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Let $S=sgp\\langle A|u=v\\rangle$ be a semigroup generated by a set $A=\\{a_1,a_2,\\dots,a_n\\},\\ n\\in \\mathbb{N}$ with defining relation $u=v$, where $u,v\\in A^*$ and $A^*$ is the free monoid generated by $A$. Such a semigroup is called a one-relator semigroup. Suppose that $|v|\\leq|u|\\leq3$, where $|u|$ is the length of the word $u$. Suppose that $a,b\\in A,\\ a\\neq b$. Then we have the following: (1) $S$ is prefix-automatic if $u=v\\not\\in \\{ab"},"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":"1702.03355","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-02-10T23:40:36Z","cross_cats_sorted":[],"title_canon_sha256":"553b108e781adc8e7343af5b5a0ddc1be05847a01aaf94294c65b13e96275ea7","abstract_canon_sha256":"fe45e5c857621e9f22a1d0522881bf47a748c63963492e4f9e203d5db6376231"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:42:58.511627Z","signature_b64":"EE0J89jbABbs2OCSkSmDdIHbgqYYSDSQAUpIqm9G1cx20KnsfKsTgCPIV1wGYENwzcfh1pQoK5B3V680y5zkAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"65afd9e954b9fe1ec097a7a1941b40f7196599fc156ae0140e13a4fa44531006","last_reissued_at":"2026-05-18T00:42:58.510884Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:42:58.510884Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Automaticity of one-relator semigroups with length less than or equal to three","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Haibin Wu, Honglian Xie, Yuqun Chen","submitted_at":"2017-02-10T23:40:36Z","abstract_excerpt":"The main results of this paper is to give a complete characterization of the automaticity of one-relator semigroups with length less than or equal to three. Let $S=sgp\\langle A|u=v\\rangle$ be a semigroup generated by a set $A=\\{a_1,a_2,\\dots,a_n\\},\\ n\\in \\mathbb{N}$ with defining relation $u=v$, where $u,v\\in A^*$ and $A^*$ is the free monoid generated by $A$. Such a semigroup is called a one-relator semigroup. Suppose that $|v|\\leq|u|\\leq3$, where $|u|$ is the length of the word $u$. Suppose that $a,b\\in A,\\ a\\neq b$. Then we have the following: (1) $S$ is prefix-automatic if $u=v\\not\\in \\{ab"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.03355","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":"1702.03355","created_at":"2026-05-18T00:42:58.511012+00:00"},{"alias_kind":"arxiv_version","alias_value":"1702.03355v1","created_at":"2026-05-18T00:42:58.511012+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.03355","created_at":"2026-05-18T00:42:58.511012+00:00"},{"alias_kind":"pith_short_12","alias_value":"MWX5T2KUXH7B","created_at":"2026-05-18T12:31:31.346846+00:00"},{"alias_kind":"pith_short_16","alias_value":"MWX5T2KUXH7B5QEX","created_at":"2026-05-18T12:31:31.346846+00:00"},{"alias_kind":"pith_short_8","alias_value":"MWX5T2KU","created_at":"2026-05-18T12:31:31.346846+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/MWX5T2KUXH7B5QEXU6QZIG2A64","json":"https://pith.science/pith/MWX5T2KUXH7B5QEXU6QZIG2A64.json","graph_json":"https://pith.science/api/pith-number/MWX5T2KUXH7B5QEXU6QZIG2A64/graph.json","events_json":"https://pith.science/api/pith-number/MWX5T2KUXH7B5QEXU6QZIG2A64/events.json","paper":"https://pith.science/paper/MWX5T2KU"},"agent_actions":{"view_html":"https://pith.science/pith/MWX5T2KUXH7B5QEXU6QZIG2A64","download_json":"https://pith.science/pith/MWX5T2KUXH7B5QEXU6QZIG2A64.json","view_paper":"https://pith.science/paper/MWX5T2KU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1702.03355&json=true","fetch_graph":"https://pith.science/api/pith-number/MWX5T2KUXH7B5QEXU6QZIG2A64/graph.json","fetch_events":"https://pith.science/api/pith-number/MWX5T2KUXH7B5QEXU6QZIG2A64/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MWX5T2KUXH7B5QEXU6QZIG2A64/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MWX5T2KUXH7B5QEXU6QZIG2A64/action/storage_attestation","attest_author":"https://pith.science/pith/MWX5T2KUXH7B5QEXU6QZIG2A64/action/author_attestation","sign_citation":"https://pith.science/pith/MWX5T2KUXH7B5QEXU6QZIG2A64/action/citation_signature","submit_replication":"https://pith.science/pith/MWX5T2KUXH7B5QEXU6QZIG2A64/action/replication_record"}},"created_at":"2026-05-18T00:42:58.511012+00:00","updated_at":"2026-05-18T00:42:58.511012+00:00"}