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 (nₛ = 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: nₛ = 1 − Kgauge/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 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.