{"paper":{"title":"A Density-Based Continuous Local Symmetry Measure","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Local symmetry in molecules can be measured continuously from electron density localization.","cross_cats":[],"primary_cat":"physics.chem-ph","authors_text":"Devin A. Matthews, Duc Anh Lai","submitted_at":"2026-03-23T18:44:58Z","abstract_excerpt":"Although continuous symmetry theory has attracted increasing attention in modern chemistry, local symmetry remains under-investigated. As a consequence, the relationship between symmetry and chemical behavior is often obscured, limiting the practical use of fuzzy symmetry measures. In this study, we introduce a novel framework for evaluating local symmetry based on electron density localization, and present continuous symmetry representations for several representative molecules. Our approach not only quantitatively captures global symmetry, but also reveals distinctive features of symmetry in"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We introduce a novel framework for evaluating local symmetry based on electron density localization, and present continuous symmetry representations for several representative molecules.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That localizing electron density provides a valid and sufficient basis for defining and quantifying local symmetry without post-hoc adjustments or external benchmarks.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"A novel density-based continuous local symmetry measure is introduced that captures both global and local symmetry features in molecules along with related local chirality concepts.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Local symmetry in molecules can be measured continuously from electron density localization.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"f387d317cc894de1ed65c8e7438fbc760808954f1da697012d19af376d4a6a93"},"source":{"id":"2603.22476","kind":"arxiv","version":2},"verdict":{"id":"c008e9fb-6feb-4773-9a30-4e08b7035edd","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-15T06:22:49.184110Z","strongest_claim":"We introduce a novel framework for evaluating local symmetry based on electron density localization, and present continuous symmetry representations for several representative molecules.","one_line_summary":"A novel density-based continuous local symmetry measure is introduced that captures both global and local symmetry features in molecules along with related local chirality concepts.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That localizing electron density provides a valid and sufficient basis for defining and quantifying local symmetry without post-hoc adjustments or external benchmarks.","pith_extraction_headline":"Local symmetry in molecules can be measured continuously from electron density localization."},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":2,"snapshot_sha256":"61b4dbc6747f5b7bdf03d748a25be44828e05d7ebe1338f40aa623323ef8e640"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}