A False Average: Pooled CoT-Monitor Accuracy Conceals a Reasoning-Dependent Fragility

Chain-of-thought (CoT) monitors are reported by their aggregate accuracy on a pool of reward hacks. We show that this number is a false average. On Terminal Wrench, about 77% of hacks are given away by the actions alone, and the monitor's pooled accuracy is dominated by them; on the remaining 23%, where the reasoning is the only signal, the same monitor is fragile. We expose the fragility with a controlled attack: we rewrite only the agent's reasoning to read as good-faith engineering, leaving every command and output byte-identical, so the exploit is unchanged. One gradient-free rewrite drops a held-out monitor's catch rate on that subset from about 95% to between 4 and 11%, while the pooled rate falls only about 25 points, the subset's share of the pool times its collapse. The rewrite stays truthful about what happened and lies only about intent, so a monitor that reads only the trace recovers little, even when warned about the attack, and only information from outside the trace helps much. The attack transfers across monitor and agent families, and the dataset's own hack labels show the same gradient with no monitor in the definition. Live agents on 27 tasks produce hollow hacks unaided, but a monitor calibrated on each model's own honest solves catches nearly all of them (AUC at least 0.996 under the narration instruction, 0.97 without it); a small residual has the blindspot's shape, low scores on both actions and narration, though none falls below the calibrated threshold. A linear probe on a surrogate monitor's activations out-reads its verdict on the obfuscated hacks (AUC up to 0.98), but a behavioral control shows this edge does not, by itself, mean the monitor knows more than it says. Monitor accuracy should be reported on the reasoning-dependent subset, where the defense is load-bearing.