{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:YERPSGOYMDMEKELB44XD3BAU3Y","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":"2a5cf64ae07f561c33c0cb8416714314d57f3c3d35f4cee27ca9f0cbf7fb9c55","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2020-08-03T16:45:26Z","title_canon_sha256":"48ac2f699b07d7bbb8a30099e0d149452a150ba633f6a17feafa4a6cfbcc5ce7"},"schema_version":"1.0","source":{"id":"2008.01008","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2008.01008","created_at":"2026-07-05T01:25:27Z"},{"alias_kind":"arxiv_version","alias_value":"2008.01008v2","created_at":"2026-07-05T01:25:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2008.01008","created_at":"2026-07-05T01:25:27Z"},{"alias_kind":"pith_short_12","alias_value":"YERPSGOYMDME","created_at":"2026-07-05T01:25:27Z"},{"alias_kind":"pith_short_16","alias_value":"YERPSGOYMDMEKELB","created_at":"2026-07-05T01:25:27Z"},{"alias_kind":"pith_short_8","alias_value":"YERPSGOY","created_at":"2026-07-05T01:25:27Z"}],"graph_snapshots":[{"event_id":"sha256:d2b4011aa5fbf63ce30f29b08dda64e036350345cb1eca9c75d186ac0404044f","target":"graph","created_at":"2026-07-05T01:25:27Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2008.01008/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this note we introduce generalised pairs from the perspective of the evolution of the notion of space in birational algebraic geometry. We describe some applications of generalised pairs in recent years and then mention a few open problems.","authors_text":"Caucher Birkar","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2020-08-03T16:45:26Z","title":"Generalised pairs in birational geometry"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2008.01008","kind":"arxiv","version":2},"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":"sha256:4d2a31b6ec2fca55283e97df9468ef661b42651494b0316f35f56c2019691cdd","target":"record","created_at":"2026-07-05T01:25:27Z","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":"2a5cf64ae07f561c33c0cb8416714314d57f3c3d35f4cee27ca9f0cbf7fb9c55","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2020-08-03T16:45:26Z","title_canon_sha256":"48ac2f699b07d7bbb8a30099e0d149452a150ba633f6a17feafa4a6cfbcc5ce7"},"schema_version":"1.0","source":{"id":"2008.01008","kind":"arxiv","version":2}},"canonical_sha256":"c122f919d860d8451161e72e3d8414de37f2d4ac2c610781173d4cb5976218d7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c122f919d860d8451161e72e3d8414de37f2d4ac2c610781173d4cb5976218d7","first_computed_at":"2026-07-05T01:25:27.198690Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:25:27.198690Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SNocdooKixp3GLW27+vZ/vZ64e3wSo1sGYT5n/eYF6JyiQ+beHMYeSpi7j9nZo8WZ0fCab3svhCIpWxK8qIKBA==","signature_status":"signed_v1","signed_at":"2026-07-05T01:25:27.199070Z","signed_message":"canonical_sha256_bytes"},"source_id":"2008.01008","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4d2a31b6ec2fca55283e97df9468ef661b42651494b0316f35f56c2019691cdd","sha256:d2b4011aa5fbf63ce30f29b08dda64e036350345cb1eca9c75d186ac0404044f"],"state_sha256":"7c98fad46161d3dcbd433948862f4baf4747176cb2bc205cc9193c00628ead67"}