and §6 narrows to ~5%. The BAO-optimized f_b = 0.254 corresponds to curvature exponent α = 3/2 in the family f_b = 2γ/x^α; the BDP selects α = 1. The four horizon connections, JWST predictions, w = −1, structure formation, ℓ₁ ≈ 180, σ₈ = 0.578, and the DESI BAO fit are all unaffected. v1.1 correction (Paper 5, DOI: 10.5281/zenodo.18889865): This paper's references to the Vaidya radiation phase for early-universe thermodynamics (§5.2 nucleosynthesis timing, §5.4 Vaidya phase duration, §7 and §8 Vaidya-related open problems) are mathematically superseded by the continuous mixed-fluid FRW model derived in Paper 5. Independent symbolic tensor analysis (Wolfram/ChatGPT 5.3) proved the Vaidya null dust metric is fundamentally incompatible with the isotropic thermal bath required for CMB acoustic oscillations and BBN. The mixed-fluid model gives H_IO/H_ΛCDM = 0.955 at BBN, transforming nucleosynthesis from a catastrophic failure to a 5% tension. All other results — the four horizon connections, JWST predictions, w = −1, structure formation, ℓ₁ ≈ 180, σ₈ = 0.578, and the DESI BAO fit — are unaffected. Paper 6 confirms ℓ₁ = 180 via the full CLASS Boltzmann code. Companion to Paper 1 (DOI: 10.5281/zenodo.18854813), Paper 2 (DOI: 10.5281/zenodo.18868612), Paper 3 (DOI: 10.5281/zenodo.18876346), Paper 5 (DOI: 10.5281/zenodo.18889865), and Paper 6 (DOI: 10.5281/zenodo.18891475).