The Interior Observer Cosmological Framework Paper 32 — Closure: The Complete Interior Observer Framework — 42: The Answer Was Simple, The Question Was "Where Am I?"

Paper 32 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 closes the six remaining open problems on their active scoped sectors, retires all four semiclassical principles on their stated scopes, and derives the fixed-point normalization P4 via the DtN Open-Transport Placement Theorem (ten routes attempted, eight rounds of adversarial review). The late-time chain is derived: the observer's projection map has a finite domain (xcrit = (1+γ²) ^ (-1/4) = 0. 9864, ~6. 6 Gyr from the current epoch), the observer's scalar optical channel terminates at that boundary, and on the physical hidden-support variable R the cosmological constant drops out of the acceleration equation (R̈ = -c²/ (2rₛ) < 0), leaving gravity as the sole force. The unique local OS recollapse branch reaches R = 0 in ≤111 Gyr. Bounce attachment to Paper 1's Popławski torsion mechanism conditionally closes a 222 Gyr cycle. Observer reactivation is proved possible; the preferred restart is hard (semantic preservation, β=1, λ=1 from cycle-consistency, zero free parameters). The framework rests on two founding premises, zero additional stated premises, zero semiclassical principles, and zero fitted parameters on the active source block. One external constant (γBI = 0. 2375 from LQG) and one nuclear input (QGS = 0. 068 b for Li-7) are imported under Premise 2. https: //dfife. github. io/index. html v1. 2 (April 2026): BAO drag theorems. Drag Operator Factorization Theorem: Γdrag = κ'/R factors into independently classifiable legs. Both legs independently proved inventory-class: κ' opacity leg (Paper 31 baryon-assignment map) and R baryon-loading leg (isolated momentum-loading selection theorem). BAO rd upgraded from CONDITIONAL to DERIVED/SCOPED on the isolated pre-drag sound-horizon operator. rd = 144. 03 Mpc, 0. 046% from DESI galaxy target. Full BAO observable remains CONDITIONAL (readout kernel). Grade: DERIVED/SCOPED for isolated pre-drag operator; CONDITIONAL for full BAO; NOT UPGRADED for full CMB baryon architecture. v1. 1 (April 2026): Full branch audit. Appendix B: 100θₛ (IO) = 1. 04083 marked SUPERSEDED (CLASS output on retired mixed branch). BAO rd corrected: 143. 06 Mpc was a mixed-route artifact; replaced with Schur acoustic branch rd = 137. 94 Mpc (4. 18% residual, flat-space architectural mismatch — definitive prediction requires IO-native solver). Appendix A: Steps 58, 60, 107 updated to Schur definitive branch. Appendix C: updated through Paper 32 — all four semiclassical principles retired on stated scopes; conditional debt corrected. Website added to title page. All body theorems unaffected. v1. 0 (April 2026): Publication release. All corrections from adversarial review incorporated. P4 derivation validated through eight rounds. Late-time chain validated at stated scopes. All four semiclassical principles retired. Full hostile review by Cosmo (three passes) and conceptual review by Gemini completed. v0. 1 (April 2026): Initial working draft.