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

Paper 1 used a dimensionless factor γ = √(r_s/l_P) 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 = T_Hawking × T_Planck 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 γ_BI 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."

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v1.6 (March 2026): Cycloid parameterization correction. The OS cycloid has been corrected from a(η) = (r_s/2)(1+cos η) (contracting phase) to a(η) = (r_s/2)(1−cos η) (expanding phase). η_s shifts from 1.249 to 1.893; η_t shifts from 0.196 to 1.371. τ(η_s) = 33.4 Gyr (was 77.6). The temporal decoupling ratio Δ_cycloid changes from 5.621 to 2.418 and no longer matches Δ_geometric = 5.624; the strong temporal-matching claim is withdrawn as a historical false route superseded by the purely spatial Δ_geometric. 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(η_s)/N_horizon = 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, Λ_IO) 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 (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).