Operator-Level Physics, UHF VS Flagship AI CLAUDE 4.5 TEST Public-Facing Experiment 12/21/2025 Reduction.

This work presents a rigorous operator-level physics framework, the Unified Harmonic Framework (UHF), for modeling quantum-gravitational systems. We conduct a public-facing benchmark comparing flagship AI systems, including untrained base models and large-scale transformer models, against a human-in-the-loop approach grounded in UHF mathematics. The study demonstrates that conventional AI, even when exposed to partial domain knowledge, cannot derive new operator-level physics or recover Einstein field equations from first principles. Using a master Hilbert Engine operator formalism, we explicitly encode nonlinear metric dynamics, dynamic mode interactions, time-dependent cosmological backgrounds, and quantized graviton modes. The results highlight the unique capability of the UHF and associated human-guided methodology to generate mathematically rigorous and fully defensible physical derivations that remain inaccessible to AI operating without complete framework knowledge