{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:WPLF2FOBTQOJ5SNZFHCVAYWZOP","short_pith_number":"pith:WPLF2FOB","schema_version":"1.0","canonical_sha256":"b3d65d15c19c1c9ec9b929c55062d973f60e7424c919a80eb36902f3e2b364a0","source":{"kind":"arxiv","id":"1210.3285","version":1},"attestation_state":"computed","paper":{"title":"A 2-base for inverse semigroups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Joao Araujo, Michael Kinyon, R. Padmanabhan","submitted_at":"2012-10-11T16:14:51Z","abstract_excerpt":"An open problem in the theory of inverse semigroups was whether the variety of such semigroups, when viewed as algebras with a binary operation and a unary operation, is 2-based, that is, has a base for its identities consisting of 2 independent axioms. In this note, we announce the affirmative solution to this problem: the identities \\[ \\quad x(x'x) = x \\qquad \\quad x (x' (y (y' ((z u)' w')'))) = y (y' (x (x' ((w z) u)))) \\] form a base for inverse semigroups where ${}'$ turns out to be the natural inverse operation. We recount here the history of the problem including our previous efforts to"},"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":"1210.3285","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2012-10-11T16:14:51Z","cross_cats_sorted":[],"title_canon_sha256":"535ce4365b08179bcba8877c75a14d1b36379aaa38c9c096635b2b7db5e0e8a2","abstract_canon_sha256":"d40d4a63d9a9a37ea8ae14f94f885fc115462733a798f2c8a9c053d775527b1d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:43:27.807153Z","signature_b64":"5cHV/5w9XxgQESLh2eee8O3RoARtSkd5oe0bXNBGo0ARm6xVLVQEmmyivJr19rLgMGlfG+PRwza8z1hYuURqDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b3d65d15c19c1c9ec9b929c55062d973f60e7424c919a80eb36902f3e2b364a0","last_reissued_at":"2026-05-18T03:43:27.806619Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:43:27.806619Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A 2-base for inverse semigroups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Joao Araujo, Michael Kinyon, R. Padmanabhan","submitted_at":"2012-10-11T16:14:51Z","abstract_excerpt":"An open problem in the theory of inverse semigroups was whether the variety of such semigroups, when viewed as algebras with a binary operation and a unary operation, is 2-based, that is, has a base for its identities consisting of 2 independent axioms. In this note, we announce the affirmative solution to this problem: the identities \\[ \\quad x(x'x) = x \\qquad \\quad x (x' (y (y' ((z u)' w')'))) = y (y' (x (x' ((w z) u)))) \\] form a base for inverse semigroups where ${}'$ turns out to be the natural inverse operation. We recount here the history of the problem including our previous efforts to"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.3285","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":"1210.3285","created_at":"2026-05-18T03:43:27.806690+00:00"},{"alias_kind":"arxiv_version","alias_value":"1210.3285v1","created_at":"2026-05-18T03:43:27.806690+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.3285","created_at":"2026-05-18T03:43:27.806690+00:00"},{"alias_kind":"pith_short_12","alias_value":"WPLF2FOBTQOJ","created_at":"2026-05-18T12:27:25.539911+00:00"},{"alias_kind":"pith_short_16","alias_value":"WPLF2FOBTQOJ5SNZ","created_at":"2026-05-18T12:27:25.539911+00:00"},{"alias_kind":"pith_short_8","alias_value":"WPLF2FOB","created_at":"2026-05-18T12:27:25.539911+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/WPLF2FOBTQOJ5SNZFHCVAYWZOP","json":"https://pith.science/pith/WPLF2FOBTQOJ5SNZFHCVAYWZOP.json","graph_json":"https://pith.science/api/pith-number/WPLF2FOBTQOJ5SNZFHCVAYWZOP/graph.json","events_json":"https://pith.science/api/pith-number/WPLF2FOBTQOJ5SNZFHCVAYWZOP/events.json","paper":"https://pith.science/paper/WPLF2FOB"},"agent_actions":{"view_html":"https://pith.science/pith/WPLF2FOBTQOJ5SNZFHCVAYWZOP","download_json":"https://pith.science/pith/WPLF2FOBTQOJ5SNZFHCVAYWZOP.json","view_paper":"https://pith.science/paper/WPLF2FOB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1210.3285&json=true","fetch_graph":"https://pith.science/api/pith-number/WPLF2FOBTQOJ5SNZFHCVAYWZOP/graph.json","fetch_events":"https://pith.science/api/pith-number/WPLF2FOBTQOJ5SNZFHCVAYWZOP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WPLF2FOBTQOJ5SNZFHCVAYWZOP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WPLF2FOBTQOJ5SNZFHCVAYWZOP/action/storage_attestation","attest_author":"https://pith.science/pith/WPLF2FOBTQOJ5SNZFHCVAYWZOP/action/author_attestation","sign_citation":"https://pith.science/pith/WPLF2FOBTQOJ5SNZFHCVAYWZOP/action/citation_signature","submit_replication":"https://pith.science/pith/WPLF2FOBTQOJ5SNZFHCVAYWZOP/action/replication_record"}},"created_at":"2026-05-18T03:43:27.806690+00:00","updated_at":"2026-05-18T03:43:27.806690+00:00"}