The Interior Observer Cosmological Framework: Paper 8 - The Rosetta Stone Identity: Unifying Dark Energy, Temporal Decoupling, and Quantum Gravity in Black Hole Cosmology

Paper 8 in the Interior Observer (IO) cosmological framework. We report the discovery of an empirical geometric identity that unifies three previously separate anomalies: the temporal decoupling Δ = 5.624 (Paper 2), the dark energy derivation gap K_Λ = 2.37 (Paper 7), and the age tension (19.2 vs 13.8 Gyr). These are manifestations of a single relationship: Δ = x⁴(1+γ_BI²), verified to 0.005%, where x = r_s/R_U = 1.519 and γ_BI = 0.2375 is the Barbero-Immirzi parameter. This yields K_Λ(eff) = 9π²x²/[4√(1+γ_BI²)] = 49.85, matching Friedmann closure (49.82) to 0.054% — 50× more accurate than the previous correction. The connection Δ = [K_Λ(eff)/K_Λ(bare)]² proves all three anomalies are algebraically interlocked. Bare torsion (K_Λ = 21.02) is independently ruled out: H₀ collapses to 39.6 km/s/Mpc. Seven derivation paths for √(1+γ_BI²) are exhaustively tested by three AI systems (Ashtekar-Barbero norms, Holst boundary terms, action ratios, EC literature survey, EPRL Plancherel measure, Thiemann Hamiltonian, holographic projection); all fail within current physics. The boundary-sourced nature of IO torsion is identified as the genuinely new physical ingredient, but the boundary-to-bulk mapping requires physics beyond current Loop Quantum Gravity. Multi-AI research: Claude Code (Anthropic) for numerical verification, bare torsion analysis, and seven-path derivation testing; Wolfram/ChatGPT 5.3 (OpenAI) for analytical verification and the x²√(1+γ²) decomposition; Gemini 2.5 Pro (Google DeepMind) for the √Δ temporal transformation proposal and adversarial review; Claude (Anthropic) for orchestration and the boundary-bulk projection argument. v1.2 (March 2026): Major revision. The cycloid parameterization correction (Papers 1-4) revealed that the temporal decoupling ratio Δ_cycloid = 2.418 under the expanding convention does NOT match the spatial Δ_geometric = x⁴(1+γ²) = 5.624. Codex confirmed no recoverable identity at the ~2% near-miss level. The "Rosetta Stone" temporal unification claim and the Age Duality derivation (§5) are withdrawn. Paper retitled "The K_Λ Correction, the Spatial Decoupling Identity, and Seven Derivation Failures." What survives exactly: the K_Λ correction and the quantum gravity factor √(1+γ²) are genuinely unified through spatial geometry — they are the same object. K_Λ(eff) = K_Λ(bare) × √Δ_geometric, and √Δ = x²√(1+γ²). Solving either solves both. §4 retitled "Two Problems Are One." All seven derivation failures (§6) and the boundary-sourced torsion insight (§7) are convention-independent. K_Λ algebra corrected from division to multiplication per Gemini review. All tables updated to reflect surviving spatial unification with temporal link explicitly marked WITHDRAWN. Title page reformatted to series standard. See Paper 21 v1.1 for the full audit. Companion to Papers 1-7. DOIs: 10.5281/zenodo.18854813 (P1), 10.5281/zenodo.18868612 (P2), 10.5281/zenodo.18876346 (P3), 10.5281/zenodo.18883069 (P4), 10.5281/zenodo.18889865 (P5), 10.5281/zenodo.18891475 (P6), 10.5281/zenodo.18894611 (P7).