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: ηIO = 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 ΣIO = 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 Nₑff = Δ identification, conditionally closes the galaxy BAO ruler at 0. 046% residual against DESI DR2, settles the optical depth at τ = Kgauge/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 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.