{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:PMITIJMQMVHEZE7W6VDVFGVHNH","short_pith_number":"pith:PMITIJMQ","schema_version":"1.0","canonical_sha256":"7b11342590654e4c93f6f547529aa769c7ec3a04502f5752137c398359691343","source":{"kind":"arxiv","id":"2603.03055","version":2},"attestation_state":"computed","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."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":true},"canonical_record":{"source":{"id":"2603.03055","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2026-03-03T14:53:49Z","cross_cats_sorted":["math-ph","math.MP","math.NT"],"title_canon_sha256":"1f7894537ba403c909b07a9c503adc048ac9cd2fcaf859cc387036204052599a","abstract_canon_sha256":"a171e485a722fa7bba90704abcbfc70ebdd4198209bae1c42bacd298bc4fbd6c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:38:59.807923Z","signature_b64":"TCW8uO1vWag6HuwmBoCswBoKv2hvFmgZ+/EsN3W/Bpk/FX9RDDtUYZU06dtG1YMVJfP49JqfT9ChowevOEbHBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7b11342590654e4c93f6f547529aa769c7ec3a04502f5752137c398359691343","last_reissued_at":"2026-05-17T23:38:59.807371Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:38:59.807371Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2603.03055","created_at":"2026-05-17T23:38:59.807455+00:00"},{"alias_kind":"arxiv_version","alias_value":"2603.03055v2","created_at":"2026-05-17T23:38:59.807455+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2603.03055","created_at":"2026-05-17T23:38:59.807455+00:00"},{"alias_kind":"pith_short_12","alias_value":"PMITIJMQMVHE","created_at":"2026-05-18T12:33:37.589309+00:00"},{"alias_kind":"pith_short_16","alias_value":"PMITIJMQMVHEZE7W","created_at":"2026-05-18T12:33:37.589309+00:00"},{"alias_kind":"pith_short_8","alias_value":"PMITIJMQ","created_at":"2026-05-18T12:33:37.589309+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":2,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/PMITIJMQMVHEZE7W6VDVFGVHNH","json":"https://pith.science/pith/PMITIJMQMVHEZE7W6VDVFGVHNH.json","graph_json":"https://pith.science/api/pith-number/PMITIJMQMVHEZE7W6VDVFGVHNH/graph.json","events_json":"https://pith.science/api/pith-number/PMITIJMQMVHEZE7W6VDVFGVHNH/events.json","paper":"https://pith.science/paper/PMITIJMQ"},"agent_actions":{"view_html":"https://pith.science/pith/PMITIJMQMVHEZE7W6VDVFGVHNH","download_json":"https://pith.science/pith/PMITIJMQMVHEZE7W6VDVFGVHNH.json","view_paper":"https://pith.science/paper/PMITIJMQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2603.03055&json=true","fetch_graph":"https://pith.science/api/pith-number/PMITIJMQMVHEZE7W6VDVFGVHNH/graph.json","fetch_events":"https://pith.science/api/pith-number/PMITIJMQMVHEZE7W6VDVFGVHNH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PMITIJMQMVHEZE7W6VDVFGVHNH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PMITIJMQMVHEZE7W6VDVFGVHNH/action/storage_attestation","attest_author":"https://pith.science/pith/PMITIJMQMVHEZE7W6VDVFGVHNH/action/author_attestation","sign_citation":"https://pith.science/pith/PMITIJMQMVHEZE7W6VDVFGVHNH/action/citation_signature","submit_replication":"https://pith.science/pith/PMITIJMQMVHEZE7W6VDVFGVHNH/action/replication_record"}},"created_at":"2026-05-17T23:38:59.807455+00:00","updated_at":"2026-05-17T23:38:59.807455+00:00"}