{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:VC4WF2SODWHMFVRYSIWYIZSVHK","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"3c5f9f209f47e9cc371d2ffb78c37e2043e7cdefbf6fd3d6f8616cf81d7be734","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2010-03-21T21:01:20Z","title_canon_sha256":"9f1f9c955ffee3e26c89cac8f8425b85d0476dd1b37c74c782ef18699e9c6969"},"schema_version":"1.0","source":{"id":"1003.4028","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1003.4028","created_at":"2026-05-18T03:44:34Z"},{"alias_kind":"arxiv_version","alias_value":"1003.4028v3","created_at":"2026-05-18T03:44:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1003.4028","created_at":"2026-05-18T03:44:34Z"},{"alias_kind":"pith_short_12","alias_value":"VC4WF2SODWHM","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_16","alias_value":"VC4WF2SODWHMFVRY","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_8","alias_value":"VC4WF2SO","created_at":"2026-05-18T12:26:15Z"}],"graph_snapshots":[{"event_id":"sha256:42298f7265debb63b2097569487db8dcc8b6e7023d257011be86c2c36359602e","target":"graph","created_at":"2026-05-18T03:44:34Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"It is well known that in every inverse semigroup the binary operation and the unary operation of inversion satisfy the following three identities: [\\quad x=(xx')x \\qquad \\quad (xx')(y'y)=(y'y)(xx') \\qquad \\quad (xy)z=x(yz\"). ] The goal of this note is to prove the converse, that is, we prove that an algebra of type $<2,1>$ satisfying these three identities is an inverse semigroup and the unary operation coincides with the usual inversion on such semigroups.","authors_text":"Joao Araujo, Michael Kinyon","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2010-03-21T21:01:20Z","title":"An elegant 3-basis for inverse semigroups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.4028","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:33e713d70ceb296be4c4ea73ef7bcef45e7872967b73635845f5b9f5076611a7","target":"record","created_at":"2026-05-18T03:44:34Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"3c5f9f209f47e9cc371d2ffb78c37e2043e7cdefbf6fd3d6f8616cf81d7be734","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2010-03-21T21:01:20Z","title_canon_sha256":"9f1f9c955ffee3e26c89cac8f8425b85d0476dd1b37c74c782ef18699e9c6969"},"schema_version":"1.0","source":{"id":"1003.4028","kind":"arxiv","version":3}},"canonical_sha256":"a8b962ea4e1d8ec2d638922d8466553a8cdd5588d8899b0ec49b99adede3e541","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a8b962ea4e1d8ec2d638922d8466553a8cdd5588d8899b0ec49b99adede3e541","first_computed_at":"2026-05-18T03:44:34.153617Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:44:34.153617Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1dY6t5i+l1riWmSFYPExwRsRVV67FYXdEdKyExVr4WCmitnZuyRsXZttQNsxHc3z6xUvW5/EenC2ml+3Gp9qDw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:44:34.154207Z","signed_message":"canonical_sha256_bytes"},"source_id":"1003.4028","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:33e713d70ceb296be4c4ea73ef7bcef45e7872967b73635845f5b9f5076611a7","sha256:42298f7265debb63b2097569487db8dcc8b6e7023d257011be86c2c36359602e"],"state_sha256":"9cc23c49a0a759bf70555dcd7a3e51c9fe44bbca84c691cb22c34f1d9314002a"}