{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:TVTNMIVIKN2MYKWDK6W67I4UOP","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"38ec7204741382fb06a9bb3d9e5a19b8edd2a4b784bbfe3dd285280754ce90ed","cross_cats_sorted":["math.AG","math.CT","math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2012-03-30T12:56:12Z","title_canon_sha256":"79b08816a0e721e3b7f7fd815ca00b840f5d3e137cf846bcbb47ef826525a5f9"},"schema_version":"1.0","source":{"id":"1203.6796","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.6796","created_at":"2026-05-18T03:09:34Z"},{"alias_kind":"arxiv_version","alias_value":"1203.6796v3","created_at":"2026-05-18T03:09:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.6796","created_at":"2026-05-18T03:09:34Z"},{"alias_kind":"pith_short_12","alias_value":"TVTNMIVIKN2M","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"TVTNMIVIKN2MYKWD","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"TVTNMIVI","created_at":"2026-05-18T12:27:23Z"}],"graph_snapshots":[{"event_id":"sha256:076619e7a1f73eebff8487c345dadedd9f422d7a1031efc3e485ce17afcf7a57","target":"graph","created_at":"2026-05-18T03:09:34Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Reflexive functors of modules naturally appear in Algebraic Geometry, mainly in the theory of linear representations of group schemes, and in \"duality theories\". In this paper we study and determine reflexive functors and we give many properties of reflexive functors.","authors_text":"C. Sancho, J. Navarro, P. Sancho","cross_cats":["math.AG","math.CT","math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2012-03-30T12:56:12Z","title":"Reflexive functors of modules in Commutative Algebra"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.6796","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:38e9bc97109d743810de9d6a71db23989c07de8f7eaa588f3e8c34965088d720","target":"record","created_at":"2026-05-18T03:09:34Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"38ec7204741382fb06a9bb3d9e5a19b8edd2a4b784bbfe3dd285280754ce90ed","cross_cats_sorted":["math.AG","math.CT","math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2012-03-30T12:56:12Z","title_canon_sha256":"79b08816a0e721e3b7f7fd815ca00b840f5d3e137cf846bcbb47ef826525a5f9"},"schema_version":"1.0","source":{"id":"1203.6796","kind":"arxiv","version":3}},"canonical_sha256":"9d66d622a85374cc2ac357adefa39473e35d5ca924c21e7734f1cc7748e7ae18","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9d66d622a85374cc2ac357adefa39473e35d5ca924c21e7734f1cc7748e7ae18","first_computed_at":"2026-05-18T03:09:34.222667Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:09:34.222667Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KlRI/XSgu0M5dazXqIBC+AHOkLellxR3Lt9LNrL4HUzdQVUMy2JkpQ6709sJK+I2D32swMh78Yu4hxJor3/+Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:09:34.223386Z","signed_message":"canonical_sha256_bytes"},"source_id":"1203.6796","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:38e9bc97109d743810de9d6a71db23989c07de8f7eaa588f3e8c34965088d720","sha256:076619e7a1f73eebff8487c345dadedd9f422d7a1031efc3e485ce17afcf7a57"],"state_sha256":"372eacda5c3c97342517530dbcd57a8a382469d04f46b2d973cab86230fe6812"}