The Interior Observer Cosmological Framework: Paper 26 - The Primordial Scalar Amplitude from the Hawking Boundary State, Toward IO-Native Replacements for ΛCDM-Borrowed Inputs, Source-Side Reduction, the CMB Baryon Class Diagnostic, and the Effective Optical Damping Parameter
Year: 2026
Type: preprint
Abstract: Paper 26 of the Interior Observer (IO) Cosmological Framework. Beginning from two premises — (1) the observable universe exists inside a Schwarzschild black hole, and (2) the physics inside the horizon is the same as outside — this paper proposes IO-native replacements for ΛCDM-borrowed inputs in the framework's confrontation with Planck 2018 CMB data, with zero fitted parameters. The headline result is a conditional forward prediction for the primordial scalar amplitude from the Hawking boundary state on the S² horizon: A_s = (25/9) × [γ²/(1+γ²)] × [1/√2] × 1/(exp(4π√2) − 1) = 2.007 × 10⁻⁹ (Planck: 2.100 ± 0.030 × 10⁻⁹, deviation −4.4%). The formula contains one external input (γ_BI = 0.2375 from Loop Quantum Gravity) and the mathematical constant π. All dependence on M_U, r_s, ℏ, c, G, k_B, and l_P cancels exactly in the Hawking exponent β_H ω₁ = 4π√2. Part II establishes that Paper 19's late-time clustering theorem does not authorize ω_b,clustering in CMB perturbation slots, resolving a catastrophic χ² failure. The Thomson Kernel Lemma proves that the visibility function and acoustic oscillations share the same primitive opacity factor. The visibility readout is conditionally assigned to the acoustic baryon class (ω_b,eff = 0.02910). Part III proposes an effective optical damping parameter τ_eff,IO = K_gauge/2 = (1/2)ln(1+γ²) = 0.02744 from the inverse of the tangential horizon operator. The combined effective amplitude A_eff = A_s × exp(−K_gauge) = 1.900 × 10⁻⁹ matches the ΛCDM TT extraction (1.885 × 10⁻⁹) to 0.8%. Part IV shows CLASS reionization shape defaults are numerically irrelevant for TT high-ℓ (Δχ² < 0.4). Four conditional framework-internal identifications (C1, C2c, AV1, C3) are required, each explicitly documented with assumptions, limitations, and promotion paths. Includes Lemma C2.1 (background/perturbation channel separation) and Lemma C2.2 (carrier identification via Hopf lift), both derived, resolving the radial-vs-angular mode counting tension. Full cumulative Appendix A catalog (Steps 1–398) spanning Papers 1–26. https://dfife.github.io/index.html v1.1 (April 2026): Full appendix from Paper 25 v1.1 clean + Paper 26 enriched results (Steps 382–409). Open/Closed tracking added. Author block updated. Rosetta terminology retired.
Author: Fife, David
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7142506598
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