{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:3ZRJGGQV6AS473D3LV2GQTXDHT","short_pith_number":"pith:3ZRJGGQV","schema_version":"1.0","canonical_sha256":"de62931a15f025cfec7b5d74684ee33ccade9f398f414b5a3adbd198f5ec51e1","source":{"kind":"arxiv","id":"1111.1294","version":5},"attestation_state":"computed","paper":{"title":"When the associated graded ring of a semigroup ring is Complete Intersection","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Alessio Sammartano, Marco D'Anna, Vincenzo Micale","submitted_at":"2011-11-05T10:31:51Z","abstract_excerpt":"Let (R, m) be the semigroup ring associated to a numerical semigroup S. In this paper we study the property of its associated graded ring G(m) to be Complete Intersection. In particular, we introduce and characterise beta-rectangular and gamma-rectangular Ap\\'ery sets, which will be the fundamental concepts of the paper and will provide, respectively, a sufficient condition and a characterisation for G(m) to be Complete Intersection. Then we use these notions to give four equivalent conditions for G(m) in order to be Complete Intersection."},"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":"1111.1294","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-11-05T10:31:51Z","cross_cats_sorted":[],"title_canon_sha256":"c1ef5069cc6716b9a01dbfdad5e19bcd580738d5330b3237575a378e02787232","abstract_canon_sha256":"1de2e6bf2432fcd88934db77d7d37c45418d36e24c0d866c89c31c55fcbe1ace"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:35:41.300274Z","signature_b64":"mMwv2/N86sZVnHPb4tlvBcW0zol2bdShrp0Ldn54+LsdvCPB3T+aUDJfkTEfj4aJ6WxRpSzOD8T2yiQKPjsFBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"de62931a15f025cfec7b5d74684ee33ccade9f398f414b5a3adbd198f5ec51e1","last_reissued_at":"2026-05-18T03:35:41.299421Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:35:41.299421Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"When the associated graded ring of a semigroup ring is Complete Intersection","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Alessio Sammartano, Marco D'Anna, Vincenzo Micale","submitted_at":"2011-11-05T10:31:51Z","abstract_excerpt":"Let (R, m) be the semigroup ring associated to a numerical semigroup S. In this paper we study the property of its associated graded ring G(m) to be Complete Intersection. In particular, we introduce and characterise beta-rectangular and gamma-rectangular Ap\\'ery sets, which will be the fundamental concepts of the paper and will provide, respectively, a sufficient condition and a characterisation for G(m) to be Complete Intersection. Then we use these notions to give four equivalent conditions for G(m) in order to be Complete Intersection."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.1294","kind":"arxiv","version":5},"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":"1111.1294","created_at":"2026-05-18T03:35:41.299575+00:00"},{"alias_kind":"arxiv_version","alias_value":"1111.1294v5","created_at":"2026-05-18T03:35:41.299575+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.1294","created_at":"2026-05-18T03:35:41.299575+00:00"},{"alias_kind":"pith_short_12","alias_value":"3ZRJGGQV6AS4","created_at":"2026-05-18T12:26:20.644004+00:00"},{"alias_kind":"pith_short_16","alias_value":"3ZRJGGQV6AS473D3","created_at":"2026-05-18T12:26:20.644004+00:00"},{"alias_kind":"pith_short_8","alias_value":"3ZRJGGQV","created_at":"2026-05-18T12:26:20.644004+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/3ZRJGGQV6AS473D3LV2GQTXDHT","json":"https://pith.science/pith/3ZRJGGQV6AS473D3LV2GQTXDHT.json","graph_json":"https://pith.science/api/pith-number/3ZRJGGQV6AS473D3LV2GQTXDHT/graph.json","events_json":"https://pith.science/api/pith-number/3ZRJGGQV6AS473D3LV2GQTXDHT/events.json","paper":"https://pith.science/paper/3ZRJGGQV"},"agent_actions":{"view_html":"https://pith.science/pith/3ZRJGGQV6AS473D3LV2GQTXDHT","download_json":"https://pith.science/pith/3ZRJGGQV6AS473D3LV2GQTXDHT.json","view_paper":"https://pith.science/paper/3ZRJGGQV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1111.1294&json=true","fetch_graph":"https://pith.science/api/pith-number/3ZRJGGQV6AS473D3LV2GQTXDHT/graph.json","fetch_events":"https://pith.science/api/pith-number/3ZRJGGQV6AS473D3LV2GQTXDHT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3ZRJGGQV6AS473D3LV2GQTXDHT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3ZRJGGQV6AS473D3LV2GQTXDHT/action/storage_attestation","attest_author":"https://pith.science/pith/3ZRJGGQV6AS473D3LV2GQTXDHT/action/author_attestation","sign_citation":"https://pith.science/pith/3ZRJGGQV6AS473D3LV2GQTXDHT/action/citation_signature","submit_replication":"https://pith.science/pith/3ZRJGGQV6AS473D3LV2GQTXDHT/action/replication_record"}},"created_at":"2026-05-18T03:35:41.299575+00:00","updated_at":"2026-05-18T03:35:41.299575+00:00"}