{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:2XG3WBQCW7SPU4JJ3TPCZSYQVD","short_pith_number":"pith:2XG3WBQC","schema_version":"1.0","canonical_sha256":"d5cdbb0602b7e4fa7129dcde2ccb10a8c6594013dbf9eb7f3ebc29b160473ead","source":{"kind":"arxiv","id":"1301.4249","version":3},"attestation_state":"computed","paper":{"title":"Regularity and algebraic properties of certain lattice ideals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.CO"],"primary_cat":"math.AC","authors_text":"Jorge Neves, Maria Vaz Pinto, Rafael H. Villarreal","submitted_at":"2013-01-17T21:37:00Z","abstract_excerpt":"We study the regularity and the algebraic properties of certain lattice ideals. We establish a map I --> I\\~ between the family of graded lattice ideals in an N-graded polynomial ring over a field K and the family of graded lattice ideals in a polynomial ring with the standard grading. This map is shown to preserve the complete intersection property and the regularity of I but not the degree. We relate the Hilbert series and the generators of I and I\\~. If dim(I)=1, we relate the degrees of I and I\\~. It is shown that the regularity of certain lattice ideals is additive in a certain sense. The"},"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":"1301.4249","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2013-01-17T21:37:00Z","cross_cats_sorted":["math.AG","math.CO"],"title_canon_sha256":"75856fd3cb3692d35fe511c1e0f1e2eeb6f0b36e52b23fe5bad9d22aab567ada","abstract_canon_sha256":"7e1baa8603d439a1c8e5877abc07a84cc64dc72cb851bef7bd5b4f8c15fedf2b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:29:45.736011Z","signature_b64":"RdV7+eRjDTrKpi2Z1EZVU6DHTCUa+6yQYI6+An1qFb45jkzpgJOIf4kA5YmsEVToctN751fW17avGPNRjTmoCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d5cdbb0602b7e4fa7129dcde2ccb10a8c6594013dbf9eb7f3ebc29b160473ead","last_reissued_at":"2026-05-18T02:29:45.735647Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:29:45.735647Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Regularity and algebraic properties of certain lattice ideals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.CO"],"primary_cat":"math.AC","authors_text":"Jorge Neves, Maria Vaz Pinto, Rafael H. Villarreal","submitted_at":"2013-01-17T21:37:00Z","abstract_excerpt":"We study the regularity and the algebraic properties of certain lattice ideals. We establish a map I --> I\\~ between the family of graded lattice ideals in an N-graded polynomial ring over a field K and the family of graded lattice ideals in a polynomial ring with the standard grading. This map is shown to preserve the complete intersection property and the regularity of I but not the degree. We relate the Hilbert series and the generators of I and I\\~. If dim(I)=1, we relate the degrees of I and I\\~. It is shown that the regularity of certain lattice ideals is additive in a certain sense. The"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.4249","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":"1301.4249","created_at":"2026-05-18T02:29:45.735702+00:00"},{"alias_kind":"arxiv_version","alias_value":"1301.4249v3","created_at":"2026-05-18T02:29:45.735702+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.4249","created_at":"2026-05-18T02:29:45.735702+00:00"},{"alias_kind":"pith_short_12","alias_value":"2XG3WBQCW7SP","created_at":"2026-05-18T12:27:32.513160+00:00"},{"alias_kind":"pith_short_16","alias_value":"2XG3WBQCW7SPU4JJ","created_at":"2026-05-18T12:27:32.513160+00:00"},{"alias_kind":"pith_short_8","alias_value":"2XG3WBQC","created_at":"2026-05-18T12:27:32.513160+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/2XG3WBQCW7SPU4JJ3TPCZSYQVD","json":"https://pith.science/pith/2XG3WBQCW7SPU4JJ3TPCZSYQVD.json","graph_json":"https://pith.science/api/pith-number/2XG3WBQCW7SPU4JJ3TPCZSYQVD/graph.json","events_json":"https://pith.science/api/pith-number/2XG3WBQCW7SPU4JJ3TPCZSYQVD/events.json","paper":"https://pith.science/paper/2XG3WBQC"},"agent_actions":{"view_html":"https://pith.science/pith/2XG3WBQCW7SPU4JJ3TPCZSYQVD","download_json":"https://pith.science/pith/2XG3WBQCW7SPU4JJ3TPCZSYQVD.json","view_paper":"https://pith.science/paper/2XG3WBQC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1301.4249&json=true","fetch_graph":"https://pith.science/api/pith-number/2XG3WBQCW7SPU4JJ3TPCZSYQVD/graph.json","fetch_events":"https://pith.science/api/pith-number/2XG3WBQCW7SPU4JJ3TPCZSYQVD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2XG3WBQCW7SPU4JJ3TPCZSYQVD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2XG3WBQCW7SPU4JJ3TPCZSYQVD/action/storage_attestation","attest_author":"https://pith.science/pith/2XG3WBQCW7SPU4JJ3TPCZSYQVD/action/author_attestation","sign_citation":"https://pith.science/pith/2XG3WBQCW7SPU4JJ3TPCZSYQVD/action/citation_signature","submit_replication":"https://pith.science/pith/2XG3WBQCW7SPU4JJ3TPCZSYQVD/action/replication_record"}},"created_at":"2026-05-18T02:29:45.735702+00:00","updated_at":"2026-05-18T02:29:45.735702+00:00"}