The Interior Observer Cosmological Framework: Paper 5 - The Kerr Limit, the Radiation Phase, and Early-Time Physics in Black Hole Cosmology

Paper 5 in the Interior Observer (IO) cosmological framework, which proposes the observable universe exists inside a Schwarzschild black hole. This paper presents three major results: (1) Kerr Spin Bound: The IO temperature prediction TIO = 2. 6635 K monotonically decreases with black hole spin, proving the framework is optimally defined in the Schwarzschild limit (a/M < 0. 096 at 2. 5% tolerance). (2) Vaidya Incompatibility: Independent symbolic tensor analysis proves the Vaidya null dust metric — proposed in Paper 3 for the radiation-dominated phase — is fundamentally incompatible with the isotropic thermal bath required for CMB acoustic oscillations and Big Bang nucleosynthesis. The Vaidya metric describes anisotropic radial streaming, not a cosmological fluid. This self-correction supersedes Paper 3's radiation-phase model. (3) Mixed-Fluid CMB Peak: Replacing Vaidya with a continuous mixed-fluid closed FRW interior (radiation + dust + curvature + Λ), the first acoustic peak is confirmed at ℓ₁ ≈ 181 (18% below observed 220). This tension is fundamental to the IO geometric parameters (Ωₘ = 0. 197, Ωₖ = −0. 130), not an artifact of the radiation-phase metric. The IO expansion rate at BBN is within 5% of ΛCDM (HIO/H_ΛCDM = 0. 955), transforming nucleosynthesis from a catastrophic failure to a quantifiable tension. Additional results: critical collapse parameter λ* = 0. 50 (cosmic censorship satisfied), self-similar mass function M (v) = λv proven unique by homothetic symmetry, observer position x = rₛ/RU = 1. 519 naturally within the expected self-similar range 1–2. Multi-AI research methodology: Claude and Claude Code (Anthropic) for orchestration and numerical computation; Wolfram/ChatGPT 5. 3 (OpenAI + Wolfram) for symbolic tensor analysis and junction conditions; Gemini 2. 5 Pro (Google DeepMind) for adversarial peer review. All AI contributions explicitly attributed in text. Corrects Paper 3 (DOI: 10. 5281/zenodo. 18876346): Vaidya radiation phase replaced by continuous mixed-fluid FRW. BAO fit results unaffected. v1. 1: Added note clarifying that the exact inclusion of Ωᵣ in the mixed-fluid boundary condition shifts H₀ from 58. 41 km/s/Mpc (Papers 1, 3, 4; dust-only) to 58. 2 km/s/Mpc. Self-consistency correction, not a parameter change. Companion references updated. v1. 2: Added bibliography, no other changes. v1. 3 (Paper 12, DOI: 10. 5281/zenodo. 18936508): Baryon sector annotations per Paper 12 (Baryon Dictionary Principle). Paper 12 derived fb = 2γ/x = 0. 313, giving ωb, geom = 0. 021 (~5% below ΛCDM, vs. 24% at fb = 0. 25). The BBN tensions flagged in §6. 4 and §7 as "requiring dedicated computation" are resolved: D/H = 2. 49 × 10⁻⁵ (−1. 2σ). The Kerr spin bound, Vaidya incompatibility, mixed-fluid peak ℓ₁ = 181, and HIO/H_ΛCDM = 0. 955 are all unaffected. Companion to Paper 1 (DOI: 10. 5281/zenodo. 18854813), Paper 2 (DOI: 10. 5281/zenodo. 18868612), Paper 3 (DOI: 10. 5281/zenodo. 18876346), Paper 4 (DOI: 10. 5281/zenodo. 18883069), and Paper 6 (DOI: 10. 5281/zenodo. 18891475).