{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:QKQ5SIIPUY2ME3NUPTV2O5K3HS","short_pith_number":"pith:QKQ5SIIP","schema_version":"1.0","canonical_sha256":"82a1d9210fa634c26db47ceba7755b3c84e725aeed50fa05150796ef7fa61f2a","source":{"kind":"arxiv","id":"0904.0541","version":1},"attestation_state":"computed","paper":{"title":"The Corona Factorization Property and Refinement Monoids","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Eduard Ortega, Francesc Perera, Mikael Rordam","submitted_at":"2009-04-03T10:10:39Z","abstract_excerpt":"The Corona Factorization Property of a C*-algebra, originally defined to study extensions of C*-algebras, has turned out to say something important about intrinsic structural properties of the C*-algebra. We show in this paper that a \\sigma-unital C*-algebra A of real rank zero has the Corona Factorization roperty if and only if its monoid V(A) of Murray-von Neumann equivalence classes of projections in matrix algebras over A has a certain (rather weak) comparability property that we call the Corona Factorization Property (for monoids). We show that a projection in such a C*-algebra is properl"},"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":"0904.0541","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2009-04-03T10:10:39Z","cross_cats_sorted":[],"title_canon_sha256":"d9970b1ea68092c04b65e7282bf2b0d31de508db8a0428e904a722de05b37c08","abstract_canon_sha256":"fdd7ad39f2b2f6337d50b3af79085088d0ee91c7de1e799e4b3669f49351be5b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:35:52.173805Z","signature_b64":"W6FfYWt2l5RC2PeGRIo5MmJGYp4av1XK8zioBwI8hL7s9MSrrTuynLmRjHm2VG/U/7+70wQsVVae5M2U1HmGAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"82a1d9210fa634c26db47ceba7755b3c84e725aeed50fa05150796ef7fa61f2a","last_reissued_at":"2026-05-18T03:35:52.173119Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:35:52.173119Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Corona Factorization Property and Refinement Monoids","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Eduard Ortega, Francesc Perera, Mikael Rordam","submitted_at":"2009-04-03T10:10:39Z","abstract_excerpt":"The Corona Factorization Property of a C*-algebra, originally defined to study extensions of C*-algebras, has turned out to say something important about intrinsic structural properties of the C*-algebra. We show in this paper that a \\sigma-unital C*-algebra A of real rank zero has the Corona Factorization roperty if and only if its monoid V(A) of Murray-von Neumann equivalence classes of projections in matrix algebras over A has a certain (rather weak) comparability property that we call the Corona Factorization Property (for monoids). We show that a projection in such a C*-algebra is properl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0904.0541","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":"0904.0541","created_at":"2026-05-18T03:35:52.173230+00:00"},{"alias_kind":"arxiv_version","alias_value":"0904.0541v1","created_at":"2026-05-18T03:35:52.173230+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0904.0541","created_at":"2026-05-18T03:35:52.173230+00:00"},{"alias_kind":"pith_short_12","alias_value":"QKQ5SIIPUY2M","created_at":"2026-05-18T12:26:01.383474+00:00"},{"alias_kind":"pith_short_16","alias_value":"QKQ5SIIPUY2ME3NU","created_at":"2026-05-18T12:26:01.383474+00:00"},{"alias_kind":"pith_short_8","alias_value":"QKQ5SIIP","created_at":"2026-05-18T12:26:01.383474+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/QKQ5SIIPUY2ME3NUPTV2O5K3HS","json":"https://pith.science/pith/QKQ5SIIPUY2ME3NUPTV2O5K3HS.json","graph_json":"https://pith.science/api/pith-number/QKQ5SIIPUY2ME3NUPTV2O5K3HS/graph.json","events_json":"https://pith.science/api/pith-number/QKQ5SIIPUY2ME3NUPTV2O5K3HS/events.json","paper":"https://pith.science/paper/QKQ5SIIP"},"agent_actions":{"view_html":"https://pith.science/pith/QKQ5SIIPUY2ME3NUPTV2O5K3HS","download_json":"https://pith.science/pith/QKQ5SIIPUY2ME3NUPTV2O5K3HS.json","view_paper":"https://pith.science/paper/QKQ5SIIP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0904.0541&json=true","fetch_graph":"https://pith.science/api/pith-number/QKQ5SIIPUY2ME3NUPTV2O5K3HS/graph.json","fetch_events":"https://pith.science/api/pith-number/QKQ5SIIPUY2ME3NUPTV2O5K3HS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QKQ5SIIPUY2ME3NUPTV2O5K3HS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QKQ5SIIPUY2ME3NUPTV2O5K3HS/action/storage_attestation","attest_author":"https://pith.science/pith/QKQ5SIIPUY2ME3NUPTV2O5K3HS/action/author_attestation","sign_citation":"https://pith.science/pith/QKQ5SIIPUY2ME3NUPTV2O5K3HS/action/citation_signature","submit_replication":"https://pith.science/pith/QKQ5SIIPUY2ME3NUPTV2O5K3HS/action/replication_record"}},"created_at":"2026-05-18T03:35:52.173230+00:00","updated_at":"2026-05-18T03:35:52.173230+00:00"}