{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:3LDERVXZ7UNN4URPA4WB6OCF2T","short_pith_number":"pith:3LDERVXZ","schema_version":"1.0","canonical_sha256":"dac648d6f9fd1ade522f072c1f3845d4c766c6ea43cfb9ca435ef6443919e5e7","source":{"kind":"arxiv","id":"1503.03733","version":1},"attestation_state":"computed","paper":{"title":"Invariant means on Boolean inverse monoids","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CT","authors_text":"Daniel H. Lenz, Ganna Kudryavtseva, Mark V. Lawson, Pedro Resende","submitted_at":"2015-03-12T14:21:35Z","abstract_excerpt":"The classical theory of invariant means, which plays an important role in the theory of paradoxical decompositions, is based upon what are usually termed `pseudogroups'. Such pseudogroups are in fact concrete examples of the Boolean inverse monoids which give rise to etale topological groupoids under non-commutative Stone duality. We accordingly initiate the theory of invariant means on arbitrary Boolean inverse monoids. Our main theorem is a characterization of when a Boolean inverse monoid admits an invariant mean. This generalizes the classical Tarski alternative proved, for example, by de "},"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":"1503.03733","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2015-03-12T14:21:35Z","cross_cats_sorted":[],"title_canon_sha256":"fd4d49de5b77a7e190a249e8322858ced82a98c5f20ffce0f751c71428d1cde7","abstract_canon_sha256":"b463d3cbf7d9ab41cf2917f32c31f189e98604be2a96ca69b8fa336c18c96b99"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:24:27.512056Z","signature_b64":"2L+4dXCphdqTO7ZvGXibcmq7TqpcCdkZaeAkWYX2fwZ4t2I7LAcaE04HiXKfq9vuwL9bmosZ4dAt8EUxc1q+Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dac648d6f9fd1ade522f072c1f3845d4c766c6ea43cfb9ca435ef6443919e5e7","last_reissued_at":"2026-05-18T02:24:27.511264Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:24:27.511264Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Invariant means on Boolean inverse monoids","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CT","authors_text":"Daniel H. Lenz, Ganna Kudryavtseva, Mark V. Lawson, Pedro Resende","submitted_at":"2015-03-12T14:21:35Z","abstract_excerpt":"The classical theory of invariant means, which plays an important role in the theory of paradoxical decompositions, is based upon what are usually termed `pseudogroups'. Such pseudogroups are in fact concrete examples of the Boolean inverse monoids which give rise to etale topological groupoids under non-commutative Stone duality. We accordingly initiate the theory of invariant means on arbitrary Boolean inverse monoids. Our main theorem is a characterization of when a Boolean inverse monoid admits an invariant mean. This generalizes the classical Tarski alternative proved, for example, by de "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.03733","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":"1503.03733","created_at":"2026-05-18T02:24:27.511411+00:00"},{"alias_kind":"arxiv_version","alias_value":"1503.03733v1","created_at":"2026-05-18T02:24:27.511411+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.03733","created_at":"2026-05-18T02:24:27.511411+00:00"},{"alias_kind":"pith_short_12","alias_value":"3LDERVXZ7UNN","created_at":"2026-05-18T12:29:02.477457+00:00"},{"alias_kind":"pith_short_16","alias_value":"3LDERVXZ7UNN4URP","created_at":"2026-05-18T12:29:02.477457+00:00"},{"alias_kind":"pith_short_8","alias_value":"3LDERVXZ","created_at":"2026-05-18T12:29:02.477457+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/3LDERVXZ7UNN4URPA4WB6OCF2T","json":"https://pith.science/pith/3LDERVXZ7UNN4URPA4WB6OCF2T.json","graph_json":"https://pith.science/api/pith-number/3LDERVXZ7UNN4URPA4WB6OCF2T/graph.json","events_json":"https://pith.science/api/pith-number/3LDERVXZ7UNN4URPA4WB6OCF2T/events.json","paper":"https://pith.science/paper/3LDERVXZ"},"agent_actions":{"view_html":"https://pith.science/pith/3LDERVXZ7UNN4URPA4WB6OCF2T","download_json":"https://pith.science/pith/3LDERVXZ7UNN4URPA4WB6OCF2T.json","view_paper":"https://pith.science/paper/3LDERVXZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1503.03733&json=true","fetch_graph":"https://pith.science/api/pith-number/3LDERVXZ7UNN4URPA4WB6OCF2T/graph.json","fetch_events":"https://pith.science/api/pith-number/3LDERVXZ7UNN4URPA4WB6OCF2T/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3LDERVXZ7UNN4URPA4WB6OCF2T/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3LDERVXZ7UNN4URPA4WB6OCF2T/action/storage_attestation","attest_author":"https://pith.science/pith/3LDERVXZ7UNN4URPA4WB6OCF2T/action/author_attestation","sign_citation":"https://pith.science/pith/3LDERVXZ7UNN4URPA4WB6OCF2T/action/citation_signature","submit_replication":"https://pith.science/pith/3LDERVXZ7UNN4URPA4WB6OCF2T/action/replication_record"}},"created_at":"2026-05-18T02:24:27.511411+00:00","updated_at":"2026-05-18T02:24:27.511411+00:00"}