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
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2026
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| _version_ | 1866901955378413568 |
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| author | Fife, David |
| author_facet | Fife, David |
| contents | <p>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.</p> <p>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.</p> <p>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).</p> <p>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%.</p> <p>Part IV shows CLASS reionization shape defaults are numerically irrelevant for TT high-ℓ (Δχ² < 0.4).</p> <p>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.</p> <p><a title="Framework Github Site" href="https://dfife.github.io/index.html" target="_blank" rel="noopener">https://dfife.github.io/index.html</a></p> <div></div> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19296329 |
| institution | Zenodo |
| language | eng |
| publishDate | 2026 |
| publisher | Zenodo |
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| spellingShingle | 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 Fife, David black hole cosmology primordial scalar amplitude Hawking radiation interior observer CMB power spectrum baryon acoustic oscillations Loop Quantum Gravity Barbero-Immirzi parameter holographic cosmology zero fitted parameters Multi AI research <p>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.</p> <p>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.</p> <p>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).</p> <p>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%.</p> <p>Part IV shows CLASS reionization shape defaults are numerically irrelevant for TT high-ℓ (Δχ² < 0.4).</p> <p>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.</p> <p><a title="Framework Github Site" href="https://dfife.github.io/index.html" target="_blank" rel="noopener">https://dfife.github.io/index.html</a></p> <div></div> |
| title | 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 |
| topic | black hole cosmology primordial scalar amplitude Hawking radiation interior observer CMB power spectrum baryon acoustic oscillations Loop Quantum Gravity Barbero-Immirzi parameter holographic cosmology zero fitted parameters Multi AI research |
| url | https://doi.org/10.5281/zenodo.19296329 |