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

arXiv: https://arxiv.org/abs/2608.13326 · HTML: https://mlsanity.com/paper/2608.13326/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning.
- Builds on 9 of its 21 references that are in the map.
- First posted on arXiv 13 Aug 2026.

## Placed in

- LLM reasoning / [Test-time compute and efficient thinking](https://mlsanity.com/lr/test-time-compute-and-efficient-thinking/)

## Builds on (most cited first, 9 of 9)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [Language Models Don't Always Say What They Think: Unfaithful Explanations in Chain-of-Thought Prompting](https://mlsanity.com/paper/2305.04388/) (2023)
- [Measuring Faithfulness in Chain-of-Thought Reasoning](https://mlsanity.com/paper/2307.13702/) (2023)
- [GSM-Symbolic: Understanding the Limitations of Mathematical Reasoning in Large Language Models](https://mlsanity.com/paper/2410.05229/) (2024)
- [Measurement to Meaning: A Validity-Centered Framework for AI Evaluation](https://mlsanity.com/paper/2505.10573/) (2025)
- [Dissociation of Faithful and Unfaithful Reasoning in LLMs](https://mlsanity.com/paper/2405.15092/) (2024)
- [Compared to What? Baselines and Metrics for Counterfactual Prompting](https://mlsanity.com/paper/2605.01048/) (2026)

## Abstract (arXiv)

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.