Empirical Falsification of Pairwise-Only Explanations for an Engineered Parity Benchmark on a 133-Qubit Superconducting Processor

Scalable quantum characterization and error-mitigation workflows often rely on the assumption that relevant device noise and readout contamination can be adequately captured by low-weight, predominantly pairwise interactions. We report a compact hardware experiment designed to operationally distinguish pairwise-only explanations from irreducible triplet-order predictive structure. The A1/A1b protocol implements a parity-structured binary label on a 133-qubit IBM superconducting processor ibm_torino and analyzes the resulting data through a classical M"obius decomposition of subset mutual informations. In the A1 baseline, we observe a macroscopic triplet correlation of f(123) = 0.72609 bits p <= 1.0e-4, permutation floor. In the strict A1b loophole-reduction follow-up, role-symmetry averaging sharply suppresses singleton leakage, modestly reduces pairwise mismatch, and preserves a large irreducible triplet term of f(123) = 0.56521 bits. Crucially, a principled pairwise maximum-entropy baseline consistent with the empirical 1- and 2-body marginals implies only f(123) 6.6e-6 bits, in strong contradiction with the observed hardware data. On A1b, a classifier built exclusively from pairwise features reaches only 0.617 held-out accuracy (chance 0.5), whereas a triplet-inclusive model reaches 0.910. These results provide a concise, open-data demonstration that pairwise benchmarking proxies can be fundamentally blind to higher-order contextual structure in present-day superconducting experiments.