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

Context: This manuscript belongs to the empirical hardware-validation track of the DAGI (Directed Acyclic Graph Interpretation) research program at Whytics. It provides an operational demonstration of how high-order synergistic information can map to known global algebraic constraints on noisy superconducting quantum hardware. Abstract: We report a hardware validation of the DAGI 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 $v \equiv k\,u \pmod{16}$, producing a visually distinct ridge in the joint $(u,v)$ distribution. Executed on ibm_torino in a single SamplerV2 job (8 keys, 1024 shots/key, $N=8192$ total shots), the ridge persists under hardware noise with ridge-hit probability $p_{\mathrm{hit}}=0.1830$ (uniform baseline 1/16), corresponding to a ridge contrast of 2.93$\times$ (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 $\mathrm{I}(K;D_S)$ over detector-bit subsets $S$ via a Möbius inversion pipeline and evaluate targeted positive synergy $\mathrm{CPS}_K$ at order $k_{\max}=3$. We observe $\mathrm{CPS}_K(k=3)=0.08788$ with significance under label-shuffle permutation tests (accuracy $p=0.001996$, $\mathrm{CPS}_K$ $p=0.004975$). 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 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. Key Highlights: Hardware-Resilient Algebra: Proves that low-dimensional global algebraic signatures (modular ridges) survive transpilation and noise on physical IBM Heron processors. Synergy vs. Marginals: Demonstrates via Möbius inversion that latent key information resides predominantly in cross-register, higher-order correlations, while single-bit marginals remain indistinguishable from uniform noise. Statistical Reliability: Establishes rigorous bootstrap reliability frontiers ($\mathrm{CV} \le 1$) and label-shuffle permutation tests to prevent the over-interpretation of sampling noise in multiscale information analysis.