The Interior Observer Cosmological Framework Paper 19 - Baryon Scalarization, the Universal Projector No-Go, the Boundary-Hamiltonian IO Friedmann Equation, and the Foundation Closure Audit

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 — Paper 19 diagnoses the P (k) catastrophe of Paper 18, derives the Baryon Scalarization Theorem, and constructs the conditional homogeneous-background IO Friedmann equation. The P (k) crisis (χ² = 1056 on 84 BOSS DR12 points) is diagnosed as baryon-driven, not radiation-driven. The Baryon Scalarization Theorem proves fb = 2γ/x is a gauge-coupling inventory fraction with observable-class Jacobians: ωb (O) = ωb^ (α=1) × x^ (1−αO). For clustering: α = 3/2, ωb = 0. 01705. BOSS DR12 χ² drops to 73. 06 (ΛCDM: 70. 32). Wolfram-validated through three adversarial review rounds. Paper 10's universal √Δ energy projector is proved dead. The replacement architecture projects the Hamiltonian constraint, not the fluid. The IO Friedmann equation is derived through a six-link Regge-Teitelboim upgrade chain: H²ₒbs = √Δ × (8πG/3) (ρₘ + ρᵣ + ρ_Λ) − k/a² One global readout factor on the entire bare GR constraint. The cross-sector assembly problem dissolves at the homogeneous-background level. Wolfram grade: A- conditional, same epistemic tier as Papers 15-18. A level-mixing no-go proves two distinct expansion rates: Hₒbs (optical, boundary-calibrated) and Hbare ≈ 43 km/s/Mpc (local, gauge-blind) — a falsifiable structural prediction. Foundation punch list: four items closed or conditionally closed (#1 sector-specific projection map, #3 boundary-to-bulk propagator, #5 operator audit, #6 observable-class Jacobians). Six items deferred to Paper 20 (#2 Schur N-slot/bare background closure, #4 reduced → full algebra extension, #7-#10 new math/physics). Fifteen no-go theorems documented. https: //dfife. github. io/index. html v1. 3 (April 2026): Appendix replaced. A7c/Rosetta retired. V (α) closed. Open/Closed tracking. Author block. v1. 2 (April 2026): Schur branch correction. The age-closed global readout branch (H₀ = 66. 33) derived in this paper is SUPERSEDED by the Schur definitive branch (H₀ = 68. 91, Paper 29). The boundary-Hamiltonian Friedmann equation, universal projector no-go, baryon scalarization theorem, and all structural results are branch-independent and unaffected. Only the specific numerical H₀ prediction changes. Appendix Steps 107, 116–129 and open-problem items updated. Title page standardized. v1. 1 (March 2026): Cycloid parameterization correction. Φ₀ → Φ_π in CMP references. Full Appendix A catalog inherited from Paper 18 (Steps 1–114) with Paper 19 results appended (Steps 115–129). Title page reformatted. See Paper 21 v1. 1 for the full audit. This is Paper 19 of the Interior Observer series.