Chain-of-thought (CoT) faithfulness is measured almost exclusively in single-turn settings, leaving open how the reasoning-trace-to-answer relationship evolves as conversations lengthen. We introduce turn-level CoT counterfactual deletion: at every assistant turn we regenerate the answer at five truncation levels of the current-turn thinking block under greedy decoding, and label a turn anchored—a descriptive label for causal redundancy of the trace, not a mechanistic claim—when all five regenerations agree on the same answer. Across 67 multi-turn sharded-GSM8K conversations from DeepSeek-R1-Distill-Qwen-7B, the anchored fraction grows 3.9× from short (< 10 turns, 7.2%) to long (> 20 turns, 28.4%). Strict early < mid < late monotone ordering holds in five of seven reasoning models from three base families and four post-training pipelines (binomial sign test, p=0.002). A supplementary pooled GEE across all seven models converges on this direction (β=1.12, p=5.1×10⁻⁸, n=2,838 turn-level rows). A surface-feature predictor flags anchored turns at AUC= 0.71 (+0.07 over a length-only baseline) without additional generation, providing a cheap online signal for CoT monitors calibrated on short conversations. Single-turn CoT benchmarks, by construction, cannot detect this gradient.