# Does CoT-Pass@k Really Check the CoT? A Multilingual Mathematical Audit

arXiv: https://arxiv.org/abs/2609.32622 · HTML: https://mlsanity.com/paper/2609.32622/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 28 of its 46 references that are in the map.
- First posted on arXiv 26 Sep 2026.

## Builds on (most cited first, 28 of 28)

- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Language Models Don't Always Say What They Think: Unfaithful Explanations in Chain-of-Thought Prompting](https://mlsanity.com/paper/2305.04388/) (2023)
- [DeepSeek-V4: Towards Highly Efficient Million-Token Context Intelligence](https://mlsanity.com/paper/2606.19348/) (2026)
- [Large Language Monkeys: Scaling Inference Compute with Repeated Sampling](https://mlsanity.com/paper/2407.21787/) (2024)
- [Does Reinforcement Learning Really Incentivize Reasoning Capacity in LLMs Beyond the Base Model?](https://mlsanity.com/paper/2504.13837/) (2025)
- [Solving math word problems with process- and outcome-based feedback](https://mlsanity.com/paper/2211.14275/) (2022)
- [ProcessBench: Identifying Process Errors in Mathematical Reasoning](https://mlsanity.com/paper/2412.06559/) (2024)
- [Reinforcement Learning with Verifiable Rewards Implicitly Incentivizes Correct Reasoning in Base LLMs](https://mlsanity.com/paper/2506.14245/) (2025)
- [Adding Error Bars to Evals: A Statistical Approach to Language Model Evaluations](https://mlsanity.com/paper/2411.00640/) (2024)
- [Measuring what Matters: Construct Validity in Large Language Model Benchmarks](https://mlsanity.com/paper/2511.04703/) (2025)
- [PRMBench: A Fine-grained and Challenging Benchmark for Process-Level Reward Models](https://mlsanity.com/paper/2501.03124/) (2025)
- [A Chain-of-Thought Is as Strong as Its Weakest Link: A Benchmark for Verifiers of Reasoning Chains](https://mlsanity.com/paper/2402.00559/) (2024)
- [Are Your LLMs Capable of Stable Reasoning?](https://mlsanity.com/paper/2412.13147/) (2024)
- [Crosslingual Reasoning through Test-Time Scaling](https://mlsanity.com/paper/2505.05408/) (2025)
- [Linguistic Generalizability of Test-Time Scaling in Mathematical Reasoning](https://mlsanity.com/paper/2502.17407/) (2025)
- [Don't Pass@k: A Bayesian Framework for Large Language Model Evaluation](https://mlsanity.com/paper/2510.04265/) (2025)
- [Exposing the Achilles' Heel: Evaluating LLMs Ability to Handle Mistakes in Mathematical Reasoning](https://mlsanity.com/paper/2406.10834/) (2024)
- [MaskLID: Code-Switching Language Identification through Iterative Masking](https://mlsanity.com/paper/2406.06263/) (2024)
- [Beyond Pass@k: Breadth-Depth Metrics for Reasoning Boundaries](https://mlsanity.com/paper/2510.08325/) (2025)
- [Cetvel: A Unified Benchmark for Evaluating Language Understanding, Generation and Cultural Capacity of LLMs for Turkish](https://mlsanity.com/paper/2508.16431/) (2025)
- [A Comprehensive Evaluation of Multilingual Chain-of-Thought Reasoning: Performance, Consistency, and Faithfulness Across Languages](https://mlsanity.com/paper/2510.09555/) (2025)
- [Outcome Rewards Do Not Guarantee Verifiable or Causally Important Reasoning](https://mlsanity.com/paper/2604.22074/) (2026)
- [MathMist: A Parallel Multilingual Benchmark Dataset for Mathematical Problem Solving and Reasoning](https://mlsanity.com/paper/2510.14305/) (2025)
- [TurkBench: A Benchmark for Evaluating Turkish Large Language Models](https://mlsanity.com/paper/2601.07020/) (2026)
- [How Long Reasoning Chains Influence LLMs' Judgment of Answer Factuality](https://mlsanity.com/paper/2604.06756/) (2026)
- [MATH-PT: A Math Reasoning Benchmark for European and Brazilian Portuguese](https://mlsanity.com/paper/2604.25926/) (2026)
- [An Enigma of Artificial Reason: Investigating the Production-Evaluation Gap in Large Reasoning Models](https://mlsanity.com/paper/2606.01462/) (2026)

## Abstract (arXiv)

Pass@k measures whether a model reaches a correct answer under repeated sampling, but never how: a lucky guess counts the same as sound reasoning. CoT-Pass@k was proposed to close that gap, adding an LLM-as-judge that must assess a solution's reasoning chain before it counts. Its value rests entirely on one assumption: that the judge catches flawed reasoning. That assumption has never been tested inside the metric that depends on it, and never outside English, though the metric's claims concern models used in many languages. We report the first audit of that verification step, run under the metric's own protocol on a multilingual suite of five mathematical benchmarks in English, Turkish and Portuguese, two of them natively written. We corrupt correct solutions with deterministic edits that damage the chain and the final answer separately. We observe that all three judges accept corrupted chains almost as often as clean ones. V4-Flash and Qwen3.6 reject a solution sharply only when its final answer is wrong and accept a wrong answer more readily when the chain agrees with it; the metric's own judge accepts most wrong answers as well. Our study shows that chain-answer agreement dominates the two larger judges' verdicts and that all three fail to reliably detect the tested reasoning errors. Consequently the difference Pass@k - CoT-Pass@k averages 19.7 points on an earlier solver generation but only 4.1 on the current one. What little remains depends on the token budgets on both sides and on the generation mode; raising the generation budget moves Pass@64 by more than fifty points while the difference stays at zero. We close with two checks any judged reasoning metric should pass before its numbers are read as evidence about reasoning.