Foundational paper of the Interior Observer (IO) cosmological framework. Beginning from two premises - (1) the observable universe exists inside a Schwarzschild black hole, and (2) physics inside the horizon equals physics outside - this paper presents the framework's origin story (formation event, horizon containment, hot mostly-radiation boundary state) and enumerates the ten structural consequences that fall out before any derivation work begins. The paper then derives three results that originate in Paper 1 and remain load-bearing across the 35-paper series: the CMB temperature formula via 1+1D CFT mode counting on the horizon (TIO = 2. 6635 K, 2. 3% from FIRAS), the Interior Observer Spectral Theorem proving greybody factor Γ = 1 exactly, and the dark energy density ρ_Λ = 5. 82 × 10⁻²⁷ kg/m³ from Einstein-Cartan-Holst torsion (2. 4% from observed, zero fitted parameters). §6 summarizes the framework's closure through Paper 32 and the consequence phase across Papers 33-35. v4. 0 is a structural rebuild of Paper 1 as an origin story. "If the theory is correct, the math will just work. " https: //dfife. github. io/index. html v4. 0 (May 2026): Structural rebuild of Paper 1 as an origin story. The paper opens with the formation event - the moment a containing black hole closes around a region of spacetime - and unfolds the framework from there. §2 enumerates the ten structural consequences that fall out of the two premises before any derivation work begins, giving the reader the framework as a single object rather than as a sequence of discoveries. New §2. 6 derives the hot mostly-radiation first-cycle boundary state from horizon containment of the formation event's outward pressure, replacing the v3. 5 treatment of the initial singularity as an inherited Oppenheimer-Snyder endpoint. The temperature formula, the spectral theorem, and the Einstein-Cartan-Holst dark energy derivation are preserved from v3. 5 with voiced openings. The DESI confrontation, MOND identification, and CMB power spectrum sections from v3. 5 are superseded by published Paper 17 v1. 5, Paper 29, Paper 31, Paper 32 v2. 0, Paper 34 v2. 0, and Paper 35 v2. 0 content and are removed from Paper 1; pointers are retained in the consequence chain. New §6 distinguishes the framework's closure (Papers 2-32) from the consequence phase (Papers 33-35). New §7 falsifiability section names the experiments that would force the framework into rework. Notation moved to Appendix A. Numerical constants updated to the current published values. Dash discipline: hyphens only. Numerical correction in §5: at the v4. 0-stated γBI = 0. 2375, the dark energy chain gives ρ_Λ, torsion = 2. 52 × 10⁻²⁷ kg/m³ and ρ_Λ, eff = 5. 82 × 10⁻²⁷ kg/m³ (2. 4% from observed), correcting the v3. x legacy values 2. 62 × 10⁻²⁷ / 6. 05 × 10⁻²⁷ (1. 5%) which had been carried forward from the v3. x γBI = 0. 1274 (Meissner 2004) convention. The geometric mechanism and (lP/rₛ) ² hierarchy argument are unchanged; only the input γBI value shifts the numerical result. Paper 32 v2. 0 SHA reference updated to current public-repo manifest (2e1ff99e). Reproducibility bundle paper1-v4. 0 published (SHA256 prefix 812ed680, validator 24/24 PASS, release tag paper1-v4. 0). See https: //github. com/dfife/io-framework-public/tree/main for claim naming convention. v3. 5 (March 2026): Cycloid parameterization correction. The OS cycloid has been corrected from a (η) = (rₛ/2) (1+cos η) (contracting phase) to a (η) = (rₛ/2) (1−cos η) (expanding phase), consistent with observed cosmological expansion. η=0 is the Big Bang (a=0) ; η=π is maximum expansion (a=rₛ). The current-epoch conformal time shifts from η ≈ 0. 196 to η ≈ 1. 371 (temporal) and from ηₛ = 1. 249 to ηₛ = 1. 893 (spatial). The geometric ratio x = rₛ/RU = 1. 519 and all derived observables (TIO, ρ_Λ, a₀, H₀) are invariant. §6. 4 ρ_Λ evolution direction corrected for expanding convention. Title page reformatted to series standard. See Paper 21 v1. 1 for the full audit. v3. 4 correction note: v3. 2 reported χ² = 15. 1 at zero free parameters. Paper 3 identified two errors: (1) the Ωₖ normalization used a = rₛ instead of the correct a = RU, shifting Ωₖ from −0. 057 to −0. 130; (2) the DESI comparison used DV/rd at all redshifts, but data at z ≥ 0. 510 reports DM/rd. Both errors independently verified by Gemini. Core predictions (TCMB, ρ_Λ, a₀, γ derivation) are completely unaffected. v3. 4 additionally corrected Paper 1 Table 2 values (H₀ 58. 5→58. 4, Ω_Λ 0. 919→0. 933) and standardized decimal precision across all constants. See Paper 3 for full correction analysis. Three changes: TCMB 2. 66→2. 663, a₀ 1. 35→1. 345, and the correction note updated from v3. 3 to v3. 4 with the Table 2 and precision fixes documented. Everything else unchanged and consistent with Paper 3 v1. 3. Paper 4 status: All four core predictions from Paper 1 are verified and extended in Paper 4. The ρ_Λ derivation is confirmed via two independent routes, recovering the Barbero-Immirzi parameter γBI to 2. 9% of the LQG value (25/25 SymPy checks). The MOND scale a₀ = c²/rₛ is confirmed as a zero-parameter prediction; the interpolation function μ (a/a₀) is identified as requiring quantum gravity completion. Paper 1 §6. 4's claim that w = −1 is confirmed by CAMB (w = −1/3 ruled out at χ² = 716). Structure formation is proven viable: the OS dust clusters gravitationally, identifying dark matter as the interior geometry itself. The CMB first acoustic peak is predicted at ℓ₁ ≈ 180 (Planck: 220), an 18% tension driven by Ωₘ h² = 0. 067, which is the framework's most significant open problem. Paper 1 Open Questions #1–5 are all addressed in Paper 4. Companion to Paper 2 (DOI: 10. 5281/zenodo. 18868612), Paper 3 (DOI: 10. 5281/zenodo. 18876346), Paper 4 (DOI: 10. 5281/zenodo. 18883069), Paper 5 (DOI: 10. 5281/zenodo. 18889865), and Paper 6 (DOI: 10. 5281/zenodo. 18891475).
David Fife (Wed,) studied this question.