The Interior Observer Cosmological Framework Paper 18 — Modular Completion: Operator-Level Closure of the Conformal Modular Principle and the Baryon Dictionary Principle via Relative Modular Operators and Gauge-Sector Projection

Paper 18 completes the operator-level closure program for the Interior Observer framework by upgrading the Conformal Modular Principle and the Baryon Dictionary Principle from semiclassical principles to theorem-level results within the reduced observer algebra. It realizes the geometric modular term as a commutative relative modular operator on the abelian gravitational history algebra, derives the baryon fraction fb=2γ/xf_b = 2\gamma/xfb=2γ/x from open covariant transport and boundary-to-bulk 1-form scaling, and proves that V(α)=−2ln⁡(cos⁡α)V(\alpha) = -2\ln(\cos\alpha)V(α)=−2ln(cosα) is the unique normalized real logarithmic generator of the one-dimensional reduced gauge center. The paper also states that the IO framework now has zero semiclassical principles remaining within its stated reduced-sector scopes. v1.2 - Paper 19 correction annotations. Abstract updated with two founding premises. Core results entirely unaffected: CMP modular realization (Theorem 18.C), BDP modular derivation (Theorem 18.B), V(α) uniqueness, Bogoliubov spectrum theorem. N_eff = Δ Friedmann identification (already withdrawn in §21) structurally superseded: Δ is now the global readout factor in Paper 19. Per-source projection architecture superseded. Both H₀ = 67.58 (Paper 10) and H₀ = 68.91 (Schur N=Δ) superseded by H₀ = 66.33 on Paper 19 age-closed branch. Internal H₀ tension dissolved by new architecture. Appendix background-dependent entries annotated.