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, Omegaₘ = 0. 349, Omegaₖ = -0. 046, OmegaLambda = 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/m³, 2. 4%) and the active Friedmann route (5. 98e-27 kg/m³, 0. 3%) ; the MOND acceleration scale a0 = c²/rₛ (12%) ; and the amplification factor sqrt (rₛ/lP) 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, Yₚ +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 (l₁ = 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” (ωb 24% low, Vaidya thermal history) is superseded by the rate-dressing result of Papers 22 and 24, which places D/H, Yₚ, 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 tbare) 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) = (rₛ/2) (1+cos η) to a (η) = (rₛ/2) (1−cos η) (expanding phase) ; ηₛ updated from 1. 249 to 1. 893. §5. 4 (Vaidya Phase Duration) removed: τVaidya = 70. 66 Gyr and τₜotal = 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 fb = 2γ/x = 0. 313, superseding the BAO-optimized fb = 0. 254 used in this paper. Under the BDP: Ωb = 0. 062, ωb = 0. 021 (vs. 0. 050 and 0. 017 at fb = 0. 254). The "24% below ΛCDM" ωb tension described in §5. 2 and §6 narrows to ~5%. The BAO-optimized fb = 0. 254 corresponds to curvature exponent α = 3/2 in the family fb = 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 HIO/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).
David Fife (Sun,) studied this question.