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 = √ (rₛ/lP). 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 ΛIO 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 (zₘax = 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 (Ωₖ 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 Ωₘ = 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 TIO, a₀, or any of the precision-affected constants. Paper 4 verification: The ΛIO bridge derivation was verified by Paper 4 §2. 2, recovering the Barbero-Immirzi parameter γBI = 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/ρPlanck = O (1) × (lP/rₛ) 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 = √ (rₛ/lP) as the holographic dimensional reduction ratio. Statements of the form "TIO/THawking = γ" in the abstract, §4, and §10 require clarification: the full observed temperature relationship is TIO = γ × THawking × x, where x = rₛ/RU = 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 RU rather than at the horizon rₛ. The geometric mean identity TIO² = THawking × TPlanck uses TIO at the horizon surface (R = rₛ) and is unaffected. The observed temperature TIO = 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).