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. 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).