We introduce κ-profiles: a low-overhead, context-resolved diagnostic for Z-diagonal unitaries that reveals context-dependent phase structure—structure that scalar benchmarks compress away by design. Such structure, arising from higher-order diagonal interactions, can silently corrupt variational algorithms and Hamiltonian simulations while passing conventional health checks. Full tomography can in principle catch it, but at intractable cost as processors scale. κ-profiles exploit plaquette curvature—a gauge-invariant quantity that is context-independent under 2-local diagonal structure but can become context-dependent when higher-order terms involve the diagnostic pair. The readout requires only four circuit settings per spectator context, using single-qubit Cliffords and Z-basis measurement in addition to the unitary under test. We prove that 2-local diagonal unitaries yield flat κ-profiles, and that terms of weight ≥ 3 involving the diagnostic pair can break this flatness. Simulations (n = 2–7) confirm the predicted contrast, and IBM QPU experiments corroborate that it is observable under real-device noise: profile dispersion grows with injected 3-local content while scalar summaries remain nearly unchanged. Sampling-based by design, the measurement overhead scales with the desired statistical precision—not qubit count—making κ-profiles practical for near-term processors and larger devices on the horizon.