Probing the LQG-Holography Transition via OTOC Measurements on Quantum Hardware: Theoretical Framework, Experimental Verification, and Emergent Geometry

We introduce and experimentally probe a continuous interpolation parameter λ ∈ 0,1 that operationally connects integrable dynamics—characteristic of Loop Quantum Gravity (LQG)-like regimes—with maximally scrambling dynamics associated with holographic theories. The relation α(λ) = -1/2 - λ emerges independently from tensor network coarse-graining and holographic quantum error correction arguments. Experiments on IBM Quantum processors verify the formula across multiple circuit models. NEW IN v2: We extend the framework by showing that promoting λ to a dynamical field obeying an RG flow equation uniquely determines AdS₂ as the emergent geometry compatible with RG invariance. This demonstrates that geometry appears as an OUTPUT of information accessibility dynamics, not as an input assumption.