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+γBI²), verified to 0. 005%, where x = rₛ/RU = 1. 519 and γBI = 0. 2375 is the Barbero-Immirzi parameter. This yields K_Λ (eff) = 9π²x²/4√ (1+γBI²) = 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+γBI²) 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).