{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:VDC3R533QXQHGWCWSLEHX2B6RV","short_pith_number":"pith:VDC3R533","schema_version":"1.0","canonical_sha256":"a8c5b8f77b85e073585692c87be83e8d6b22b135112f62dfe6f5b9344c503259","source":{"kind":"arxiv","id":"1101.1856","version":2},"attestation_state":"computed","paper":{"title":"A characterization of semiprojectivity for commutative C*-algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GN"],"primary_cat":"math.OA","authors_text":"Adam P. W. S{\\o}rensen, Hannes Thiel","submitted_at":"2011-01-10T16:06:14Z","abstract_excerpt":"Given a compact, metric space X, we show that the commutative C*-algebra C(X) is semiprojective if and only if X is an absolute neighborhood retract of dimension at most one. This confirms a conjecture of Blackadar. Generalizing to the non-unital setting, we derive a characterization of semiprojectivity for separable, commutative C*-algebras. As further application of our findings we verify two conjectures of Loring and Blackadar in the commutative case, and we give a partial answer to the question, when a commutative C*-algebra is weakly (semi-)projective."},"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":"1101.1856","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2011-01-10T16:06:14Z","cross_cats_sorted":["math.GN"],"title_canon_sha256":"6b74ec94634a15815028535bfcd16a8fbc8d525479d28ab439891fd5c6ffbd30","abstract_canon_sha256":"d7e0fc3861f81999f388be7787e127b98be0667128ecf01aad3eefef182b50ec"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:34:46.507410Z","signature_b64":"ZueJmD1sRrNW+eQtXTFJisXd2HGZ18S0u5Wq/h7Pwg/sa2SU9q7nmSG1TPJYujnnWxAt8PdI9c+/pMDFZwBkAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a8c5b8f77b85e073585692c87be83e8d6b22b135112f62dfe6f5b9344c503259","last_reissued_at":"2026-05-18T03:34:46.506827Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:34:46.506827Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A characterization of semiprojectivity for commutative C*-algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GN"],"primary_cat":"math.OA","authors_text":"Adam P. W. S{\\o}rensen, Hannes Thiel","submitted_at":"2011-01-10T16:06:14Z","abstract_excerpt":"Given a compact, metric space X, we show that the commutative C*-algebra C(X) is semiprojective if and only if X is an absolute neighborhood retract of dimension at most one. This confirms a conjecture of Blackadar. Generalizing to the non-unital setting, we derive a characterization of semiprojectivity for separable, commutative C*-algebras. As further application of our findings we verify two conjectures of Loring and Blackadar in the commutative case, and we give a partial answer to the question, when a commutative C*-algebra is weakly (semi-)projective."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.1856","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":"1101.1856","created_at":"2026-05-18T03:34:46.506916+00:00"},{"alias_kind":"arxiv_version","alias_value":"1101.1856v2","created_at":"2026-05-18T03:34:46.506916+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.1856","created_at":"2026-05-18T03:34:46.506916+00:00"},{"alias_kind":"pith_short_12","alias_value":"VDC3R533QXQH","created_at":"2026-05-18T12:26:42.757692+00:00"},{"alias_kind":"pith_short_16","alias_value":"VDC3R533QXQHGWCW","created_at":"2026-05-18T12:26:42.757692+00:00"},{"alias_kind":"pith_short_8","alias_value":"VDC3R533","created_at":"2026-05-18T12:26:42.757692+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/VDC3R533QXQHGWCWSLEHX2B6RV","json":"https://pith.science/pith/VDC3R533QXQHGWCWSLEHX2B6RV.json","graph_json":"https://pith.science/api/pith-number/VDC3R533QXQHGWCWSLEHX2B6RV/graph.json","events_json":"https://pith.science/api/pith-number/VDC3R533QXQHGWCWSLEHX2B6RV/events.json","paper":"https://pith.science/paper/VDC3R533"},"agent_actions":{"view_html":"https://pith.science/pith/VDC3R533QXQHGWCWSLEHX2B6RV","download_json":"https://pith.science/pith/VDC3R533QXQHGWCWSLEHX2B6RV.json","view_paper":"https://pith.science/paper/VDC3R533","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1101.1856&json=true","fetch_graph":"https://pith.science/api/pith-number/VDC3R533QXQHGWCWSLEHX2B6RV/graph.json","fetch_events":"https://pith.science/api/pith-number/VDC3R533QXQHGWCWSLEHX2B6RV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VDC3R533QXQHGWCWSLEHX2B6RV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VDC3R533QXQHGWCWSLEHX2B6RV/action/storage_attestation","attest_author":"https://pith.science/pith/VDC3R533QXQHGWCWSLEHX2B6RV/action/author_attestation","sign_citation":"https://pith.science/pith/VDC3R533QXQHGWCWSLEHX2B6RV/action/citation_signature","submit_replication":"https://pith.science/pith/VDC3R533QXQHGWCWSLEHX2B6RV/action/replication_record"}},"created_at":"2026-05-18T03:34:46.506916+00:00","updated_at":"2026-05-18T03:34:46.506916+00:00"}