{"paper":{"title":"Hasse-Witt invariants of Calabi-Yau varieties","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Hasse-Witt invariants of Calabi-Yau varieties admit two definitions that the paper conjectures are equivalent.","cross_cats":["math-ph","math.MP","math.NT"],"primary_cat":"math.AG","authors_text":"Hossein Movasati, Jin Cao, Mohamed Elmi","submitted_at":"2026-03-03T14:53:49Z","abstract_excerpt":"We define the Hasse-Witt invariant of Calabi-Yau varieties in two different ways. The first method is through Cartier operator and the second method is through the theory of Calabi-Yau modular forms developed by the third author. We conjecture that these two definitions are equivalent and provide many examples of Calabi-Yau varieties in support of this conjecture."},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We conjecture that these two definitions are equivalent and provide many examples of Calabi-Yau varieties in support of this conjecture.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The examples chosen are representative enough that agreement on them implies the two definitions coincide for all Calabi-Yau varieties.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Two independent definitions of the Hasse-Witt invariant for Calabi-Yau varieties are conjectured to coincide, backed by explicit examples.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Hasse-Witt invariants of Calabi-Yau varieties admit two definitions that the paper conjectures are equivalent.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"a8b2e60611ad58a83dad0e0cdabe0e2991ea1fce660b36408e0de414f98e36b0"},"source":{"id":"2603.03055","kind":"arxiv","version":2},"verdict":{"id":"d2dc8a6f-2941-4666-98c4-0c8efda3277b","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-15T16:43:46.070577Z","strongest_claim":"We conjecture that these two definitions are equivalent and provide many examples of Calabi-Yau varieties in support of this conjecture.","one_line_summary":"Two independent definitions of the Hasse-Witt invariant for Calabi-Yau varieties are conjectured to coincide, backed by explicit examples.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The examples chosen are representative enough that agreement on them implies the two definitions coincide for all Calabi-Yau varieties.","pith_extraction_headline":"Hasse-Witt invariants of Calabi-Yau varieties admit two definitions that the paper conjectures are equivalent."},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":2,"snapshot_sha256":"b6332b7beea4623af911f34e2e8687e351d35459b1dc3f57acea0a3179150468"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}