{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:K5WE5S6UVQVEQGSBWNA3PJIZYR","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":"6c32a96abd7d5ace5b36044ad3b79468a7c9ba972f478331cf7c1109fb1c6507","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-08-01T16:47:22Z","title_canon_sha256":"6fb56a76610194e5509c985e9332bfd9d3384d7742dd62da90cb34cccd3085a9"},"schema_version":"1.0","source":{"id":"1208.0269","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.0269","created_at":"2026-05-18T01:22:12Z"},{"alias_kind":"arxiv_version","alias_value":"1208.0269v1","created_at":"2026-05-18T01:22:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.0269","created_at":"2026-05-18T01:22:12Z"},{"alias_kind":"pith_short_12","alias_value":"K5WE5S6UVQVE","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_16","alias_value":"K5WE5S6UVQVEQGSB","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_8","alias_value":"K5WE5S6U","created_at":"2026-05-18T12:27:11Z"}],"graph_snapshots":[{"event_id":"sha256:e91d2d4faa1c2391eef776ead084ba748363d7da433a706b46572147879f3355","target":"graph","created_at":"2026-05-18T01:22:12Z","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":"We study the fixed singularities imposed on members of a linear system of surfaces in P^3_C by its base locus Z. For a 1-dimensional subscheme Z \\subset P^3 with finitely many points p_i of embedding dimension three and d >> 0, we determine the nature of the singularities p_i \\in S for general S in |H^0 (P^3, I_Z (d))| and give a method to compute the kernel of the restriction map Cl S \\to Cl O_{S,p_i}. One tool developed is an algorithm to identify the type of an A_n singularity via its local equation. We illustrate the method for representative Z and use Noether-Lefschetz theory to compute P","authors_text":"John Brevik, Scott Nollet","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-08-01T16:47:22Z","title":"Picard Groups of Normal Surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.0269","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:fec06c771c408a92f4f77b2bcac0e6249660baee987d1189b956676b5bf5ebdf","target":"record","created_at":"2026-05-18T01:22:12Z","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":"6c32a96abd7d5ace5b36044ad3b79468a7c9ba972f478331cf7c1109fb1c6507","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-08-01T16:47:22Z","title_canon_sha256":"6fb56a76610194e5509c985e9332bfd9d3384d7742dd62da90cb34cccd3085a9"},"schema_version":"1.0","source":{"id":"1208.0269","kind":"arxiv","version":1}},"canonical_sha256":"576c4ecbd4ac2a481a41b341b7a519c448afd812b88674e33aeb29ebf3234b45","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"576c4ecbd4ac2a481a41b341b7a519c448afd812b88674e33aeb29ebf3234b45","first_computed_at":"2026-05-18T01:22:12.913309Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:22:12.913309Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"feNshZlRi8OsKWolm6UgO9a5eQEcN35vl1pgn8AYOC/PxV/ZMMArbCtyo5sJTt7MusYsdm9W4hX2J8QleQxrBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:22:12.913839Z","signed_message":"canonical_sha256_bytes"},"source_id":"1208.0269","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fec06c771c408a92f4f77b2bcac0e6249660baee987d1189b956676b5bf5ebdf","sha256:e91d2d4faa1c2391eef776ead084ba748363d7da433a706b46572147879f3355"],"state_sha256":"5fc7455bda243f74b7504de29701ed7ee964d7d61c86673d4ede318e016d9057"}