{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:DIP56VLOMFM3OXGUSGOGW5MWJU","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":"dea61c7910dce33b514df4e7ec459797a0fafc4e675bb197b61451b79841e7d1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-04-11T16:35:15Z","title_canon_sha256":"7dab907c2e66547f3fe1252475af8e932be357d797fa7f7864c0f32578877b6c"},"schema_version":"1.0","source":{"id":"1804.04078","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.04078","created_at":"2026-05-18T00:18:42Z"},{"alias_kind":"arxiv_version","alias_value":"1804.04078v1","created_at":"2026-05-18T00:18:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.04078","created_at":"2026-05-18T00:18:42Z"},{"alias_kind":"pith_short_12","alias_value":"DIP56VLOMFM3","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_16","alias_value":"DIP56VLOMFM3OXGU","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_8","alias_value":"DIP56VLO","created_at":"2026-05-18T12:32:19Z"}],"graph_snapshots":[{"event_id":"sha256:fde1d975e340a0198605a7940d7529dd27ac92af9f6dfb33c55e73d3ff1427e0","target":"graph","created_at":"2026-05-18T00:18:42Z","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":"Extending work of Meinhardt and Partsch, we prove that two varieties are isomorphic in codimension c if and only if certain quotients of their categories of coherent sheaves are equivalent. This result interpolates between Gabriel's reconstruction theorem and the fact that two varieties are birational if and only if they have the same function field.","authors_text":"John Calabrese, Roberto Pirisi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-04-11T16:35:15Z","title":"Gabriel's theorem and birational geometry"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.04078","kind":"arxiv","version":1},"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":"sha256:23828da4d4954c7296bacaab20fbae19d62d49fa8c1b60f69072e20b22030a7c","target":"record","created_at":"2026-05-18T00:18:42Z","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":"dea61c7910dce33b514df4e7ec459797a0fafc4e675bb197b61451b79841e7d1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-04-11T16:35:15Z","title_canon_sha256":"7dab907c2e66547f3fe1252475af8e932be357d797fa7f7864c0f32578877b6c"},"schema_version":"1.0","source":{"id":"1804.04078","kind":"arxiv","version":1}},"canonical_sha256":"1a1fdf556e6159b75cd4919c6b75964d259d1eac5d10920be5441128e39a3260","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1a1fdf556e6159b75cd4919c6b75964d259d1eac5d10920be5441128e39a3260","first_computed_at":"2026-05-18T00:18:42.161616Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:18:42.161616Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GHkJqBj4GkAnohXRf4W+tpHxrC8rrgKPMIq0UPZbaAtYH+dPSP/mVsW6/Lu6BuzexzHPgq/kKqJGIvbUptFmBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:18:42.162264Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.04078","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:23828da4d4954c7296bacaab20fbae19d62d49fa8c1b60f69072e20b22030a7c","sha256:fde1d975e340a0198605a7940d7529dd27ac92af9f6dfb33c55e73d3ff1427e0"],"state_sha256":"bdeb79c08bf92c238f2061e3568f0b5ada2d107a4f7c4f1051b7df23581272fc"}