Medical large language models can produce fluent long-form responses containing contradicted, insufficiently supported, or over-specified clinical claims. We introduce ClinClaim-ARC, an evidence-constrained framework for post-generation clinical claim repair. The framework decomposes responses into structured claims, assigns four evidence states (supported, contradicted, unsupported, and partially supported), and constructs provenance-constrained repair candidates through a Clinical Claim Repair Graph. Unresolved claims trigger claim-targeted evidence acquisition, while Learn-then-Test certifies complete repair policies against Contradiction Retention Risk and Insufficient-Evidence Retention Risk. On a PubMedQA-derived answer-level repair benchmark, ClinClaim-ARC achieves a 76.4% valid repair rate and 87.9% supported-information retention, with held-out empirical contradiction and insufficient-evidence retention risks of 0.032 and 0.074, respectively, against pre-specified calibration targets of 0.05 and 0.10. On K-QA, the framework reduces Hall from 0.214 to 0.103 while maintaining a completeness score of 0.594 and a response rate of 93.5%. Ablation results further show that structured repair, four-state verification, and claim-targeted evidence acquisition each contribute to information-preserving reliability. These results show that evidence-constrained repair reduces reference-evidence-defined factual risk while retaining more supportable clinical information than filtering- only approaches.