{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:GINZJYPUSFFZTW6IGWP6UJB43B","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":"169ed48436c68ed7485cb4a591dd8140509ff052b43ecabb87b9af71155d0f97","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-03-08T13:18:14Z","title_canon_sha256":"4cc1b3eab9a395906b55fccc4462ef8698653d8d0e0edba44369d9d528dbdaed"},"schema_version":"1.0","source":{"id":"1703.02827","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.02827","created_at":"2026-05-18T00:49:05Z"},{"alias_kind":"arxiv_version","alias_value":"1703.02827v1","created_at":"2026-05-18T00:49:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.02827","created_at":"2026-05-18T00:49:05Z"},{"alias_kind":"pith_short_12","alias_value":"GINZJYPUSFFZ","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_16","alias_value":"GINZJYPUSFFZTW6I","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_8","alias_value":"GINZJYPU","created_at":"2026-05-18T12:31:18Z"}],"graph_snapshots":[{"event_id":"sha256:715a4a6d0cd3c930254546489ee53a1d9a990c7a83916e0129ac0e59a8f8a792","target":"graph","created_at":"2026-05-18T00:49:05Z","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 paper, the containment problem for the defining ideal of a special type of zero dimensional subschemes of $\\mathbb{P}^2$, so called quasi star configurations, is investigated. Some sharp bounds for the resurgence of these types of ideals are given. As an application of this result, for every real number $0 < \\varepsilon < \\frac{1}{2}$, we construct an infinite family of homogeneous radical ideals of points in $\\mathbb{K}[\\mathbb{P}^2]$ such that their resurgences lie in the interval $[2- \\varepsilon ,2)$. Moreover, the Castelnuovo-Mumford regularity of all ordinary powers of defining i","authors_text":"Hassan Haghighi, Mohammad Mosakhani","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-03-08T13:18:14Z","title":"Containment problem for the quasi star configurations of points in $\\mathbb{P}^2$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.02827","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":"sha256:2f9c4022c04614ee257a30f4758d153dfbf547c1e70fe53842631798932677f3","target":"record","created_at":"2026-05-18T00:49:05Z","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":"169ed48436c68ed7485cb4a591dd8140509ff052b43ecabb87b9af71155d0f97","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-03-08T13:18:14Z","title_canon_sha256":"4cc1b3eab9a395906b55fccc4462ef8698653d8d0e0edba44369d9d528dbdaed"},"schema_version":"1.0","source":{"id":"1703.02827","kind":"arxiv","version":1}},"canonical_sha256":"321b94e1f4914b99dbc8359fea243cd87000e0ee9a38bd4c81c5d02b17ff5037","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"321b94e1f4914b99dbc8359fea243cd87000e0ee9a38bd4c81c5d02b17ff5037","first_computed_at":"2026-05-18T00:49:05.526957Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:49:05.526957Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EAaN0ZzLoCEbac0nUivnlI0ZUG0bmGTnxAQwwZ1uKLa8/qoRh/JLCGvVv/f50U/PVJJS0TnI5D6tylzmDZ1fBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:49:05.527427Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.02827","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2f9c4022c04614ee257a30f4758d153dfbf547c1e70fe53842631798932677f3","sha256:715a4a6d0cd3c930254546489ee53a1d9a990c7a83916e0129ac0e59a8f8a792"],"state_sha256":"a60f33dcd257a724fda05bc34b2bdbe9b8b07feec0a4b3b5c9601215b3d3ecb6"}