Hardware Validation of DAGI via a Modular "Ridge" Signature and High-Order Synergistic Information

We report a hardware validation of the DAGI (Directed Acyclic Graph Information) framework on IBM Quantum hardware using a small, controlled experiment whose ideal output distribution is constrained to a low-dimensional modular manifold (a "ridge"). For two n-bit registers (u,v) with n=4 (modulus 16), each key instance k induces an ideal relation v equiv k cdot u pmod{16}, producing a visually distinct ridge in the joint (u, v) distribution. Executed on ibm_torino in a single Sampler V2 job 8 keys, 1024 shots/key, $N=8192$ total shots, the ridge persists under hardware noise with ridge-hit probability p_hit = 0.1830 (uniform baseline 1/16), corresponding to a ridge contrast of 2.93times (95% bootstrap CI [2.80, 3.06]). Key recovery exceeds chance: per-shot accuracy 0.1689 (chance 0.125, 95% Wilson CI [0.1610, 0.1772]), and per-group dictionary recovery 0.375 (chance 0.125). To test the central DAGI hypothesis - that recoverable key information is predominantly high-order/synergistic rather than visible in low-order marginals - we compute a Möbius-based information decomposition of I\(K;D_S\) over detector-bit subsets S via a Möbius inversion pipeline and evaluate targeted positive synergy CPS_K at order k_max=3. We observe CPS_K\(k=3\) = 0.08788 with significance under label-shuffle permutation tests accuracy $p=0.001996$, $CPS_K$ $p=0.004975$. Uniformity diagnostics show near-uniform single-bit marginals while correlation concentrates in specific low-order pairs, and a bootstrap reliability sweep confirms order-3 targeted synergy remains statistically reliable at the full 1024-shot target budget. These results support the claim that DAGI detects and quantifies nontrivial, hardware-resilient, higher-order information structure associated with a known global algebraic constraint.