Large Reasoning Models (LRMs) are valuable intellectual property due to their substantial training and alignment costs, creating a need for reliable ownership verification under black-box access, where a verifier can only query a suspect model and inspect its returned output. Existing trigger–response fingerprints are easy to test but are often weakly coupled with Chain-of-Thought (CoT) reasoning and can be fragile under paraphrasing or post-hoc model modifications. We propose CoT-Lock, a reasoning-mediated fingerprinting framework that casts ownership verification as a structured conflict-resolution task. CoT-Lock constructs verification queries in which a default semantic constraint is superseded only by a higher-priority meta-override rule, training the model to resolve fingerprint activation through priority-based arbitration. Our primary ownership test is output-only on confidential held-out probes; when reasoning traces are visible, trace-level verification further checks the expected arbitration process. Experiments on representative reasoning architectures show that CoT-Lock achieves stable black-box verification while preserving reasoning ability with minimal performance degradation, low false positives, and improved robustness against paraphrasing, fine-tuning, pruning, and quantization. Our code is available at https://github.com/acang425/CoT-Lock.