The Interior Observer Cosmological Framework: Paper 31 — Gravitational Slip from Schwarzschild Interior Geometry: η = 0.623, the S₈ Tension, and a Scoped Audit of the IO 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 presents a zero-parameter gravitational slip prediction: η_IO = 2x^{−1/2} − 1 = 0.623, derived from the observable-class Jacobian distinction between the Weyl curvature potential (α = 2, intrinsic slice-curvature descent on S³) and the density contrast (α = 3/2, dust-current continuity descent). The resulting lensing-to-clustering response Σ_IO = x^{−1/2} = 0.811 alleviates the S₈ weak-lensing tension within the linear scalar sector, bringing S₈ from 1.004 to 0.793 — near current weak-lensing survey values — with zero fitted parameters. The paper also retires the long-standing N_eff = Δ identification, conditionally closes the galaxy BAO ruler at 0.046% residual against DESI DR2, settles the optical depth at τ = K_gauge/2 via three independent routes plus a no-go ceiling, and maps the complete IO Boltzmann solver architecture through systematic elimination of ~20 candidate routes. The reionization sector is classified as inherited external astrophysics with a clock-transport pipeline. A full CMB power spectrum confrontation is deferred: existing flat-space Boltzmann codes cannot represent the IO three-baryon architecture, and the S³-native recombination calculation is identified as the remaining barrier. https://dfife.github.io/index.html v2.0 (May 2026): The CMB Weyl half-order kernel (§13.6) is upgraded from RECONSTRUCTION to DERIVED/CONDITIONAL_VERIFIED via a new scoped theorem package (Definitions 31.KS1–31.KS2, Lemmas 31.KS3–31.KS4, Theorems 31.KS5–31.KS6, and Corollary 31.KS7; §13.6.1). The kernel exponent is now derived from the observable-class gap α_δ − α_Φ = −1/2 on the scalar Born/Weyl typed readout quotient and the single-character IO-admissible kernel class; raw-algebra finite-shell uniqueness is explicitly not claimed (Corollary 31.KS7). A Code and Data Availability section is added with the public reproducibility bundle (immutable release tag paper31-v2.0, SHA256 prefix 52381e0a, validator 62/62 PASS). See https://github.com/dfife/io-framework-public/tree/main for claim-naming convention. v1.2 (April 2026): Rebuild audit. Paper 10 legacy branch confirmed as sole survivor after conditional Schur branch retirement (Paper 29). All branch-dependent values updated. Appendix replaced with Paper 30 v1.3 clean chain. Appendices B and C removed. Open/Closed Problems and Acknowledgments added. Branch labels, AI verification tags, and author block corrected. v1.1 (April 2026): Paper 24 v2.0 consistency update. TBSb promoted from SEMICLASSICAL PRINCIPLE to DERIVED/SCOPED on the physical Paper 24 TT observable class via the Modular Intertwiner Theorem (Paper 24 v2.0 §13.2). BBN conditional status updated. Debt summary updated. v1.1 (April 2026): Paper 24 v2.0 consistency update. TBSb promoted from SEMICLASSICAL PRINCIPLE to DERIVED/SCOPED on the physical Paper 24 TT observable class via the Modular Intertwiner Theorem (Paper 24 v2.0 §13.2). BBN conditional status updated. Debt summary updated.