Material claims in papers, patents, etc., often involve physical feasibility (e.g., stability under conditions, property consistency), not just textual feasibility. Yet most claim verifiers operate over language, therefore producing ungrounded judgments. On the other hand, directfirst-principles verification (e.g., density functional theory, DFT) is inflexible and hard to invoke from underspecified free-form claims.Therefore, we introduce **PhyVer**, a **phy**sics-grounded material claim **ver**ification system that bridges this gap by translating claimsinto multi-fidelity physical evidence and interpretable verdicts. To support human-in-the-loop inspection, we present an interactive web interface that visualizes the instantiated structure, optimization trajectories, DFT summaries, and the final decision. On expert-labeled claims, **PhyVer** improves agreement with experts over text-only GPT-5.1, reducing MAE from 1.54 to 1.20 and Signed MAE from0.95 to 0.82, and increasing Accuracy@±1 from 50% to 70%.