HEA-Bench: An AI-Agent-Optimized Calculator of High-Entropy Alloy and Oxide Descriptors and Phase-Prediction Rules

The empirical descriptors of high-entropy alloys and oxides, from the mixing entropy and atomic-size mismatch to the Miedema enthalpies and the Ω, Φ, and φ stability parameters, are quoted in nearly every design study, yet they are reimplemented ad hoc by individual groups, by closed web calculators, and now inside language-model agent frameworks, where fabrication of property values is a documented failure mode. The resulting numbers disagree and cannot be traced or reproduced. We present HEA-Bench, an open calculator in which every descriptor is a closed-form expression over a curated, literature-cited element-property table, with the six canonical phase-prediction rules reported alongside their thresholds and sources rather than as predictions. One calculation core is delivered as a dependency-free Python (version 3.10 or later) library, a zero-install browser application, an offline desktop executable, and a Model Context Protocol server that exposes it to AI agents as deterministic tools, returning every value with its unit, citation key, and version so an agent's reasoning trace can be audited. The implementation reproduces published per-alloy and per-oxide anchor values to their printed precision and extends to high-entropy oxides in four structure families. The numerical instability of Ω near zero mixing enthalpy is quantified and exposed as a callable check.