arXiv:2607.18240v1 Announce Type: new Abstract: Large language models (LLMs) can achieve strong fact-checking accuracy, yet forced binary decisions conceal a critical reliability problem: systems may issue confident verdicts even when supporting evidence is weak, sparse, or internally inconsistent. We address this issue through Evidence Chain Evaluation (ECE), a selective fact-checking framework that permits abstention via an uncertain verdict instead of requiring a true/false decision for every claim. The evaluated system is a tool-using verification agent that gathers evidence through web search, scholarly search, and executable checks, and then returns a structured verdict with confidence and source-level metadata. On ECE-Bench, ECE achieves 91.6% standard accuracy, 93.7% coverage, and 97.8% selective accuracy on answered claims. Although ECE does not outperform the strongest retrieval baseline on aggregate calibration metrics such as Expected Calibration Error, Brier score, or AURC, it delivers a clear selective-prediction trade-off: the system maintains very high accuracy on answered claims while deferring 6 of 95 cases. These deferred cases are concentrated in lower-reliabili