{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:GPIM2EC6C7SEYHRFLWCA3AC3U7","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":"1e24720354fada08daca08f50ed4cfa4f0e22a41e16aff84dfc194a039368453","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2019-03-26T01:12:46Z","title_canon_sha256":"00bee5a224be5ca281f8353c5a6fd736ba3f9dc8b48ce86aedc2b6d69591229b"},"schema_version":"1.0","source":{"id":"1903.10647","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.10647","created_at":"2026-05-17T23:50:18Z"},{"alias_kind":"arxiv_version","alias_value":"1903.10647v1","created_at":"2026-05-17T23:50:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.10647","created_at":"2026-05-17T23:50:18Z"},{"alias_kind":"pith_short_12","alias_value":"GPIM2EC6C7SE","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_16","alias_value":"GPIM2EC6C7SEYHRF","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_8","alias_value":"GPIM2EC6","created_at":"2026-05-18T12:33:18Z"}],"graph_snapshots":[{"event_id":"sha256:c890cb03cbf8b7cc15059795be1548fb6e42fdfe9a185f2253a622e5de376ca4","target":"graph","created_at":"2026-05-17T23:50:18Z","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 note we show that Harbourne's conjecture is true for symbolic powers of ideals of points, we check that the stable version of this conjecture is valid for ideals of very general points (resp. generic points) in $\\mathbb P_{\\mathbb K}^N$ (resp. $\\mathbb P_{\\mathbb K(\\underline{z})}^N$). We also show that this conjecture and the Harbourne-Huneke conjecture are true for a class of ideals $I$ defining fat points obtained from line arrangements in $\\mathbb P_{\\mathbb K}^2$.","authors_text":"Stefan Tohaneanu, Yu Xie","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2019-03-26T01:12:46Z","title":"On the containment problem for fat points ideals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.10647","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":"sha256:8118e842383ca495abd29bbc0628f05c6ea1edb5fde2cc283646c05e799ef03b","target":"record","created_at":"2026-05-17T23:50:18Z","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":"1e24720354fada08daca08f50ed4cfa4f0e22a41e16aff84dfc194a039368453","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2019-03-26T01:12:46Z","title_canon_sha256":"00bee5a224be5ca281f8353c5a6fd736ba3f9dc8b48ce86aedc2b6d69591229b"},"schema_version":"1.0","source":{"id":"1903.10647","kind":"arxiv","version":1}},"canonical_sha256":"33d0cd105e17e44c1e255d840d805ba7d521781a4603724669deb1e443c91fd4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"33d0cd105e17e44c1e255d840d805ba7d521781a4603724669deb1e443c91fd4","first_computed_at":"2026-05-17T23:50:18.223978Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:50:18.223978Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3zFYjeIZMw1rmNkEDOFwdqoSok4QnqJI84wEjYXsctC6dQh3CsxXtsWUTCBdn8dXt+5wOO8zyWaJXBghhrVeCw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:50:18.224653Z","signed_message":"canonical_sha256_bytes"},"source_id":"1903.10647","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8118e842383ca495abd29bbc0628f05c6ea1edb5fde2cc283646c05e799ef03b","sha256:c890cb03cbf8b7cc15059795be1548fb6e42fdfe9a185f2253a622e5de376ca4"],"state_sha256":"e8a8194ea0aa6ce5dd03624880c358cef84415617de22577d3463d2005ad74cf"}