The QIG Lock: A Holographic Proof of the Unification of Mass and Gauge Sectors

This paper derives and completes a full holographic embedding of the Quantum Informational Gravity (QIG) framework within a dynamically consistent scalar-gravity theory. We construct an explicit UV-AdS fixed point, solve for the domain wall and black brane background, and recover a natural "drift window" where the QIG scalar exhibits logarithmic flow. The resulting two-point function is shown to display a robust log-Gaussian bump — a unique signature not reproducible by standard Einstein-dilaton models. Real lattice QCD and AdS/QCD data overlays are presented, aligning with the QIG-predicted anomaly structure. This final derivation includes full beta-function flow, renormalization analysis, and invariant signature plots that validate QIG’s superiority over traditional scalar-gravity embeddings. The included Colab notebook numerically solves all background equations and generates the final figure. This work establishes QIG as a UV-complete, testable, and physically grounded gravitational model — a potential cornerstone for the next generation of quantum gravity.