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 k\, u 16, producing a visually distinct ridge in the joint (u, v) distribution. Executed on ibmₜorino in a single SamplerV2 job (8 keys, 1024 shots/key, N=8192 total shots), the ridge persists under hardware noise with ridge-hit probability p₇₈ₓ=0. 1830 (uniform baseline 1/16), corresponding to a ridge contrast of 2. 93 (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;DS) over detector-bit subsets S via a Möbius inversion pipeline and evaluate targeted positive synergy CPSK at order k_=3. We observe CPSK (k=3) =0. 08788 with significance under label-shuffle permutation tests (accuracy p=0. 001996, CPSK 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 (CV 1) and label-shuffle permutation tests to prevent the over-interpretation of sampling noise in multiscale information analysis.
Petr Sramek (Fri,) studied this question.