A Page-Time Synergy Peak on IBM Quantum Hardware: Threshold-Lock Demonstration of High-Order DAGI Structure on ibm_torino

Context: This manuscript belongs to the empirical hardware-validation track of the DAGI (Directed Acyclic Graph Interpretation) research program at Whytics. It provides direct experimental evidence for high-order informational thresholding, a concept central to the framework's treatment of emergent spacetime and black hole information. Abstract: The Directed Acyclic Graph Interpretation (DAGI) framework predicts that certain globally coherent variables are not locally accessible, but instead reside in irreducible high-order information structures (synergy) that become available only when sufficiently many degrees of freedom are jointly accessed. Motivated by Page-time transitions in black-hole information and by entanglement-wedge thresholds in holographic quantum error correction, we design a deliberately minimal "threshold-lock" circuit family whose measurement statistics implement a synergy-only encoding of a binary label $K$: all 1- and 2-bit marginals of the early radiation are (ideally) independent of $K$ while the 3-bit prefix jointly reveals $K$. We execute this experiment on IBM Quantum ibm_torino with $n=6$ measured qubits and 2048 shots per key, alongside a "leaky" control in which low-order information is intentionally present. Using a Möbius/DAGI decomposition of the mutual information over the prefix subset lattice, we observe a sharp Page-like turn-on for the locked variant, with cumulative positive synergy dominated entirely by an intrinsic order-3 term. A bootstrap reliability sweep confirms that the locked order-3 synergy mass is statistically stable, while the leaky order-3 signal remains unstable. These results constitute a compact, falsifiable hardware demonstration that DAGI can detect and distinguish high-order, thresholded information release from low-order leakage in real quantum measurement data, supporting the use of DAGI Möbius diagnostics as experimental probes of Page-like information transitions and as design tools for DAG-inspired QECCs. Key Highlights: Hardware-Verified Thresholds: Demonstrates a distinct Page-curve-like accessibility transition on a superconducting IBM Quantum processor. Synergy vs. Leakage: Proves the efficacy of the DAGI Möbius decomposition in distinguishing true irreducible high-order synergy from low-order hardware leakage. Holographic Analogs: Provides an operational, circuit-level analog for entanglement-wedge reconstruction phenomena utilized in emergent gravity and holographic error correction.