{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:525PKCGNOQPCMGL4P5FR5QVG7E","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":"1b2119fff587079c4d1a3c8c01b6e2a34a05afe28f39dbf6a7022caf4c5c7c61","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-04-13T15:23:12Z","title_canon_sha256":"36253a868db224cc71b402ed3b3a08f6d663e3073a64ad274031e58fdb0e63f8"},"schema_version":"1.0","source":{"id":"1204.3027","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.3027","created_at":"2026-05-18T03:57:54Z"},{"alias_kind":"arxiv_version","alias_value":"1204.3027v1","created_at":"2026-05-18T03:57:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.3027","created_at":"2026-05-18T03:57:54Z"},{"alias_kind":"pith_short_12","alias_value":"525PKCGNOQPC","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_16","alias_value":"525PKCGNOQPCMGL4","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_8","alias_value":"525PKCGN","created_at":"2026-05-18T12:26:53Z"}],"graph_snapshots":[{"event_id":"sha256:d7cd50b4f1a06ded3e72491cacc514b9bf37d62b2f8d963b80a4f682ba271228","target":"graph","created_at":"2026-05-18T03:57:54Z","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":"Let K denote an algebraically closed field. We study the relation between an ideal I in K[x1,...,xn] and its cross sections I_a=I+<x1-a>. In particular, we study under what conditions I can be recovered from the set I_S={(a,I_a):a in S} with S a subset of K. For instance, we show that an ideal I=cap_i Q_i, where Q_i is primary and Q_i cap K[x1]={0}, is uniquely determined by I_S when S is infinite. Moreover, there exists a function B(d,n) such that, if I is generated by polynomials of degree at most d, then I is uniquely determined by I_S when |S|>=B(d,n). If I is also known to be principal, t","authors_text":"Jorge Ortigas-Galindo, Martin Avendano","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-04-13T15:23:12Z","title":"Interpolation of Ideals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.3027","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:b91f4d44175337e55939cb4d82390be6c37186091bbc6b2a7e67ec61d2fa59e0","target":"record","created_at":"2026-05-18T03:57:54Z","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":"1b2119fff587079c4d1a3c8c01b6e2a34a05afe28f39dbf6a7022caf4c5c7c61","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-04-13T15:23:12Z","title_canon_sha256":"36253a868db224cc71b402ed3b3a08f6d663e3073a64ad274031e58fdb0e63f8"},"schema_version":"1.0","source":{"id":"1204.3027","kind":"arxiv","version":1}},"canonical_sha256":"eebaf508cd741e26197c7f4b1ec2a6f90796535d9b1f8689491707aa5c8bbd42","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eebaf508cd741e26197c7f4b1ec2a6f90796535d9b1f8689491707aa5c8bbd42","first_computed_at":"2026-05-18T03:57:54.122707Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:57:54.122707Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Pa1bvZ3P7FvSox9aqNp5X/0FDTRM/OVYcFYk4cClMOhWB/WJTkrELFKENXcdxBodz9zvQHMTQ3O0KGIoLKwjAg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:57:54.125523Z","signed_message":"canonical_sha256_bytes"},"source_id":"1204.3027","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b91f4d44175337e55939cb4d82390be6c37186091bbc6b2a7e67ec61d2fa59e0","sha256:d7cd50b4f1a06ded3e72491cacc514b9bf37d62b2f8d963b80a4f682ba271228"],"state_sha256":"74cfbbd20bc03a0fbf236da2fe15f7080251586048f203021d686d4f7c900b33"}