{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2007:EAEUCRXE4U2L753OGVSFW7Q7FN","short_pith_number":"pith:EAEUCRXE","schema_version":"1.0","canonical_sha256":"20094146e4e534bff76e35645b7e1f2b70afcf2e4928ee4caa61c3e700586748","source":{"kind":"arxiv","id":"0711.4625","version":1},"attestation_state":"computed","paper":{"title":"Toward classfication of rational vertex operator algebras with central charges less than 1","license":"","headline":"","cross_cats":["math.RT"],"primary_cat":"math.QA","authors_text":"C. Dong, W. Zhang","submitted_at":"2007-11-28T23:52:01Z","abstract_excerpt":"The rational and C_2-cofinite simple vertex operator algebras whose effective central charges and the central charges c are equal and less than 1 are classified. Such a vertex operator algebra is zero if c<0 and C if c=0. If c>0, it is an extension of discrete Virasoro vertex operator algebra L(c_{p,q},0) by its irreducible modules. It is also proved that for any rational and C_2-cofinite simple vertex operator algebra whose effective central charge and central charge are equal, the vertex operator subalgebra generated by the Virasoro vector is simple."},"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":false},"canonical_record":{"source":{"id":"0711.4625","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.QA","submitted_at":"2007-11-28T23:52:01Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"d41abd0c427a0faf24d87621c56b867d6f1a961b2fb519d8f4c722dbbac8bb57","abstract_canon_sha256":"d5d7c057ff80aa74c92df5404507778d80abf4633bf031c98e2d699218b0a276"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:05:56.013948Z","signature_b64":"g+LE8lAVqQdU7eGn1xCnnte9wXIbXo5cS+Xz+YQx7agyAuoRC8XtAnZQ7mUQbI1QxK67MWVgkQrI44yyRcslAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"20094146e4e534bff76e35645b7e1f2b70afcf2e4928ee4caa61c3e700586748","last_reissued_at":"2026-07-04T15:05:56.013535Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:05:56.013535Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Toward classfication of rational vertex operator algebras with central charges less than 1","license":"","headline":"","cross_cats":["math.RT"],"primary_cat":"math.QA","authors_text":"C. Dong, W. Zhang","submitted_at":"2007-11-28T23:52:01Z","abstract_excerpt":"The rational and C_2-cofinite simple vertex operator algebras whose effective central charges and the central charges c are equal and less than 1 are classified. Such a vertex operator algebra is zero if c<0 and C if c=0. If c>0, it is an extension of discrete Virasoro vertex operator algebra L(c_{p,q},0) by its irreducible modules. It is also proved that for any rational and C_2-cofinite simple vertex operator algebra whose effective central charge and central charge are equal, the vertex operator subalgebra generated by the Virasoro vector is simple."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0711.4625","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/0711.4625/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"0711.4625","created_at":"2026-07-04T15:05:56.013603+00:00"},{"alias_kind":"arxiv_version","alias_value":"0711.4625v1","created_at":"2026-07-04T15:05:56.013603+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0711.4625","created_at":"2026-07-04T15:05:56.013603+00:00"},{"alias_kind":"pith_short_12","alias_value":"EAEUCRXE4U2L","created_at":"2026-07-04T15:05:56.013603+00:00"},{"alias_kind":"pith_short_16","alias_value":"EAEUCRXE4U2L753O","created_at":"2026-07-04T15:05:56.013603+00:00"},{"alias_kind":"pith_short_8","alias_value":"EAEUCRXE","created_at":"2026-07-04T15:05:56.013603+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/EAEUCRXE4U2L753OGVSFW7Q7FN","json":"https://pith.science/pith/EAEUCRXE4U2L753OGVSFW7Q7FN.json","graph_json":"https://pith.science/api/pith-number/EAEUCRXE4U2L753OGVSFW7Q7FN/graph.json","events_json":"https://pith.science/api/pith-number/EAEUCRXE4U2L753OGVSFW7Q7FN/events.json","paper":"https://pith.science/paper/EAEUCRXE"},"agent_actions":{"view_html":"https://pith.science/pith/EAEUCRXE4U2L753OGVSFW7Q7FN","download_json":"https://pith.science/pith/EAEUCRXE4U2L753OGVSFW7Q7FN.json","view_paper":"https://pith.science/paper/EAEUCRXE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0711.4625&json=true","fetch_graph":"https://pith.science/api/pith-number/EAEUCRXE4U2L753OGVSFW7Q7FN/graph.json","fetch_events":"https://pith.science/api/pith-number/EAEUCRXE4U2L753OGVSFW7Q7FN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EAEUCRXE4U2L753OGVSFW7Q7FN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EAEUCRXE4U2L753OGVSFW7Q7FN/action/storage_attestation","attest_author":"https://pith.science/pith/EAEUCRXE4U2L753OGVSFW7Q7FN/action/author_attestation","sign_citation":"https://pith.science/pith/EAEUCRXE4U2L753OGVSFW7Q7FN/action/citation_signature","submit_replication":"https://pith.science/pith/EAEUCRXE4U2L753OGVSFW7Q7FN/action/replication_record"}},"created_at":"2026-07-04T15:05:56.013603+00:00","updated_at":"2026-07-04T15:05:56.013603+00:00"}