{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:X55DQX5CB2GZWN4JSOSL3O6KDM","short_pith_number":"pith:X55DQX5C","schema_version":"1.0","canonical_sha256":"bf7a385fa20e8d9b378993a4bdbbca1b26a738ff688f5ec5f7ce7740da3b9185","source":{"kind":"arxiv","id":"1304.0257","version":2},"attestation_state":"computed","paper":{"title":"Numerically finite hereditary categories with Serre duality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.CT","authors_text":"Adam-Christiaan van Roosmalen","submitted_at":"2013-03-31T21:46:07Z","abstract_excerpt":"Let A be an abelian hereditary category with Serre duality. We provide a classification of such categories up to derived equivalence under the additional condition that the Grothendieck group modulo the radical of the Euler form is a free abelian group of finite rank. Such categories are called numerically finite, and this condition is satisfied by the category of coherent sheaves on a smooth projective variety."},"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":"1304.0257","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2013-03-31T21:46:07Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"8ceb02f28675c4725c8e93b4efa49167d2b7d23b5b493c9601bdbee89df02ba9","abstract_canon_sha256":"c96ea1fd74a8e5a890f98f3c5903e31b7c9e308d1555f650cf819a06f348794d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:29:32.450191Z","signature_b64":"hgjlRORH5Aqs+Xj0SaZgaLgiGDAC2wUB/vtkzWiOGHDChojsVrC9I7xD9R0nIzc6malTk6HBDWx6dWO41o28AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bf7a385fa20e8d9b378993a4bdbbca1b26a738ff688f5ec5f7ce7740da3b9185","last_reissued_at":"2026-05-18T02:29:32.449618Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:29:32.449618Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Numerically finite hereditary categories with Serre duality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.CT","authors_text":"Adam-Christiaan van Roosmalen","submitted_at":"2013-03-31T21:46:07Z","abstract_excerpt":"Let A be an abelian hereditary category with Serre duality. We provide a classification of such categories up to derived equivalence under the additional condition that the Grothendieck group modulo the radical of the Euler form is a free abelian group of finite rank. Such categories are called numerically finite, and this condition is satisfied by the category of coherent sheaves on a smooth projective variety."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.0257","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"1304.0257","created_at":"2026-05-18T02:29:32.449709+00:00"},{"alias_kind":"arxiv_version","alias_value":"1304.0257v2","created_at":"2026-05-18T02:29:32.449709+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.0257","created_at":"2026-05-18T02:29:32.449709+00:00"},{"alias_kind":"pith_short_12","alias_value":"X55DQX5CB2GZ","created_at":"2026-05-18T12:28:06.772260+00:00"},{"alias_kind":"pith_short_16","alias_value":"X55DQX5CB2GZWN4J","created_at":"2026-05-18T12:28:06.772260+00:00"},{"alias_kind":"pith_short_8","alias_value":"X55DQX5C","created_at":"2026-05-18T12:28:06.772260+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/X55DQX5CB2GZWN4JSOSL3O6KDM","json":"https://pith.science/pith/X55DQX5CB2GZWN4JSOSL3O6KDM.json","graph_json":"https://pith.science/api/pith-number/X55DQX5CB2GZWN4JSOSL3O6KDM/graph.json","events_json":"https://pith.science/api/pith-number/X55DQX5CB2GZWN4JSOSL3O6KDM/events.json","paper":"https://pith.science/paper/X55DQX5C"},"agent_actions":{"view_html":"https://pith.science/pith/X55DQX5CB2GZWN4JSOSL3O6KDM","download_json":"https://pith.science/pith/X55DQX5CB2GZWN4JSOSL3O6KDM.json","view_paper":"https://pith.science/paper/X55DQX5C","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1304.0257&json=true","fetch_graph":"https://pith.science/api/pith-number/X55DQX5CB2GZWN4JSOSL3O6KDM/graph.json","fetch_events":"https://pith.science/api/pith-number/X55DQX5CB2GZWN4JSOSL3O6KDM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/X55DQX5CB2GZWN4JSOSL3O6KDM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/X55DQX5CB2GZWN4JSOSL3O6KDM/action/storage_attestation","attest_author":"https://pith.science/pith/X55DQX5CB2GZWN4JSOSL3O6KDM/action/author_attestation","sign_citation":"https://pith.science/pith/X55DQX5CB2GZWN4JSOSL3O6KDM/action/citation_signature","submit_replication":"https://pith.science/pith/X55DQX5CB2GZWN4JSOSL3O6KDM/action/replication_record"}},"created_at":"2026-05-18T02:29:32.449709+00:00","updated_at":"2026-05-18T02:29:32.449709+00:00"}