{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:LPNYIOOAV7EUK6SKZCMGEYPTXH","short_pith_number":"pith:LPNYIOOA","schema_version":"1.0","canonical_sha256":"5bdb8439c0afc9457a4ac8986261f3b9f7e7df509abea8f53a44a4afed7f119a","source":{"kind":"arxiv","id":"1111.6278","version":3},"attestation_state":"computed","paper":{"title":"Vanishing ideals over graphs and even cycles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.AG","math.CO","math.IT"],"primary_cat":"math.AC","authors_text":"Jorge Neves, Maria Vaz Pinto, Rafael H. Villarreal","submitted_at":"2011-11-27T17:18:50Z","abstract_excerpt":"Let X be an algebraic toric set in a projective space over a finite field. We study the vanishing ideal, I(X), of X and show some useful degree bounds for a minimal set of generators of I(X). We give an explicit description of a set of generators of I(X), when X is the algebraic toric set associated to an even cycle or to a connected bipartite graph with pairwise disjoint even cycles. In this case, a fomula for the regularity of I(X) is given. We show an upper bound for this invariant, when X is associated to a (not necessarily connected) bipartite graph. The upper bound is sharp if the graph "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1111.6278","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-11-27T17:18:50Z","cross_cats_sorted":["cs.IT","math.AG","math.CO","math.IT"],"title_canon_sha256":"4b0fcaa0849699bdb6928c2a38dfc4700c10ac456ab9b0f1fadcebfe8fac17a2","abstract_canon_sha256":"e6877f9bd428afa55a27055b7bfc79e85144433b85e5f0c9353d8fce91403928"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:29:45.874297Z","signature_b64":"ctk1IehtZzefzEeawk1lXghfqC+4qi7TcJ5y6LTBeiF6zusp9SMB0stIodnDTcAFIts4kI/QOSSgtzK3JmsVDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5bdb8439c0afc9457a4ac8986261f3b9f7e7df509abea8f53a44a4afed7f119a","last_reissued_at":"2026-05-18T02:29:45.873936Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:29:45.873936Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Vanishing ideals over graphs and even cycles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.AG","math.CO","math.IT"],"primary_cat":"math.AC","authors_text":"Jorge Neves, Maria Vaz Pinto, Rafael H. Villarreal","submitted_at":"2011-11-27T17:18:50Z","abstract_excerpt":"Let X be an algebraic toric set in a projective space over a finite field. We study the vanishing ideal, I(X), of X and show some useful degree bounds for a minimal set of generators of I(X). We give an explicit description of a set of generators of I(X), when X is the algebraic toric set associated to an even cycle or to a connected bipartite graph with pairwise disjoint even cycles. In this case, a fomula for the regularity of I(X) is given. We show an upper bound for this invariant, when X is associated to a (not necessarily connected) bipartite graph. The upper bound is sharp if the graph "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.6278","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1111.6278","created_at":"2026-05-18T02:29:45.873992+00:00"},{"alias_kind":"arxiv_version","alias_value":"1111.6278v3","created_at":"2026-05-18T02:29:45.873992+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.6278","created_at":"2026-05-18T02:29:45.873992+00:00"},{"alias_kind":"pith_short_12","alias_value":"LPNYIOOAV7EU","created_at":"2026-05-18T12:26:34.985390+00:00"},{"alias_kind":"pith_short_16","alias_value":"LPNYIOOAV7EUK6SK","created_at":"2026-05-18T12:26:34.985390+00:00"},{"alias_kind":"pith_short_8","alias_value":"LPNYIOOA","created_at":"2026-05-18T12:26:34.985390+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/LPNYIOOAV7EUK6SKZCMGEYPTXH","json":"https://pith.science/pith/LPNYIOOAV7EUK6SKZCMGEYPTXH.json","graph_json":"https://pith.science/api/pith-number/LPNYIOOAV7EUK6SKZCMGEYPTXH/graph.json","events_json":"https://pith.science/api/pith-number/LPNYIOOAV7EUK6SKZCMGEYPTXH/events.json","paper":"https://pith.science/paper/LPNYIOOA"},"agent_actions":{"view_html":"https://pith.science/pith/LPNYIOOAV7EUK6SKZCMGEYPTXH","download_json":"https://pith.science/pith/LPNYIOOAV7EUK6SKZCMGEYPTXH.json","view_paper":"https://pith.science/paper/LPNYIOOA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1111.6278&json=true","fetch_graph":"https://pith.science/api/pith-number/LPNYIOOAV7EUK6SKZCMGEYPTXH/graph.json","fetch_events":"https://pith.science/api/pith-number/LPNYIOOAV7EUK6SKZCMGEYPTXH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LPNYIOOAV7EUK6SKZCMGEYPTXH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LPNYIOOAV7EUK6SKZCMGEYPTXH/action/storage_attestation","attest_author":"https://pith.science/pith/LPNYIOOAV7EUK6SKZCMGEYPTXH/action/author_attestation","sign_citation":"https://pith.science/pith/LPNYIOOAV7EUK6SKZCMGEYPTXH/action/citation_signature","submit_replication":"https://pith.science/pith/LPNYIOOAV7EUK6SKZCMGEYPTXH/action/replication_record"}},"created_at":"2026-05-18T02:29:45.873992+00:00","updated_at":"2026-05-18T02:29:45.873992+00:00"}