Beyond Local Accuracy: A Protocol-Level Identifiability Audit for Controlled LLM Reasoning Evaluation

LLM benchmark scores can be precise even when the observation protocol does not identify the behavioral property they are intended to measure. In a controlled, solver-grounded setting, we formalize a protocol-level identifiability audit over a finite behavioral policy class: given policies H, observation support O, and estimand $τ$, we test whether O separates every pair with different $τ$. The audit requires zero model calls and resolves our diagnostic case: base-only observation collapses seven frozen deterministic policies into one equivalence class; full support yields seven classes and no cross-estimand collisions; every leave-one-out support retains a constructive collision witness. Empirically, both constrained-generation variants have pair-validity 1.0, yet base accuracy and selective-response fidelity diverge - 0.620 versus 0.324 across six balanced oracle-transition directions (cluster-bootstrap 95% CI [0.600, 0.642] vs. [0.304, 0.345]) - and the gap recurs on a second deterministic source (0.646 vs. 0.331). The audit also synthesizes a minimum identifying support $O^*$ for the frozen policy class: two cells instead of the full 36-cell tensor. This case shows how evaluation-design validity can be checked structurally before model inference and why base correctness does not determine intervention-response fidelity.