The Interior Observer Cosmological Framework: Paper 2 — Derivation of γ from Quantum Gravity, the Bogoliubov No-Go Theorem, the Holographic Thermalization Bridge, the Space-Time Decoupling Problem, and the Holographic Timescale Hierarchy

Paper 2 of the Interior Observer Cosmological Framework. A no-go theorem establishes that semiclassical QFT on stationary Schwarzschild spacetime cannot produce the boost factor γ = √(r_s/l_P). γ is then derived from the Carlip-Virasoro horizon algebra through the dimensional reduction natural to interior observers, with SymPy residual = 0 and zero free parameters. A four-check holographic thermalization bridge connects 1+1D horizon states to the observed 3+1D CMB photon bath. The cosmological constant Λ_IO matches Planck 2018 to 2.4% with no Barbero-Immirzi dependence. The Space-Time Decoupling Δ = 5.624 is exhaustively characterized across 14 computational steps; the OS dust interior's domain boundary (z_max = 0.519) is established and the Vaidya-to-OS two-phase transition is identified as Paper 3's central calculation. All results supported by 394 automated verification checks.

v1.4.3 note: Paper 3 identified two errors in Paper 1 (Ω_k normalization and DESI observable identification; see Paper 1 v3.4). Paper 2 is unaffected — no values from Paper 1's DESI analysis appear in Paper 2. The Ω_m = 0.197 used in §10.2 was independently derived and is consistent with the Paper 1 correction. All theoretical results are unchanged. Companion reference updated to Paper 1 v3.4. Only addition is the v1.4.3 note — the body text was already correct and consistent. No numerical values in the description needed changing since it doesn't reference T_IO, a₀, or any of the precision-affected constants.

Paper 4 verification: The Λ_IO bridge derivation was verified by Paper 4 §2.2, recovering the Barbero-Immirzi parameter γ_BI = 0.231 (2.9% from the Domagala-Lewandowski LQG value) by equating the torsion and Friedmann routes to Λ. The cosmological constant hierarchy ρ_Λ/ρ_Planck = O(1) × (l_P/r_s)² ≈ 10⁻¹²³ verified exactly (25/25 SymPy checks). The Δ = 5.624 remains open (Paper 4 §7, Open Problem #8).

v1.5 clarification (Paper 5 consistency review): The Carlip-Virasoro derivation correctly produces γ = √(r_s/l_P) as the holographic dimensional reduction ratio. Statements of the form "T_IO/T_Hawking = γ" in the abstract, §4, and §10 require clarification: the full observed temperature relationship is T_IO = γ × T_Hawking × x, where x = r_s/R_U = 1.519 is the observer position correction derived in Paper 1. The factor γ is the quantum gravitational boost from the horizon algebra (derived here); the factor x arises from the observer being at radial coordinate R_U rather than at the horizon r_s. The geometric mean identity T_IO² = T_Hawking × T_Planck uses T_IO at the horizon surface (R = r_s) and is unaffected. The observed temperature T_IO = 2.6635 K has always been computed correctly using the full formula including x. All derivations, the no-go theorem, and the holographic thermalization bridge are unaffected.

Companion to Paper 1 (DOI: 10.5281/zenodo.18854813), Paper 3 (DOI: 10.5281/zenodo.18876346), Paper 4 (DOI: 10.5281/zenodo.18883069), Paper 5 (DOI: 10.5281/zenodo.18889865), and Paper 6 (v1.0, DOI: 10.5281/zenodo.18891475).