{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:VSZVKDFJYS346JEYPUNBEPLGAF","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"aa4478e64d47265bc53bea3f5a89e67b67711d28713364a41ca7a5ec7cdf9eea","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2009-03-17T07:44:56Z","title_canon_sha256":"7f1911041e09798fdb273f4b891cf603b47b57a47aba0fbd01ac9ab68fc70600"},"schema_version":"1.0","source":{"id":"0903.2917","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0903.2917","created_at":"2026-05-18T03:35:52Z"},{"alias_kind":"arxiv_version","alias_value":"0903.2917v4","created_at":"2026-05-18T03:35:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0903.2917","created_at":"2026-05-18T03:35:52Z"},{"alias_kind":"pith_short_12","alias_value":"VSZVKDFJYS34","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"VSZVKDFJYS346JEY","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"VSZVKDFJ","created_at":"2026-05-18T12:26:02Z"}],"graph_snapshots":[{"event_id":"sha256:80186730d09f9f58073751bb5d45799c2ee37609d6197d5a9104da6473685d21","target":"graph","created_at":"2026-05-18T03:35:52Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"The Corona Factorization Property, originally invented to study extensions of C*-algebras, conveys essential information about the intrinsic structure of the C*-algebras. We show that the Corona Factorization Property of a \\sigma-unital C*-algebra is completely captured by its Cuntz semigroup (of equivalence classes of positive elements in the stabilization of A). The corresponding condition in the Cuntz semigroup is a very weak comparability property termed the Corona Factorization Property for semigroups. Using this result one can for example show that all unital C*-algebras with finite deco","authors_text":"Eduard Ortega, Francesc Perera, Mikael Rordam","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2009-03-17T07:44:56Z","title":"The Corona Factorization property, Stability, and the Cuntz semigroup of a C*-algebra"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0903.2917","kind":"arxiv","version":4},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:48a02b934b8223feb45ac27b5d11a2f4fc3e39342837cfa4edc1174c16c43661","target":"record","created_at":"2026-05-18T03:35:52Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"aa4478e64d47265bc53bea3f5a89e67b67711d28713364a41ca7a5ec7cdf9eea","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2009-03-17T07:44:56Z","title_canon_sha256":"7f1911041e09798fdb273f4b891cf603b47b57a47aba0fbd01ac9ab68fc70600"},"schema_version":"1.0","source":{"id":"0903.2917","kind":"arxiv","version":4}},"canonical_sha256":"acb3550ca9c4b7cf24987d1a123d66015035073162127487e584e2028978501a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"acb3550ca9c4b7cf24987d1a123d66015035073162127487e584e2028978501a","first_computed_at":"2026-05-18T03:35:52.184847Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:35:52.184847Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"n6ggEP8g0dkVvqg9eQFaBsZxAmX0BPBE5ZmJxjav5Ze/vqjeF5Kd6IMrA9zRI0WlfwQu2NQtCYnUr7MSnRWCCA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:35:52.185897Z","signed_message":"canonical_sha256_bytes"},"source_id":"0903.2917","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:48a02b934b8223feb45ac27b5d11a2f4fc3e39342837cfa4edc1174c16c43661","sha256:80186730d09f9f58073751bb5d45799c2ee37609d6197d5a9104da6473685d21"],"state_sha256":"1be94fe8d53bf65d75db72cdf102fb8b34911957d48c2e7db1bf30ea39fb7e62"}