{"paper":{"title":"Investigation on the Relation between Active Regions' Compliance with Empirical Laws and Flare Productivity","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"astro-ph.SR","authors_text":"Jiangtao Su, Jie Jiang, Jinhui Pan, Rui Liu","submitted_at":"2026-07-09T02:05:44Z","abstract_excerpt":"It remains evasive whether solar active regions (ARs) obeying or violating Hale's polarity law, Joy's tilt law, and the hemispheric helicity rule (HHR) differ in flare productivity. Here we conduct a comprehensive statistical analysis of ARs during the Solar Cycle 24 and the ascending phase of Cycle 25. ARs are automatically detected from full-disk line-of-sight magnetograms acquired by the Michelson Doppler Imager (MDI) and the Helioseismic and Magnetic Imager (HMI). We calculate tilt angles via flux-weighted polarity centroids, estimate magnetic twist by the force-free parameter $\\alpha_{\\ma"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.08053","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.08053/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}