{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:HI4UTV3NIHOUJCMGX6M7ZGJ53Q","short_pith_number":"pith:HI4UTV3N","schema_version":"1.0","canonical_sha256":"3a3949d76d41dd448986bf99fc993ddc239b4634db4d8f8532489029d27017cc","source":{"kind":"arxiv","id":"1803.10532","version":2},"attestation_state":"computed","paper":{"title":"The Booleanization of an inverse semigroup","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CT","authors_text":"Mark V. Lawson","submitted_at":"2018-03-28T11:19:49Z","abstract_excerpt":"We prove that the forgetful functor from the category of Boolean inverse semigroups to inverse semigroups with zero has a left adjoint. This left adjoint is what we term the `Booleanization'. We establish the exact connection between the Booleanization of an inverse semigroup and Paterson's universal groupoid of the inverse semigroup and we explicitly compute the Booleanization of the polycyclic inverse monoid $P_{n}$ and demonstrate its affiliation with the Cuntz-Toeplitz algebra."},"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":"1803.10532","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2018-03-28T11:19:49Z","cross_cats_sorted":[],"title_canon_sha256":"4d22be1bab158ddfc8bea3aa63a378bde7fd60b42edb0826f841d740622ed9bc","abstract_canon_sha256":"6bd47768327e3c322bc20d196f0e05a19c8b00f33e07920cbd4b4a44dde2f31d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:55:59.232261Z","signature_b64":"bX5MGTjTd5J6DUTeD15kbUWvS9ZZKa1uQreAMvoPc/mPWI3KuBX/HNdGjGT7758vbDHe1IRxZz4wLVUbBH1oAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3a3949d76d41dd448986bf99fc993ddc239b4634db4d8f8532489029d27017cc","last_reissued_at":"2026-05-17T23:55:59.231563Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:55:59.231563Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Booleanization of an inverse semigroup","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CT","authors_text":"Mark V. Lawson","submitted_at":"2018-03-28T11:19:49Z","abstract_excerpt":"We prove that the forgetful functor from the category of Boolean inverse semigroups to inverse semigroups with zero has a left adjoint. This left adjoint is what we term the `Booleanization'. We establish the exact connection between the Booleanization of an inverse semigroup and Paterson's universal groupoid of the inverse semigroup and we explicitly compute the Booleanization of the polycyclic inverse monoid $P_{n}$ and demonstrate its affiliation with the Cuntz-Toeplitz algebra."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.10532","kind":"arxiv","version":2},"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":"1803.10532","created_at":"2026-05-17T23:55:59.231673+00:00"},{"alias_kind":"arxiv_version","alias_value":"1803.10532v2","created_at":"2026-05-17T23:55:59.231673+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.10532","created_at":"2026-05-17T23:55:59.231673+00:00"},{"alias_kind":"pith_short_12","alias_value":"HI4UTV3NIHOU","created_at":"2026-05-18T12:32:28.185984+00:00"},{"alias_kind":"pith_short_16","alias_value":"HI4UTV3NIHOUJCMG","created_at":"2026-05-18T12:32:28.185984+00:00"},{"alias_kind":"pith_short_8","alias_value":"HI4UTV3N","created_at":"2026-05-18T12:32:28.185984+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/HI4UTV3NIHOUJCMGX6M7ZGJ53Q","json":"https://pith.science/pith/HI4UTV3NIHOUJCMGX6M7ZGJ53Q.json","graph_json":"https://pith.science/api/pith-number/HI4UTV3NIHOUJCMGX6M7ZGJ53Q/graph.json","events_json":"https://pith.science/api/pith-number/HI4UTV3NIHOUJCMGX6M7ZGJ53Q/events.json","paper":"https://pith.science/paper/HI4UTV3N"},"agent_actions":{"view_html":"https://pith.science/pith/HI4UTV3NIHOUJCMGX6M7ZGJ53Q","download_json":"https://pith.science/pith/HI4UTV3NIHOUJCMGX6M7ZGJ53Q.json","view_paper":"https://pith.science/paper/HI4UTV3N","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1803.10532&json=true","fetch_graph":"https://pith.science/api/pith-number/HI4UTV3NIHOUJCMGX6M7ZGJ53Q/graph.json","fetch_events":"https://pith.science/api/pith-number/HI4UTV3NIHOUJCMGX6M7ZGJ53Q/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HI4UTV3NIHOUJCMGX6M7ZGJ53Q/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HI4UTV3NIHOUJCMGX6M7ZGJ53Q/action/storage_attestation","attest_author":"https://pith.science/pith/HI4UTV3NIHOUJCMGX6M7ZGJ53Q/action/author_attestation","sign_citation":"https://pith.science/pith/HI4UTV3NIHOUJCMGX6M7ZGJ53Q/action/citation_signature","submit_replication":"https://pith.science/pith/HI4UTV3NIHOUJCMGX6M7ZGJ53Q/action/replication_record"}},"created_at":"2026-05-17T23:55:59.231673+00:00","updated_at":"2026-05-17T23:55:59.231673+00:00"}