{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:LAVKI6Z4BHAXXZNI4I2UGUKSHZ","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":"853ffffa2edd5698dc6fa1720c4363da37c77e14331037e9b1ac3e03cd2af2c0","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2017-08-09T20:55:08Z","title_canon_sha256":"ea0c7a7608017e44a8f581c58e75d2ae2a7c92061def6895d3fdf3deb8008ca9"},"schema_version":"1.0","source":{"id":"1708.03010","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.03010","created_at":"2026-05-18T00:38:15Z"},{"alias_kind":"arxiv_version","alias_value":"1708.03010v1","created_at":"2026-05-18T00:38:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.03010","created_at":"2026-05-18T00:38:15Z"},{"alias_kind":"pith_short_12","alias_value":"LAVKI6Z4BHAX","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_16","alias_value":"LAVKI6Z4BHAXXZNI","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_8","alias_value":"LAVKI6Z4","created_at":"2026-05-18T12:31:28Z"}],"graph_snapshots":[{"event_id":"sha256:ddbec5cd318bfaca05d28416afd93585afeeb40a16e14318e4884f1a22d2a81e","target":"graph","created_at":"2026-05-18T00:38:15Z","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 survey classical and recent results on symbolic powers of ideals. We focus on properties and problems of symbolic powers over regular rings, on the comparison of symbolic and regular powers, and on the combinatorics of the symbolic powers of monomial ideals. In addition, we present some new results on these aspects of the subject.","authors_text":"Alessandro De Stefani, Craig Huneke, Elo\\'isa Grifo, Hailong Dao, Luis N\\'u\\~nez-Betancourt","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2017-08-09T20:55:08Z","title":"Symbolic powers of ideals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.03010","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":"sha256:70ac128b605a446770fa96747a1e7d6a46db9fc7ab1ca58fa04206bf84d67635","target":"record","created_at":"2026-05-18T00:38:15Z","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":"853ffffa2edd5698dc6fa1720c4363da37c77e14331037e9b1ac3e03cd2af2c0","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2017-08-09T20:55:08Z","title_canon_sha256":"ea0c7a7608017e44a8f581c58e75d2ae2a7c92061def6895d3fdf3deb8008ca9"},"schema_version":"1.0","source":{"id":"1708.03010","kind":"arxiv","version":1}},"canonical_sha256":"582aa47b3c09c17be5a8e2354351523e6e69a5c31360e56f4f8d580bd0257114","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"582aa47b3c09c17be5a8e2354351523e6e69a5c31360e56f4f8d580bd0257114","first_computed_at":"2026-05-18T00:38:15.230768Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:38:15.230768Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kznCdwPsYXCsMujUEP/jBLJp7zpldAsEgbpRo4KgiNzHpyuKgl9imZhK0UYHbRTDEccSS20yGIHh12m6UCuXAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:38:15.231357Z","signed_message":"canonical_sha256_bytes"},"source_id":"1708.03010","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:70ac128b605a446770fa96747a1e7d6a46db9fc7ab1ca58fa04206bf84d67635","sha256:ddbec5cd318bfaca05d28416afd93585afeeb40a16e14318e4884f1a22d2a81e"],"state_sha256":"4e46534af1e45d2c62644de0826aa0a693ea4a664a87642770812dcc643c0701"}