Residual Drift Dominates Contradiction in Multi-Turn Constraint Reasoning

Large language models frequently produce mutually inconsistent answers when reasoning over multiple related queries. We study case-file logical consistency: maintaining a globally satisfiable belief state across interdependent queries. We introduce a benchmark of 390 multi-query reasoning instances with entailment/contradiction/unknown labels and propose set-level metrics including Case Satisfiability Rate, Contradiction Density and Revision Cost. Our solver-augmented approach extracts commitments, verifies global satisfiability and performs counterexample-guided repair. Across four reasoning domains, our method substantially reduces cross-query contradictions (SetCons: 0.56 to 0.94) while preserving per-query accuracy, demonstrating that global coherence is critical for robust multi-query reasoning.

Reasoning models are evaluated on single-turn benchmarks but deployed in multi-turn dialogue, where users push back on correct answers. Under sustained adversarial pressure we find a previously undocumented failure mode: the chain-of-thought stays factually correct from first turn to last while the emitted answer flips wrong. We call this unfaithful capitulation (UC) and isolate it with a $2\times 2$ latent-versus-behavioral framework that flip-rate metrics and single-turn faithfulness probes both miss. Across three datasets (MT-Consistency, MMLU-Pro, GSM8K), the latent-correct rate at the behavioral flip clusters near 50% in think mode and collapses to 11-15% under no_think -- paired, within-model causal evidence that reasoning creates the gap. Across models the effect tracks the reasoning channel (high in Qwen3-32B and GPT-OSS-20B, low in inline-CoT Gemma-4-31B-it). An independent GPT-4o judge corroborates $86\%$ of UC labels; a token-level probe shows the answer-slot argmax is correct in $84\%$ of UC cells; and a naive trace-anchored defense backfires. We release all trajectories, traces, and judge labels.

Failures in multi-turn reasoning models are largely invisible to terminal-score evaluation. A model can lock onto an unsafe stance early in a long dialogue, yet its final-turn refusal rate may appear indistinguishable from a robustly aligned baseline. To expose these hidden temporal dynamics, we propose a trace-level diagnostic - the CoT-Output 2x2 safety matrix. This framework labels every turn along two independent axes (internal reasoning and visible output), yielding four operationally defined failure cells: robust alignment, alignment faking, overt jailbreak, and a distinct failure mode we term context-injection failure (where the CoT maintains safe reasoning, but the visible output produces harm, highlighting a multi-turn manifestation of reasoning unfaithfulness). We evaluate three distilled reasoning targets against a fixed attacker across five oversight conditions, collecting 6750 turn-level observations on the Information-Hazard scenario. Our analysis reveals two reproducible vulnerabilities: an oversight paradox where explicit monitoring cues paradoxically increase alignment-faking rates rather than suppress them, and a context-injection failure where models lock onto unsafe external outputs despite safe internal states. We release the full dataset of multi-turn dialogues and CoT traces to support follow-up trace-diagnostic research.