{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:Q7G44E4F2FJCSGG3JFFXX5WHXO","short_pith_number":"pith:Q7G44E4F","schema_version":"1.0","canonical_sha256":"87cdce1385d1522918db494b7bf6c7bbac85d7d136c17b8c29c5a3f7fbc45687","source":{"kind":"arxiv","id":"1208.5625","version":2},"attestation_state":"computed","paper":{"title":"The index of a numerical semigroup ring","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Oana Veliche","submitted_at":"2012-08-28T11:14:05Z","abstract_excerpt":"Let $R=k[|t^a,t^b,t^c|]$ be a complete intersection numerical semigroup ring over an infinite field $k$, where $a,b,c\\in\\BN$. The generalized Loewy length, which is Auslander's index in this case, is computed in terms of the minimal generators of the semigroup: $a,b$ and $c$. Examples provided show that the left hand side of Ding's inequality $\\mult(R)-\\inde(R)-\\codim(R)+1\\geq 0$ can be made arbitrarily large for rings $R$ with $\\edim(R)=3$ . The index of a complete intersection numerical semigroup ring with embedding dimension greater than three is also computed."},"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":"1208.5625","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2012-08-28T11:14:05Z","cross_cats_sorted":[],"title_canon_sha256":"0d1c91a44f747ce1dee63b02c28d2f023d109e4b190a1d6bef0e605c5583f53a","abstract_canon_sha256":"8fbb80db5e90d0ec1184ed6d7f9f089fa8cad814624b9ddc1d4eaace575b871a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:32:58.864650Z","signature_b64":"t0c31g/qDCuQfwi1e/deXpgxJk+HqcoyLpOcDgI6p6mResyPMKvc1LEmTHC4KZVqfCigoZbf+N4Q6T9i9n2BCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"87cdce1385d1522918db494b7bf6c7bbac85d7d136c17b8c29c5a3f7fbc45687","last_reissued_at":"2026-05-18T03:32:58.863844Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:32:58.863844Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The index of a numerical semigroup ring","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Oana Veliche","submitted_at":"2012-08-28T11:14:05Z","abstract_excerpt":"Let $R=k[|t^a,t^b,t^c|]$ be a complete intersection numerical semigroup ring over an infinite field $k$, where $a,b,c\\in\\BN$. The generalized Loewy length, which is Auslander's index in this case, is computed in terms of the minimal generators of the semigroup: $a,b$ and $c$. Examples provided show that the left hand side of Ding's inequality $\\mult(R)-\\inde(R)-\\codim(R)+1\\geq 0$ can be made arbitrarily large for rings $R$ with $\\edim(R)=3$ . The index of a complete intersection numerical semigroup ring with embedding dimension greater than three is also computed."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.5625","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":"1208.5625","created_at":"2026-05-18T03:32:58.863977+00:00"},{"alias_kind":"arxiv_version","alias_value":"1208.5625v2","created_at":"2026-05-18T03:32:58.863977+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.5625","created_at":"2026-05-18T03:32:58.863977+00:00"},{"alias_kind":"pith_short_12","alias_value":"Q7G44E4F2FJC","created_at":"2026-05-18T12:27:18.751474+00:00"},{"alias_kind":"pith_short_16","alias_value":"Q7G44E4F2FJCSGG3","created_at":"2026-05-18T12:27:18.751474+00:00"},{"alias_kind":"pith_short_8","alias_value":"Q7G44E4F","created_at":"2026-05-18T12:27:18.751474+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/Q7G44E4F2FJCSGG3JFFXX5WHXO","json":"https://pith.science/pith/Q7G44E4F2FJCSGG3JFFXX5WHXO.json","graph_json":"https://pith.science/api/pith-number/Q7G44E4F2FJCSGG3JFFXX5WHXO/graph.json","events_json":"https://pith.science/api/pith-number/Q7G44E4F2FJCSGG3JFFXX5WHXO/events.json","paper":"https://pith.science/paper/Q7G44E4F"},"agent_actions":{"view_html":"https://pith.science/pith/Q7G44E4F2FJCSGG3JFFXX5WHXO","download_json":"https://pith.science/pith/Q7G44E4F2FJCSGG3JFFXX5WHXO.json","view_paper":"https://pith.science/paper/Q7G44E4F","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1208.5625&json=true","fetch_graph":"https://pith.science/api/pith-number/Q7G44E4F2FJCSGG3JFFXX5WHXO/graph.json","fetch_events":"https://pith.science/api/pith-number/Q7G44E4F2FJCSGG3JFFXX5WHXO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Q7G44E4F2FJCSGG3JFFXX5WHXO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Q7G44E4F2FJCSGG3JFFXX5WHXO/action/storage_attestation","attest_author":"https://pith.science/pith/Q7G44E4F2FJCSGG3JFFXX5WHXO/action/author_attestation","sign_citation":"https://pith.science/pith/Q7G44E4F2FJCSGG3JFFXX5WHXO/action/citation_signature","submit_replication":"https://pith.science/pith/Q7G44E4F2FJCSGG3JFFXX5WHXO/action/replication_record"}},"created_at":"2026-05-18T03:32:58.863977+00:00","updated_at":"2026-05-18T03:32:58.863977+00:00"}