{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:GHBKY3LAPB7A26QPMI4Q3FRAIG","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":"7c1e16383d13abcc411c8d2495c6259901bf8e3c123eed88a67b3e3fcd55cb62","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-06-18T19:49:05Z","title_canon_sha256":"363b87bad4e7eb55040f29a6cb8701ab732ae512f28c08bcf8d21b6fbbe0ac5c"},"schema_version":"1.0","source":{"id":"1306.4304","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.4304","created_at":"2026-05-18T02:45:32Z"},{"alias_kind":"arxiv_version","alias_value":"1306.4304v4","created_at":"2026-05-18T02:45:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.4304","created_at":"2026-05-18T02:45:32Z"},{"alias_kind":"pith_short_12","alias_value":"GHBKY3LAPB7A","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_16","alias_value":"GHBKY3LAPB7A26QP","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_8","alias_value":"GHBKY3LA","created_at":"2026-05-18T12:27:45Z"}],"graph_snapshots":[{"event_id":"sha256:8b65b85d1689d3c8428cd4efd561715b5f6355a093e8db20bc91e1821ce4f962","target":"graph","created_at":"2026-05-18T02:45:32Z","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":"We define the notion of 1-affineness for a prestack, and prove an array of results that establish 1-affineness of certain types of prestacks.","authors_text":"Dennis Gaitsgory","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-06-18T19:49:05Z","title":"Sheaves of categories and the notion of 1-affineness"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.4304","kind":"arxiv","version":4},"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":"sha256:5c18a1df63b7da3b362caf222c61eef24be3da05646d42e0f6a6426ef1c0cce5","target":"record","created_at":"2026-05-18T02:45:32Z","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":"7c1e16383d13abcc411c8d2495c6259901bf8e3c123eed88a67b3e3fcd55cb62","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-06-18T19:49:05Z","title_canon_sha256":"363b87bad4e7eb55040f29a6cb8701ab732ae512f28c08bcf8d21b6fbbe0ac5c"},"schema_version":"1.0","source":{"id":"1306.4304","kind":"arxiv","version":4}},"canonical_sha256":"31c2ac6d60787e0d7a0f62390d9620419b5d5b3ca1765509dcb9519ad6883036","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"31c2ac6d60787e0d7a0f62390d9620419b5d5b3ca1765509dcb9519ad6883036","first_computed_at":"2026-05-18T02:45:32.023269Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:45:32.023269Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fQ2FJzhybRR7JvpLaUB+96lYBEuPXDVdUnOg4YZgzsC0Ow62J9BvEAdQPS1FV2vvJpr2C9Elwc3bsqwhsPIbCg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:45:32.023779Z","signed_message":"canonical_sha256_bytes"},"source_id":"1306.4304","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5c18a1df63b7da3b362caf222c61eef24be3da05646d42e0f6a6426ef1c0cce5","sha256:8b65b85d1689d3c8428cd4efd561715b5f6355a093e8db20bc91e1821ce4f962"],"state_sha256":"1e780d9bac10cd670b5252278d2d11f7184c5db6252b76e737ac642058a8023f"}