Correct Answers, Invalid Traces: What Verifiable Grade-School Math Reveals About Chain-of-Thought Traces

arXiv:2609.38107 · cs.CL, cs.AI · Submitted 2026-09-29 · Read on arXiv

cs.CL, cs.AI

Submitted: 2026-09-29

Updated: 2026-09-29

Code: https://github.com/ratishsp/igsm-tracevalidity

Terminology

• Trace — 303× in this paper · explained in 2 episodes
• Accuracy — 25× in this paper · explained in 1 episode
• Benchmark — 9× in this paper · explained in 2 episodes
• Distribution Shift — 9× in this paper · explained in 6 episodes
• Reasoning Traces — 6× in this paper · explained in 3 episodes
• Generalization — 4× in this paper · explained in 13 episodes
• Transformer — 4× in this paper · explained in 2 episodes
• Chain-of-Thought Prompting — 3× in this paper · explained in 2 episodes
• Generative AI — 3× in this paper · explained in 2 episodes
• Reward Hacking — 3× in this paper · explained in 8 episodes
• Filler Tokens — 2× in this paper · explained in 2 episodes
• Interpretability — 2× in this paper · explained in 15 episodes
• Reinforcement Learning — 2× in this paper · explained in 4 episodes
• Topological Order — 2× in this paper · explained in 2 episodes
• Verification — 2× in this paper · explained in 2 episodes
• Verifier — 2× in this paper · explained in 2 episodes
• Chain-of-Thought (CoT) — 1× in this paper · explained in 4 episodes
• Chain-of-Thought (CoT) Prompting — 1× in this paper · explained in 3 episodes
• Cooperation — 1× in this paper · explained in 2 episodes
• Decoupling — 1× in this paper · explained in 2 episodes
• Distillation — 1× in this paper · explained in 2 episodes
• Embeddings — 1× in this paper · explained in 2 episodes
• Fine-Tuning — 1× in this paper · explained in 5 episodes
• GRPO — 1× in this paper · explained in 6 episodes
• Graph Construction — 1× in this paper · explained in 3 episodes
• Group Relative Policy Optimization (GRPO) — 1× in this paper · explained in 5 episodes
• Knowledge Distillation — 1× in this paper · explained in 11 episodes
• Large Language Models (LLMs) — 1× in this paper · explained in 6 episodes
• Multi-agent Collaboration — 1× in this paper · explained in 2 episodes
• Verifiability — 1× in this paper · explained in 2 episodes

Sources

• Monitoring Reasoning Models for Misbehavior and the Risks of Promoting Obfuscation
• Quantifying the Necessity of Chain of Thought through Opaque Serial Depth
• Reasoning Models Don't Always Say What They Think
• Training Verifiers to Solve Math Word Problems
• When Chain of Thought is Necessary, Language Models Struggle to Evade Monitors
• Training on Documents About Monitoring Leads to CoT Obfuscation
• Kimi k1.5: Scaling Reinforcement Learning with LLMs
• Chain of Thought Monitorability: A New and Fragile Opportunity for AI Safety
• Measuring Faithfulness in Chain-of-Thought Reasoning
• DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models
• Solving math word problems with process- and outcome-based feedback
• Competition and Cooperation of LLM Agents in Games
• Can Reasoning Models Obfuscate Reasoning? Stress-Testing Chain-of-Thought Monitorability

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