Peer review is central to scientific publishing, yet reviewers frequently include claims that are subjective, rhetorical, or misaligned with the submitted work. Assessing whether review statements are factual and verifiable is crucial for fairness and accountability. At the scale of modern conferences and journals, manually inspecting the grounding of such claims is infeasible. We present Peerispect, an interactive system that operationalizes claim-level verification in peer reviews by extracting check-worthy claims from peer reviews, retrieving relevant evidence from the manuscript, and verifying the claims through natural language inference. Results are presented through a visual interface that highlights evidence directly in the paper, enabling rapid inspection and interpretation. Peerispect is designed as a modular Information Retrieval (IR) pipeline, supporting alternative retrievers, rerankers, and verifiers, and is intended for use by reviewers, authors, and program committees. We demonstrate Peerispect through a live, publicly available demo (https://app.reviewer.ly/app/peerispect) and API services (https://github.com/Reviewerly-Inc/Peerispect), accompanied by a video tutorial (https://www.youtube.com/watch?v=pc9RkvkUh14).

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