{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:ZRLJMOCQZE6COOMVY4Q5656WJ3","short_pith_number":"pith:ZRLJMOCQ","schema_version":"1.0","canonical_sha256":"cc56963850c93c273995c721df77d64ed4c1028815da593e168a20b8290e4466","source":{"kind":"arxiv","id":"1305.5006","version":1},"attestation_state":"computed","paper":{"title":"Deformation of a projection in the multipleir algebra and projection lifting from the corona algebra of a non-simple C*-algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.KT"],"primary_cat":"math.OA","authors_text":"Hyun Ho Lee","submitted_at":"2013-05-22T02:47:07Z","abstract_excerpt":"Let $X$ be a unit interval or a unit circle and let $B$ be a $\\sigma_p$-unital, purely infinite, simple $C\\sp*$-algebra such that its multiplier algebra $M(B)$ has real rank zero. Then we determine necessary and sufficient conditions for a projection in the corona algebra of $C(X)\\otimes B$ to be liftable to a projection in the multiplier algebra. This generalizes a result proved by L. Brown and the author \\cite{BL}. The main technical tools are divided into two parts. The first part is borrowed from the author's previous paper(JFA 260 (2011)). The second part is a proposition showing that we "},"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":"1305.5006","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2013-05-22T02:47:07Z","cross_cats_sorted":["math.KT"],"title_canon_sha256":"f136dcbd56bf4abc9f10a7c2bc2ef60e63061fdd391224fde6861af1222e3a7c","abstract_canon_sha256":"298f5e5afd1817a22871f169bcbcb2d6afbb790d00e95659c46558600106e285"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:25:13.798250Z","signature_b64":"hesEFta4W4cJP5DdoUoVMmY4aPnPFNtt0pT4na8XKLJ+bAvy1Q8alRBsWkIt1vatMpy+I7gs16sql5d4/voBCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cc56963850c93c273995c721df77d64ed4c1028815da593e168a20b8290e4466","last_reissued_at":"2026-05-18T03:25:13.797626Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:25:13.797626Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Deformation of a projection in the multipleir algebra and projection lifting from the corona algebra of a non-simple C*-algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.KT"],"primary_cat":"math.OA","authors_text":"Hyun Ho Lee","submitted_at":"2013-05-22T02:47:07Z","abstract_excerpt":"Let $X$ be a unit interval or a unit circle and let $B$ be a $\\sigma_p$-unital, purely infinite, simple $C\\sp*$-algebra such that its multiplier algebra $M(B)$ has real rank zero. Then we determine necessary and sufficient conditions for a projection in the corona algebra of $C(X)\\otimes B$ to be liftable to a projection in the multiplier algebra. This generalizes a result proved by L. Brown and the author \\cite{BL}. The main technical tools are divided into two parts. The first part is borrowed from the author's previous paper(JFA 260 (2011)). The second part is a proposition showing that we "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.5006","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":"1305.5006","created_at":"2026-05-18T03:25:13.797706+00:00"},{"alias_kind":"arxiv_version","alias_value":"1305.5006v1","created_at":"2026-05-18T03:25:13.797706+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.5006","created_at":"2026-05-18T03:25:13.797706+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZRLJMOCQZE6C","created_at":"2026-05-18T12:28:09.283467+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZRLJMOCQZE6COOMV","created_at":"2026-05-18T12:28:09.283467+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZRLJMOCQ","created_at":"2026-05-18T12:28:09.283467+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/ZRLJMOCQZE6COOMVY4Q5656WJ3","json":"https://pith.science/pith/ZRLJMOCQZE6COOMVY4Q5656WJ3.json","graph_json":"https://pith.science/api/pith-number/ZRLJMOCQZE6COOMVY4Q5656WJ3/graph.json","events_json":"https://pith.science/api/pith-number/ZRLJMOCQZE6COOMVY4Q5656WJ3/events.json","paper":"https://pith.science/paper/ZRLJMOCQ"},"agent_actions":{"view_html":"https://pith.science/pith/ZRLJMOCQZE6COOMVY4Q5656WJ3","download_json":"https://pith.science/pith/ZRLJMOCQZE6COOMVY4Q5656WJ3.json","view_paper":"https://pith.science/paper/ZRLJMOCQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1305.5006&json=true","fetch_graph":"https://pith.science/api/pith-number/ZRLJMOCQZE6COOMVY4Q5656WJ3/graph.json","fetch_events":"https://pith.science/api/pith-number/ZRLJMOCQZE6COOMVY4Q5656WJ3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZRLJMOCQZE6COOMVY4Q5656WJ3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZRLJMOCQZE6COOMVY4Q5656WJ3/action/storage_attestation","attest_author":"https://pith.science/pith/ZRLJMOCQZE6COOMVY4Q5656WJ3/action/author_attestation","sign_citation":"https://pith.science/pith/ZRLJMOCQZE6COOMVY4Q5656WJ3/action/citation_signature","submit_replication":"https://pith.science/pith/ZRLJMOCQZE6COOMVY4Q5656WJ3/action/replication_record"}},"created_at":"2026-05-18T03:25:13.797706+00:00","updated_at":"2026-05-18T03:25:13.797706+00:00"}