The Interior Observer Cosmological Framework: Paper 2: The Quantum Gravitational Origin of γ

Paper 1 used a dimensionless factor γ = √ (rₛ/lP) to bridge the 30-order-of-magnitude gap between the Hawking temperature of a universe-mass black hole and the observed cosmic microwave background. This paper closes two questions Paper 1 left open. First, where does γ come from? A no-go theorem shows that semiclassical quantum field theory on the stationary Schwarzschild background cannot produce γ - five candidate mechanisms in the Bogoliubov framework are excluded for structural reasons, and the 30-order-of-magnitude gap therefore requires physics beyond the smooth manifold. The Carlip-Virasoro horizon algebra supplies what the no-go opens up: γ derives exactly from a dimensional reduction natural to interior observers, recovering the geometric mean identity T² = THawking × TPlanck that was independently derived by Haug and Tatum (2024) from a separate cosmological framework. Second, does horizon temperature thermalize the interior? Four independent consistency checks confirm it does, with the Tolman-Ehrenfest relation giving the framework's predicted temperature as an algebraic identity rather than a fit. A structural feature surfaces during this investigation - the space-time decoupling on the Oppenheimer-Snyder cycloid - which Paper 3 then reframes as the observer coordinate input rather than a problem requiring resolution. A separate derivation gives the cosmological constant directly from the interior Friedmann equation with no Barbero-Immirzi dependence, addressing the natural peer-review concern that γBI is doing double duty. The framework's qualitative prediction from this paper that high-redshift galaxies have approximately 46% more cosmic time to form than ΛCDM allows was confirmed by Paper 35 §3 at 47% relief at z > 10. "If the theory is correct, the math will just work. " https: //dfife. github. io/index. html v1. 6 (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). ηₛ shifts from 1. 249 to 1. 893; ηₜ shifts from 0. 196 to 1. 371. τ (ηₛ) = 33. 4 Gyr (was 77. 6). The temporal decoupling ratio Δcycloid changes from 5. 621 to 2. 418 and no longer matches Δgeometric = 5. 624; the strong temporal-matching claim is withdrawn as a historical false route superseded by the purely spatial Δgeometric. The Kruskal lapse formula updated to expanding-phase form N (η) = 2 csc (η/2) exp (−sin² (η/2) /2) ; the horizon factor 2/√e survives at η→π. N (ηₛ) /Nₕorizon = 1. 462 is unchanged. Two convention-dependent null-geodesic rows removed from the timescale table. Vaidya radiation phase timeline corrected to Big Bang → horizon chronology. All spatial/boundary results (γ derivation, no-go theorem, thermalization bridge, ΛIO) are invariant. Version history table removed and consolidated into text block. Title page reformatted to series standard. See Paper 21 v1. 1 for the full audit. 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).