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 f_b = 2γ/x is a gauge-coupling inventory fraction with observable-class Jacobians: ω_b(O) = ω_b^(α=1) × x^(1−α_O). For clustering: α = 3/2, ω_b = 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:

H²_obs = √Δ × [(8πG/3)(ρ_m + ρ_r + 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: H_obs (optical, boundary-calibrated) and H_bare ≈ 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

v1.6 (May 2026): R4/FIRAS readout-normalization correction inherited from Paper 17 v1.5 — the optical readout normalization R4 is FIRAS-fixed (R4_FIRAS = 1.0031 ± 0.0096 via Paper 17 v1.5 Theorem 17.2), and the observed cosmic microwave background (CMB) temperature is no longer counted as an independent IO prediction. Standardized on the canonical Claims Discipline labeling from the public GitHub repository: https://github.com/dfife/io-framework-public/tree/main. Reader-facing manuscript hygiene: standard physics acronyms expanded at first use (Interior Observer, Conformal Modular Principle, Baryon Dictionary Principle, gauge thermal transfer/readout theorem, etc.); internal terminology replaced with standard physics phrasing (e.g., “Schur N-slot” → “Schur-complement curvature mode parameter”, “dead path” → “retired route”, “foundation punch list” → “remaining open problems”). The age-closed background branch parameter N_mode = 0.336 is explicitly relabeled OPEN/PREMISE_GAP (observationally selected; not theorem-fixed). Reproducibility bundle: paper19-v1.6 (release tarball SHA256 af567bd66a617ec194435cd329d6f5dcd39c6f8070cc169aaad06206826c46ea; validator 12/12 PASS).

v1.5 (May 2026): Cross-paper reference update to reflect current Paper 22 published state, plus Conventions v2.0 citation upgrade. The Paper 22 cross-reference target has advanced from v1.3 to v1.5: Paper 22 has subsequently been corrected through v1.4 (PRyMordial wrapper YPBBN → YPCMB correction, May 2026) and v1.5 (GMP/TBS premise-status corrections labeling Theorems 22.23-22.25 as DERIVED/CONDITIONAL on GMP + TBS, May 2026). Paper 19 v1.4’s active amplitude framework alignment to Paper 22 (ε_w = 0.012301, ε_n = 0.023842) remains valid - those amplitude values are unchanged in Paper 22 v1.5. Paper 19’s own corrected scorecard (Y_p = 0.24779, D/H = 2.523 × 10⁻⁵, χ²(D/H + Y_p) = 0.50) is unchanged. Bibliography entry [13] is updated to cite IO Framework Conventions v2.0 (unified: observational, labeling, versioning, and cross-paper reference conventions; https://dfife.github.io/data/conventions_v2.md), the new canonical reference deployed in May 2026 that consolidates the prior Observational Conventions v1.0 (now Section 1 of v2.0) with formal labeling, versioning, and cross-paper reference conventions in Sections 2-4. The v1.0 file remains live at its original URL for backward compatibility with already-published papers including Paper 19 v1.4; in-text references to “Observational Conventions v1” remain accurate as a historical citation. No Paper 19 numerical values, theorems, or no-go results change in v1.5; this is a reference-hygiene update only. The Master Mathematical Reference table source labels for D/H and Y_p are also updated from plain “Paper 12” to “Paper 12 / Paper 19 v1.5 corrected wrapper” to disambiguate that the displayed values are wrapper-corrected, not historical Paper 12 values (matching the Paper 21 v1.6 and Paper 20 v1.7 conventions). Paper 19’s distinctive results (Baryon Scalarization Theorem with α=3/2 clustering, BOSS DR12 χ² = 73.06, baryon observable type identification, BBN scorecard alignment) are unaffected by this update.

v1.4 (May 2026): PRyMordial output index correction (YPBBN → YPCMB) and amplitude framework alignment to Paper 22 v1.3 / Paper 24 v2.2 standard (ε_w = 0.012301, ε_n = 0.023842). Paper 19 v1.3 BBN scorecard reflected an older amplitude branch superseded by Paper 22 v1.1's Quadratic Thermal Covariance correction (√L_1 → L_1) and read PRyMordial output index 4 (YPBBN) instead of index 3 (YPCMB). Corrected scorecard: Y_p = 0.24779 (+0.70σ), D/H = 2.523 × 10⁻⁵ (−0.12σ), χ²(D/H + Y_p) = 0.50. Observational denominators per IO Framework Observational Conventions v1 (https://dfife.github.io/data/observational_conventions_v1.md). The Baryon Scalarization Theorem and BOSS DR12 χ² = 73.06 result are unaffected by this correction.

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. Φ_0 → 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.