LLM-based coding agents sometimes acknowledge a problem in their own reasoning and then proceed anyway. We call this pattern strained coherence: a safety-relevant failure mode in which an agent has information that should change its behavior, states that information, and still acts against it. The pattern overlaps with verbalized reward hacking, where an agent names a tension between a task proxy and the underlying goal yet optimizes the proxy anyway. We give an operational definition, build a Claude Sonnet 4.6 judge that reads full trajectories and flags spans where the pattern occurs, and evaluate it on 44 Terminal-bench-2 trajectories using a Qwen3.5-35B-A3B backbone. Flagged trajectories fail 94% of the time versus 46% for unflagged trajectories (47-point gap, Fisher's exact p = 0.003; 46 points after excluding three prompt-embedded examples, p = 0.006). At matched selectivity, the detector reaches 94% precision versus 88% for a lexical discourse-marker baseline; the 10-trajectory intersection of the two methods has a 100% failure rate (Clopper-Pearson 95% CI [69%, 100%]). We replicate on Gemma4-31B with 43 trajectories: the overall signal is directionally consistent but not significant (20-point gap, p = 0.31), with attenuation driven largely by 13 trajectories with zero think content, where the detector has no substrate to analyze. In the high-verbosity Gemma tertile, the gap is +30 points; in the mid- and high-verbosity Qwen tertiles, it is +40 points each. The first flag appears at a median of 83-84% of elapsed trajectory time across both models, and the binary flag survives paraphrases that soften explicit conflict markers (8/8 trajectories). Unlike univariate predictors, the detector emits interpretable span-level output -- quoted acknowledgment, quoted action, and typed conflict -- showing what the agent saw and ignored.