The Interior Observer Cosmological Framework: Paper 12 - How the Kill Shots Die — The Baryon Dictionary Principle and the Rational Correction

Paper 12 of the Interior Observer (IO) cosmological framework. An adversarial internal audit reveals that the assumed baryon fraction fb = 0. 25 (Paper 3) produces a 31. 6σ deuterium crisis at BBN. This paper resolves the crisis by introducing the Baryon Dictionary Principle — a new ontological axiom identifying baryons as the gauge-coupled subset of geometric Oppenheimer-Snyder dust, fixing fb = 2γ/x = 0. 313 from the Ashtekar-Barbero connection structure. A discrete α-ladder of geometric exponents demonstrates that the 1-form exponent α = 1 is the unique projection scaling consistent with observed D/H, and retroactively explains Paper 3's BAO-optimized value fb = 0. 254 as the curvature exponent α = 3/2. A seven-point γ-scan strongly favors the rational baryon correction (F = ⟨K⟩x/ (8γ) = 1. 381) over the exponential form, with the exact identity fb × F = ⟨K⟩/4 yielding the master formula ωb, eff = (ln Δ/4) × ωₘ, geom. Results: θ* at −0. 5σ, ℓ₁ = 220. 0, R at −0. 3σ, D/H at −1. 2σ (improved from +31. 6σ), Yₚ at +0. 6σ, BAO χ² = 19. 8 (modestly lower than ΛCDM's 22. 0). Lithium remains the sole failure: ⁷Li/H at +10. 6σ, comparable to ΛCDM's +10. 3σ. Kill Shot 1 (ruler split): resolved in the extended IO framework via the Baryon Dictionary Principle. Kill Shot 2 (curvature Ωₖ = −0. 006): survives, testable by Euclid DR1 October 2026. Kill Shot 3 (frame split): confirmed. Five of six observables pass within 2σ with zero continuously tunable parameters. UPDATE v3. 4, Lithium correction: An internal audit identified that the ⁷Li/H value reported in v3. 3 (+5. 1σ) was carried forward from Paper 7's pre-BDP baryon density (η₁₀ ≈ 5. 0) and not recalculated at Paper 12's updated η₁₀ = 6. 19. The corrected lithium prediction is ⁷Li/H ≈ 4. 8 × 10⁻¹⁰ (+10. 6σ), comparable to ΛCDM's +10. 3σ. Both frameworks fail on lithium at essentially the same level. All claims that IO outperforms ΛCDM on lithium have been removed. The pass count (5/6) and all other results are unaffected. A full correction note is included in the paper text. Figures added: Five publication-quality figures inserted as Appendix B: (1) γ-scan — rational vs exponential baryon correction at 7 γ values, (2) α-ladder — D/H selects the 1-form exponent α = 1, (3) observable scorecard — four models compared across six observables, (4) D/H as continuous function of projection exponent, (5) master identity fb × F = ⟨K⟩/4 across γ.