{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2003:2NHOGGCRCQ5UL7HZCD6M2M74CJ","short_pith_number":"pith:2NHOGGCR","schema_version":"1.0","canonical_sha256":"d34ee31851143b45fcf910fccd33fc1242c120c643ce2f3a189b94293e80c7ac","source":{"kind":"arxiv","id":"math/0312286","version":1},"attestation_state":"computed","paper":{"title":"Purely infinite C*-algebras: ideal-preserving zero homotopies","license":"","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Eberhard Kirchberg, Mikael Rordam","submitted_at":"2003-12-15T12:30:25Z","abstract_excerpt":"We show that if A is a separable, nuclear, O_infty-absorbing (or strongly purely infinite) C*-algebra, which is homotopic to zero in an ideal-system preserving way, then A is the inductive limit of C*-algebras of the form M_k(C_0(G,v)), where G is a finite graph (and C_0(G,v) is the algebra of continuous functions on G that vanish at a distinguished point v in G).\n  We show further that any separable, nuclear, stable, O_2-absorbing C*-algebra is isomorphic to a crossed product of a C*-algebra D with the integers by an action alpha, where D is an inductive limit of C*-algebras of the form M_k(C"},"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":"math/0312286","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.OA","submitted_at":"2003-12-15T12:30:25Z","cross_cats_sorted":[],"title_canon_sha256":"3090a32441c3c568a4da285da3ca49dcf1b3e17452d96c25191e0af0c894153e","abstract_canon_sha256":"6dd8c691ea5eed1449c6b9a0af88d1eb934eeb1c89f380ce0e9c2bd0e9351324"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:34:54.542697Z","signature_b64":"b8gBf7esRyoFbPA225mp46sv0hUbPRZkXfwTFH9BeiFQcm4FqU1yvT3MohsfUwRn+gyc7i8voZDSkDM4GwLtCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d34ee31851143b45fcf910fccd33fc1242c120c643ce2f3a189b94293e80c7ac","last_reissued_at":"2026-05-18T04:34:54.542303Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:34:54.542303Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Purely infinite C*-algebras: ideal-preserving zero homotopies","license":"","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Eberhard Kirchberg, Mikael Rordam","submitted_at":"2003-12-15T12:30:25Z","abstract_excerpt":"We show that if A is a separable, nuclear, O_infty-absorbing (or strongly purely infinite) C*-algebra, which is homotopic to zero in an ideal-system preserving way, then A is the inductive limit of C*-algebras of the form M_k(C_0(G,v)), where G is a finite graph (and C_0(G,v) is the algebra of continuous functions on G that vanish at a distinguished point v in G).\n  We show further that any separable, nuclear, stable, O_2-absorbing C*-algebra is isomorphic to a crossed product of a C*-algebra D with the integers by an action alpha, where D is an inductive limit of C*-algebras of the form M_k(C"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0312286","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":"math/0312286","created_at":"2026-05-18T04:34:54.542372+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0312286v1","created_at":"2026-05-18T04:34:54.542372+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0312286","created_at":"2026-05-18T04:34:54.542372+00:00"},{"alias_kind":"pith_short_12","alias_value":"2NHOGGCRCQ5U","created_at":"2026-05-18T12:25:51.375804+00:00"},{"alias_kind":"pith_short_16","alias_value":"2NHOGGCRCQ5UL7HZ","created_at":"2026-05-18T12:25:51.375804+00:00"},{"alias_kind":"pith_short_8","alias_value":"2NHOGGCR","created_at":"2026-05-18T12:25:51.375804+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/2NHOGGCRCQ5UL7HZCD6M2M74CJ","json":"https://pith.science/pith/2NHOGGCRCQ5UL7HZCD6M2M74CJ.json","graph_json":"https://pith.science/api/pith-number/2NHOGGCRCQ5UL7HZCD6M2M74CJ/graph.json","events_json":"https://pith.science/api/pith-number/2NHOGGCRCQ5UL7HZCD6M2M74CJ/events.json","paper":"https://pith.science/paper/2NHOGGCR"},"agent_actions":{"view_html":"https://pith.science/pith/2NHOGGCRCQ5UL7HZCD6M2M74CJ","download_json":"https://pith.science/pith/2NHOGGCRCQ5UL7HZCD6M2M74CJ.json","view_paper":"https://pith.science/paper/2NHOGGCR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0312286&json=true","fetch_graph":"https://pith.science/api/pith-number/2NHOGGCRCQ5UL7HZCD6M2M74CJ/graph.json","fetch_events":"https://pith.science/api/pith-number/2NHOGGCRCQ5UL7HZCD6M2M74CJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2NHOGGCRCQ5UL7HZCD6M2M74CJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2NHOGGCRCQ5UL7HZCD6M2M74CJ/action/storage_attestation","attest_author":"https://pith.science/pith/2NHOGGCRCQ5UL7HZCD6M2M74CJ/action/author_attestation","sign_citation":"https://pith.science/pith/2NHOGGCRCQ5UL7HZCD6M2M74CJ/action/citation_signature","submit_replication":"https://pith.science/pith/2NHOGGCRCQ5UL7HZCD6M2M74CJ/action/replication_record"}},"created_at":"2026-05-18T04:34:54.542372+00:00","updated_at":"2026-05-18T04:34:54.542372+00:00"}