{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:MMAXLOWYR5BKM7C255QE7RDYPI","short_pith_number":"pith:MMAXLOWY","schema_version":"1.0","canonical_sha256":"630175bad88f42a67c5aef604fc4787a34eeab25d374e71eef9f7bb9b93c419a","source":{"kind":"arxiv","id":"1307.5807","version":5},"attestation_state":"computed","paper":{"title":"Computation of the w-primality and asymptotic w-primality with applications to numerical semigroups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"A. Vigneron-Tenorio, J. I. Garc\\'ia-Garc\\'ia, M.A. Moreno-Fr\\'ias","submitted_at":"2013-07-22T18:21:50Z","abstract_excerpt":"We give an algorithm to compute the $\\omega$-primality of finitely generated atomic monoids. Asymptotic $\\w$-primality is also studied and a formula to obtain it in finitely generated quasi-Archimedean monoids is proven. The formulation is applied to numerical semigroups, obtaining an expression of this invariant in terms of its system of generators."},"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":"1307.5807","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2013-07-22T18:21:50Z","cross_cats_sorted":[],"title_canon_sha256":"24661f5bbae34c4c7e61af3cb9529e09e3aaf4ed0a3dcd3cffce9a6ffd6c0257","abstract_canon_sha256":"7a53e5d877ddd2b875a92fae2c53d640ee852c7d9b17c06e2ab6aee7b7dab85b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:56:51.908345Z","signature_b64":"oPsHqp/jtPV1dhDi3QLLhS5B2ESUynAhhMNsLxfwvFQ/eYRjajEF/WX+Cs/NVhYzmGm920t/YncIrgfIHmbnDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"630175bad88f42a67c5aef604fc4787a34eeab25d374e71eef9f7bb9b93c419a","last_reissued_at":"2026-05-18T02:56:51.907875Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:56:51.907875Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Computation of the w-primality and asymptotic w-primality with applications to numerical semigroups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"A. Vigneron-Tenorio, J. I. Garc\\'ia-Garc\\'ia, M.A. Moreno-Fr\\'ias","submitted_at":"2013-07-22T18:21:50Z","abstract_excerpt":"We give an algorithm to compute the $\\omega$-primality of finitely generated atomic monoids. Asymptotic $\\w$-primality is also studied and a formula to obtain it in finitely generated quasi-Archimedean monoids is proven. The formulation is applied to numerical semigroups, obtaining an expression of this invariant in terms of its system of generators."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.5807","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":"1307.5807","created_at":"2026-05-18T02:56:51.907950+00:00"},{"alias_kind":"arxiv_version","alias_value":"1307.5807v5","created_at":"2026-05-18T02:56:51.907950+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.5807","created_at":"2026-05-18T02:56:51.907950+00:00"},{"alias_kind":"pith_short_12","alias_value":"MMAXLOWYR5BK","created_at":"2026-05-18T12:27:52.871228+00:00"},{"alias_kind":"pith_short_16","alias_value":"MMAXLOWYR5BKM7C2","created_at":"2026-05-18T12:27:52.871228+00:00"},{"alias_kind":"pith_short_8","alias_value":"MMAXLOWY","created_at":"2026-05-18T12:27:52.871228+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/MMAXLOWYR5BKM7C255QE7RDYPI","json":"https://pith.science/pith/MMAXLOWYR5BKM7C255QE7RDYPI.json","graph_json":"https://pith.science/api/pith-number/MMAXLOWYR5BKM7C255QE7RDYPI/graph.json","events_json":"https://pith.science/api/pith-number/MMAXLOWYR5BKM7C255QE7RDYPI/events.json","paper":"https://pith.science/paper/MMAXLOWY"},"agent_actions":{"view_html":"https://pith.science/pith/MMAXLOWYR5BKM7C255QE7RDYPI","download_json":"https://pith.science/pith/MMAXLOWYR5BKM7C255QE7RDYPI.json","view_paper":"https://pith.science/paper/MMAXLOWY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1307.5807&json=true","fetch_graph":"https://pith.science/api/pith-number/MMAXLOWYR5BKM7C255QE7RDYPI/graph.json","fetch_events":"https://pith.science/api/pith-number/MMAXLOWYR5BKM7C255QE7RDYPI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MMAXLOWYR5BKM7C255QE7RDYPI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MMAXLOWYR5BKM7C255QE7RDYPI/action/storage_attestation","attest_author":"https://pith.science/pith/MMAXLOWYR5BKM7C255QE7RDYPI/action/author_attestation","sign_citation":"https://pith.science/pith/MMAXLOWYR5BKM7C255QE7RDYPI/action/citation_signature","submit_replication":"https://pith.science/pith/MMAXLOWYR5BKM7C255QE7RDYPI/action/replication_record"}},"created_at":"2026-05-18T02:56:51.907950+00:00","updated_at":"2026-05-18T02:56:51.907950+00:00"}