{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:U3O6CL5IXCBZN5USGFF5NCPSHK","short_pith_number":"pith:U3O6CL5I","schema_version":"1.0","canonical_sha256":"a6dde12fa8b88396f692314bd689f23a9c6ea9e15453109118630f6cef8b1545","source":{"kind":"arxiv","id":"1110.2124","version":2},"attestation_state":"computed","paper":{"title":"The Degree and regularity of vanishing ideals of algebraic toric sets over finite fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Maria Vaz Pinto, Rafael H. Villarreal","submitted_at":"2011-10-10T18:01:42Z","abstract_excerpt":"Let X* be a subset of an affine space A^s, over a finite field K, which is parameterized by the edges of a clutter. Let X and Y be the images of X* under the maps x --> [x] and x --> [(x,1)] respectively, where [x] and [(x,1)] are points in the projective spaces P^{s-1} and P^s respectively. For certain clutters and for connected graphs, we were able to relate the algebraic invariants and properties of the vanishing ideals I(X) and I(Y). In a number of interesting cases, we compute its degree and regularity. For Hamiltonian bipartite graphs, we show the Eisenbud-Goto regularity conjecture. We "},"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":"1110.2124","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-10-10T18:01:42Z","cross_cats_sorted":[],"title_canon_sha256":"0f1baf6ddd43a4d923630503782d99e758cf14e86bf802feae4fac9d377bfdc9","abstract_canon_sha256":"6e950503ca036ef5d7601b659f1d19f78490870dcf3d9e6dbbdf4493a0f98591"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:20:20.891367Z","signature_b64":"9TH+wEXOLghZvadfVlOBjFO4Hjs7Jk6oxIk3qrv2BvwkKbkteC2PFGBU0yvb6PTB3lO5T41YS0ZpQ6WXGRnjDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a6dde12fa8b88396f692314bd689f23a9c6ea9e15453109118630f6cef8b1545","last_reissued_at":"2026-05-18T03:20:20.890827Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:20:20.890827Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Degree and regularity of vanishing ideals of algebraic toric sets over finite fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Maria Vaz Pinto, Rafael H. Villarreal","submitted_at":"2011-10-10T18:01:42Z","abstract_excerpt":"Let X* be a subset of an affine space A^s, over a finite field K, which is parameterized by the edges of a clutter. Let X and Y be the images of X* under the maps x --> [x] and x --> [(x,1)] respectively, where [x] and [(x,1)] are points in the projective spaces P^{s-1} and P^s respectively. For certain clutters and for connected graphs, we were able to relate the algebraic invariants and properties of the vanishing ideals I(X) and I(Y). In a number of interesting cases, we compute its degree and regularity. For Hamiltonian bipartite graphs, we show the Eisenbud-Goto regularity conjecture. We "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.2124","kind":"arxiv","version":2},"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":"1110.2124","created_at":"2026-05-18T03:20:20.890909+00:00"},{"alias_kind":"arxiv_version","alias_value":"1110.2124v2","created_at":"2026-05-18T03:20:20.890909+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.2124","created_at":"2026-05-18T03:20:20.890909+00:00"},{"alias_kind":"pith_short_12","alias_value":"U3O6CL5IXCBZ","created_at":"2026-05-18T12:26:42.757692+00:00"},{"alias_kind":"pith_short_16","alias_value":"U3O6CL5IXCBZN5US","created_at":"2026-05-18T12:26:42.757692+00:00"},{"alias_kind":"pith_short_8","alias_value":"U3O6CL5I","created_at":"2026-05-18T12:26:42.757692+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/U3O6CL5IXCBZN5USGFF5NCPSHK","json":"https://pith.science/pith/U3O6CL5IXCBZN5USGFF5NCPSHK.json","graph_json":"https://pith.science/api/pith-number/U3O6CL5IXCBZN5USGFF5NCPSHK/graph.json","events_json":"https://pith.science/api/pith-number/U3O6CL5IXCBZN5USGFF5NCPSHK/events.json","paper":"https://pith.science/paper/U3O6CL5I"},"agent_actions":{"view_html":"https://pith.science/pith/U3O6CL5IXCBZN5USGFF5NCPSHK","download_json":"https://pith.science/pith/U3O6CL5IXCBZN5USGFF5NCPSHK.json","view_paper":"https://pith.science/paper/U3O6CL5I","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1110.2124&json=true","fetch_graph":"https://pith.science/api/pith-number/U3O6CL5IXCBZN5USGFF5NCPSHK/graph.json","fetch_events":"https://pith.science/api/pith-number/U3O6CL5IXCBZN5USGFF5NCPSHK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/U3O6CL5IXCBZN5USGFF5NCPSHK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/U3O6CL5IXCBZN5USGFF5NCPSHK/action/storage_attestation","attest_author":"https://pith.science/pith/U3O6CL5IXCBZN5USGFF5NCPSHK/action/author_attestation","sign_citation":"https://pith.science/pith/U3O6CL5IXCBZN5USGFF5NCPSHK/action/citation_signature","submit_replication":"https://pith.science/pith/U3O6CL5IXCBZN5USGFF5NCPSHK/action/replication_record"}},"created_at":"2026-05-18T03:20:20.890909+00:00","updated_at":"2026-05-18T03:20:20.890909+00:00"}