State-Metric Mismatch in Shallow QAOA: Non-Monotonic Relations Between Expected Energy and Constraint Feasibility

This preprint studies whether expected-energy improvement guarantees improved constraint feasibility in a shallow QAOA setting. A frozen six-point, 24-variable, K=5, p=1 simulation panel is audited across all 15 pairwise comparisons. Five pairs show opposite directional changes between expected energy and P(K=5), while ten are aligned. The 5/15 count is explicitly descriptive because the pairs are dependent. A separate high-contrast transition is retained only as an illustration. The paper distinguishes finite-shot simulator evidence from exact statevector and physical-QPU evidence, removes a non-preregistered illustrative threshold from the primary analysis, and makes no quantum-advantage or universal-QAOA claim.