{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:HNREVLPKWRRSUYNDVTJ2KPBA5E","short_pith_number":"pith:HNREVLPK","schema_version":"1.0","canonical_sha256":"3b624aadeab4632a61a3acd3a53c20e930c9e05211678f75e401c4b5c0c35755","source":{"kind":"arxiv","id":"1302.0982","version":1},"attestation_state":"computed","paper":{"title":"Monoids $\\mathrm{Mon}\\langle a,b:a^{\\alpha}b^{\\beta}a^{\\gamma}b^{\\delta}=b\\rangle$ admit finite complete rewriting systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Alan Cain, Victor Maltcev","submitted_at":"2013-02-05T10:30:12Z","abstract_excerpt":"We prove that every monoid $\\mathrm{Mon}\\langle a,b:a^{\\alpha}b^{\\beta}a^{\\gamma}b^{\\delta}=b\\rangle$ admits a finite complete rewriting system. Furthermore we prove that $\\mathrm{Mon}\\langle a,b:ab^2a^2b^2=b\\rangle$ is non-hopfian, providing an example of a finitely presented non-residually finite monoid with linear Dehn function."},"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":"1302.0982","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-02-05T10:30:12Z","cross_cats_sorted":[],"title_canon_sha256":"5070bd40e7244d393e9eea20bd7164d9afe9201f5f5c86646c43d9511d470e6c","abstract_canon_sha256":"9c4ef7ec2cead363c20624328858f4fdd4376ec5dbaf01a2c689235c498f7850"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:34:26.562149Z","signature_b64":"7TpTGfwqJXNNeu1StgspC5pAOcaSRPMJzBqFm53U2tZiiPczJsMWXzsDT3qaXfBsFi1lyZq17iVz8RhQHd1uCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3b624aadeab4632a61a3acd3a53c20e930c9e05211678f75e401c4b5c0c35755","last_reissued_at":"2026-05-18T03:34:26.561749Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:34:26.561749Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Monoids $\\mathrm{Mon}\\langle a,b:a^{\\alpha}b^{\\beta}a^{\\gamma}b^{\\delta}=b\\rangle$ admit finite complete rewriting systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Alan Cain, Victor Maltcev","submitted_at":"2013-02-05T10:30:12Z","abstract_excerpt":"We prove that every monoid $\\mathrm{Mon}\\langle a,b:a^{\\alpha}b^{\\beta}a^{\\gamma}b^{\\delta}=b\\rangle$ admits a finite complete rewriting system. Furthermore we prove that $\\mathrm{Mon}\\langle a,b:ab^2a^2b^2=b\\rangle$ is non-hopfian, providing an example of a finitely presented non-residually finite monoid with linear Dehn function."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.0982","kind":"arxiv","version":1},"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":"1302.0982","created_at":"2026-05-18T03:34:26.561813+00:00"},{"alias_kind":"arxiv_version","alias_value":"1302.0982v1","created_at":"2026-05-18T03:34:26.561813+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.0982","created_at":"2026-05-18T03:34:26.561813+00:00"},{"alias_kind":"pith_short_12","alias_value":"HNREVLPKWRRS","created_at":"2026-05-18T12:27:46.883200+00:00"},{"alias_kind":"pith_short_16","alias_value":"HNREVLPKWRRSUYND","created_at":"2026-05-18T12:27:46.883200+00:00"},{"alias_kind":"pith_short_8","alias_value":"HNREVLPK","created_at":"2026-05-18T12:27:46.883200+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/HNREVLPKWRRSUYNDVTJ2KPBA5E","json":"https://pith.science/pith/HNREVLPKWRRSUYNDVTJ2KPBA5E.json","graph_json":"https://pith.science/api/pith-number/HNREVLPKWRRSUYNDVTJ2KPBA5E/graph.json","events_json":"https://pith.science/api/pith-number/HNREVLPKWRRSUYNDVTJ2KPBA5E/events.json","paper":"https://pith.science/paper/HNREVLPK"},"agent_actions":{"view_html":"https://pith.science/pith/HNREVLPKWRRSUYNDVTJ2KPBA5E","download_json":"https://pith.science/pith/HNREVLPKWRRSUYNDVTJ2KPBA5E.json","view_paper":"https://pith.science/paper/HNREVLPK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1302.0982&json=true","fetch_graph":"https://pith.science/api/pith-number/HNREVLPKWRRSUYNDVTJ2KPBA5E/graph.json","fetch_events":"https://pith.science/api/pith-number/HNREVLPKWRRSUYNDVTJ2KPBA5E/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HNREVLPKWRRSUYNDVTJ2KPBA5E/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HNREVLPKWRRSUYNDVTJ2KPBA5E/action/storage_attestation","attest_author":"https://pith.science/pith/HNREVLPKWRRSUYNDVTJ2KPBA5E/action/author_attestation","sign_citation":"https://pith.science/pith/HNREVLPKWRRSUYNDVTJ2KPBA5E/action/citation_signature","submit_replication":"https://pith.science/pith/HNREVLPKWRRSUYNDVTJ2KPBA5E/action/replication_record"}},"created_at":"2026-05-18T03:34:26.561813+00:00","updated_at":"2026-05-18T03:34:26.561813+00:00"}