The Interior Observer Cosmological Framework: Paper 23: Primordial Perturbation Theory on the Oppenheimer-Snyder Interior — The Bridge Operator, the No-Doubling Theorem, and the Spectral Index

Paper 23 of the Interior Observer 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 establishes the primordial perturbation theory program on the Oppenheimer-Snyder interior. Part I derives scalar perturbation equations on k=+1 closed FRW with S³ spatial sections. Part II constructs the first explicit boundary-to-bulk bridge operators (scalar and tensor), proven unique by Schur's lemma. Part III derives the white baseline (n_s = 1) from isotropic puncture positions on S². Part IV proves the No-Doubling Theorem: C = B · G^(1) · B†, establishing that boundary state spectral content passes through the bridge linearly regardless of algebraic degree. Part V documents fourteen killed routes for spectral tilt generation. Part VI presents a conditional zero-parameter spectral index: n_s = 1 − K_gauge/x = 0.9639 (0.24σ from Planck), with S³ shell correction (n−1)(n+3)/(n(n+1)), conditional on two premises (PSRP and Boundary Covariance Exponent). Part VII derives tensor perturbation equations. The No-Doubling mechanism is a general result for boundary-to-bulk transfer through zero-order algebraic bridges, with implications for BBN rate dressing and the cosmological lithium problem. Produced through five-system adversarial AI collaboration. https://dfife.github.io/index.html v2.0 (May 2026): Claims Discipline normalization pass over v1.3. No physics, theorem, or numerical changes to active results; the scalar tilt 1 − n_s = K_gauge/x = 0.0361 (0.24σ from Planck) is unchanged. Body section removals (retired or dead-end content under the appendix-as-active-record rule): the Ten Killed Routes Part, the Weak Modular-Readout Closure Attempt, the Negative Literature Search, the General Mechanism duplicate, the OS Cycloid Lifecycle recap, and the No-Inflation Arguments. Theorem 23.S, the No-Doubling Theorem 23.3, and the Power-State Readout Premise covariance map relabeled DERIVED/CONDITIONAL_VERIFIED with inline dependency chains; the spatial canonical-commutation-relation lift, the Boundary Covariance Exponent, dilute-regime applicability tied to A_s, and TT γ-neutrality for n_t labeled OPEN/PREMISE_GAP. Inherited Paper 22 v2.0 numerical values and labels propagated: BBN rate-dressing scorecard (D/H × 10⁻⁵ = 2.510, Y_p = 0.24782, χ² = 0.80, Li-7/H = 5.363 × 10⁻¹⁰), θ*_pred = 0.599° (+9.2σ), Geometric Mediation and TT Budget-Saturation premises kept OPEN/PREMISE_GAP. §1.2 Notation and Abbreviations added; cross-paper references updated to current public versions (Paper 17 v1.5, Paper 18 v1.6, Paper 19 v1.6, Paper 20 v2.0, Paper 21 v2.0, Paper 22 v2.0). v1.3 (April 2026): Full appendix from Paper 22. v1.3 (April 2026): Full appendix from Paper 22 v1.3 clean + Paper 23 enriched results. Open/Closed tracking. Author block. v1.2 (March 2026): WMR status updated throughout — resolved in Paper 22 v1.1 via the Quadratic Thermal Covariance Theorem (conditional on H1–H3). §12 WMR Closure Attempt historicized. Open Problem #4 (WMR cross-link) marked RESOLVED. Steps 294, 306 updated. PSRP/spectral-index math qualified as dilute-regime result; exact quasi-free bosonic map now distinguished from dilute power-law. Theorem 23.S, abstract, Claim 7, Step 289, and conclusion updated with dilute-regime qualifier and finite-occupation caveat. Spatial CCR lift added as explicit conditional input to spectral-index theorem across all summary layers. Squeezed-state resolution paragraph added to §7.2: PSRP acts on boundary state before conformal squeezing, paralleling standard inflationary logic. Appendix inheritance updated to Paper 22 v1.1.