{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:HNNQLL7UJGWS2YLIDCCHNVAGUQ","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":"f465cc0d4d21c876d3403165c6e18f017b096fe569d9f1178b5db85744a88d2f","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2013-10-18T04:33:26Z","title_canon_sha256":"105778f715c24bf5b81c37ec464c4f6279b9284e67bafbffcd03f22531257cff"},"schema_version":"1.0","source":{"id":"1310.4915","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.4915","created_at":"2026-05-18T03:10:01Z"},{"alias_kind":"arxiv_version","alias_value":"1310.4915v1","created_at":"2026-05-18T03:10:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.4915","created_at":"2026-05-18T03:10:01Z"},{"alias_kind":"pith_short_12","alias_value":"HNNQLL7UJGWS","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_16","alias_value":"HNNQLL7UJGWS2YLI","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_8","alias_value":"HNNQLL7U","created_at":"2026-05-18T12:27:46Z"}],"graph_snapshots":[{"event_id":"sha256:982da7b11281341c49e24cdfd3cb4fbe8cad568f4c2854b8a6894dd492370329","target":"graph","created_at":"2026-05-18T03:10:01Z","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":"Given a birational parameterization of an algebraic surface S in the projective space, the purpose of this paper is to investigate the sets of points on S whose preimage consists in k or more points, counting multiplicities. They are described explicitly in terms of Fitting ideals of some graded parts of the symmetric algebra associated to this parameterization.","authors_text":"Laurent Bus\\'e (INRIA Sophia Antipolis), Marc Chardin (IMJ, Nicol\\'as Botbol (DM-UBA), UPMC)","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2013-10-18T04:33:26Z","title":"Fitting ideals and multiple-points of surface parameterizations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.4915","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":"sha256:59a8c810c4a59283ed97983479f9657b47a846b65b7579a91cd69040b491c298","target":"record","created_at":"2026-05-18T03:10:01Z","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":"f465cc0d4d21c876d3403165c6e18f017b096fe569d9f1178b5db85744a88d2f","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2013-10-18T04:33:26Z","title_canon_sha256":"105778f715c24bf5b81c37ec464c4f6279b9284e67bafbffcd03f22531257cff"},"schema_version":"1.0","source":{"id":"1310.4915","kind":"arxiv","version":1}},"canonical_sha256":"3b5b05aff449ad2d6168188476d406a40e776312c07c3c81e5a004d125f18cac","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3b5b05aff449ad2d6168188476d406a40e776312c07c3c81e5a004d125f18cac","first_computed_at":"2026-05-18T03:10:01.984374Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:10:01.984374Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"x8e2IJewXpkkiiwPq43Gcs9WyWNBw9cSSGfSnFrQaKmRdPd5p4oBJL8BRODa6/ntC1nlya2wiRbm0iZTlFRkDA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:10:01.984863Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.4915","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:59a8c810c4a59283ed97983479f9657b47a846b65b7579a91cd69040b491c298","sha256:982da7b11281341c49e24cdfd3cb4fbe8cad568f4c2854b8a6894dd492370329"],"state_sha256":"2d28df4843054bbc2922adfb68e3224865e833c41096ed248e4cfc824de2ca59"}