{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2004:ZTNNEYUTG5EI44YKQV7VDSGYR4","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":"1208f8700e9071e0b02aabacd1aa46fbce1c92936dd5e6c54c86cdeca7eb9baf","cross_cats_sorted":[],"license":"","primary_cat":"math.AG","submitted_at":"2004-07-20T14:26:02Z","title_canon_sha256":"6bc6655ec68a77a7c1cfff0f7a9fa0bb8de47a903ddba6216fb093136c39dd71"},"schema_version":"1.0","source":{"id":"math/0407340","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0407340","created_at":"2026-05-18T00:51:30Z"},{"alias_kind":"arxiv_version","alias_value":"math/0407340v1","created_at":"2026-05-18T00:51:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0407340","created_at":"2026-05-18T00:51:30Z"},{"alias_kind":"pith_short_12","alias_value":"ZTNNEYUTG5EI","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"ZTNNEYUTG5EI44YK","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"ZTNNEYUT","created_at":"2026-05-18T12:25:52Z"}],"graph_snapshots":[{"event_id":"sha256:720fb749910c0a3d9a73af6416f62383de474b2b1f64706a8642da57a622772a","target":"graph","created_at":"2026-05-18T00:51:30Z","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":"In this article we study congruences of lines in $\\mathbb{P}^n$, and in particular of order one. After giving general results, we obtain a complete classification in the case of $\\mathbb{P}^4$ in which the fundamental surface $F$ is in fact a variety-i.e. it is integral-and the congruence is the irreducible set of the trisecant lines of $F$.","authors_text":"Pietro De Poi","cross_cats":[],"headline":"","license":"","primary_cat":"math.AG","submitted_at":"2004-07-20T14:26:02Z","title":"On first order Congruences of Lines in $\\mathbb{P}^4$ with irreducible fundamental Surface"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0407340","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":"sha256:69b4ed7a1a5136075b6eb7088779a93cafd137bddcf65e9746cec3f111660b75","target":"record","created_at":"2026-05-18T00:51:30Z","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":"1208f8700e9071e0b02aabacd1aa46fbce1c92936dd5e6c54c86cdeca7eb9baf","cross_cats_sorted":[],"license":"","primary_cat":"math.AG","submitted_at":"2004-07-20T14:26:02Z","title_canon_sha256":"6bc6655ec68a77a7c1cfff0f7a9fa0bb8de47a903ddba6216fb093136c39dd71"},"schema_version":"1.0","source":{"id":"math/0407340","kind":"arxiv","version":1}},"canonical_sha256":"ccdad2629337488e730a857f51c8d88f049aaedd40a86dfd551d806ff302fd87","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ccdad2629337488e730a857f51c8d88f049aaedd40a86dfd551d806ff302fd87","first_computed_at":"2026-05-18T00:51:30.819015Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:51:30.819015Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Wk9HmL96wIO+r3ULU5mmNeUZL+yIFsJNZYLvaVwGq6qXTOAwuPBisBdQbZuNiwmtGusgeIp9o6nuwCDshHArBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:51:30.819645Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0407340","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:69b4ed7a1a5136075b6eb7088779a93cafd137bddcf65e9746cec3f111660b75","sha256:720fb749910c0a3d9a73af6416f62383de474b2b1f64706a8642da57a622772a"],"state_sha256":"fa64cf7bd2befc03b13c47a600e166c28dd6ab54c687e6e8940562fc5aee9abd"}