{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:WDCBFZXPAQOVQIMKBGZWJKE2VH","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":"d4c85ae8f9f097a9945be85a921d4d6c9cf68294b7369503c20917353d392f00","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2017-04-26T14:19:01Z","title_canon_sha256":"812c87900a32425fb84f8901a0b942d8f939b008b8d644eb93828f6b734de920"},"schema_version":"1.0","source":{"id":"1704.08132","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.08132","created_at":"2026-05-17T23:57:32Z"},{"alias_kind":"arxiv_version","alias_value":"1704.08132v3","created_at":"2026-05-17T23:57:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.08132","created_at":"2026-05-17T23:57:32Z"},{"alias_kind":"pith_short_12","alias_value":"WDCBFZXPAQOV","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_16","alias_value":"WDCBFZXPAQOVQIMK","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_8","alias_value":"WDCBFZXP","created_at":"2026-05-18T12:31:53Z"}],"graph_snapshots":[{"event_id":"sha256:84f671023c270a59a68d59c3dea238a23fb9ab346f8847e55f936843204a5b53","target":"graph","created_at":"2026-05-17T23:57:32Z","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":"This paper studies unbounded PAC fields and shows an amalgamation result for types over algebraically closed sets. It discusses various applications, for instance that omega-free PAC fields have the property NSOP3. It also contains a description of imaginaries in PAC fields.","authors_text":"Zoe Chatzidakis","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2017-04-26T14:19:01Z","title":"Amalgamation of types in pseudo-algebraically closed fields and applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.08132","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":"sha256:56533afac39b40d86c49e0dc6f00642565be87ffb20c486f6b594abfa7424cf9","target":"record","created_at":"2026-05-17T23:57:32Z","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":"d4c85ae8f9f097a9945be85a921d4d6c9cf68294b7369503c20917353d392f00","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2017-04-26T14:19:01Z","title_canon_sha256":"812c87900a32425fb84f8901a0b942d8f939b008b8d644eb93828f6b734de920"},"schema_version":"1.0","source":{"id":"1704.08132","kind":"arxiv","version":3}},"canonical_sha256":"b0c412e6ef041d58218a09b364a89aa9c642b1880b24fc5f9074f1183e42b3ac","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b0c412e6ef041d58218a09b364a89aa9c642b1880b24fc5f9074f1183e42b3ac","first_computed_at":"2026-05-17T23:57:32.927837Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:57:32.927837Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9LqWn8miQu+c8YBWVoge/OA5OrdmZBuC+aZ/KNMPPpZdMDhfe3SVCf9rMG/vqov/GXdaGEVQRq7ixr8Q2EVCAA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:57:32.928310Z","signed_message":"canonical_sha256_bytes"},"source_id":"1704.08132","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:56533afac39b40d86c49e0dc6f00642565be87ffb20c486f6b594abfa7424cf9","sha256:84f671023c270a59a68d59c3dea238a23fb9ab346f8847e55f936843204a5b53"],"state_sha256":"a06c67431b93c0596a9a40218d9d8be3d9426825fbae6df5634c3562e897b63f"}