{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:KAJ3ISILJAJDRPPIPA6UB3KG5V","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":"16269bca9e24cc07eea751d2a3889a76a1d98064c9bec6091e37b061f8914405","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2010-12-23T14:29:20Z","title_canon_sha256":"7288d28d734a826e291242c7f7480be2437dac0e8f8de9636a7ec12ab0876c36"},"schema_version":"1.0","source":{"id":"1012.5216","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.5216","created_at":"2026-05-18T04:13:15Z"},{"alias_kind":"arxiv_version","alias_value":"1012.5216v3","created_at":"2026-05-18T04:13:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.5216","created_at":"2026-05-18T04:13:15Z"},{"alias_kind":"pith_short_12","alias_value":"KAJ3ISILJAJD","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"KAJ3ISILJAJDRPPI","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"KAJ3ISIL","created_at":"2026-05-18T12:26:09Z"}],"graph_snapshots":[{"event_id":"sha256:9c49327bdcd2783b85c0e45fb385959b6ad877346d2dd280b7b559f9acacd986","target":"graph","created_at":"2026-05-18T04:13:15Z","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":"We define a Riesz type interpolation property for the Cuntz semigroup of a $C^*$-algebra and prove it is satisfied by the Cuntz semigroup of every $C^*$-algebra with the ideal property. Related to this, we obtain two characterizations of the ideal property in terms of the Cuntz semigroup of the $C^*$-algebra. Some additional characterizations are proved in the special case of the stable, purely infinite $C^*$-algebras, and two of them are expressed in language of the Cuntz semigroup. We introduce a notion of comparison of positive elements for every unital $C^*$-algebra that has (normalized) q","authors_text":"Cornel Pasnicu, Francesc Perera","cross_cats":["math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2010-12-23T14:29:20Z","title":"The Cuntz semigroup, a Riesz type interpolation property, comparison and the ideal property"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.5216","kind":"arxiv","version":3},"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":"sha256:56c46e780028f7c9ea863738e67d6dae953983d09e622993d2f4a3547051d74b","target":"record","created_at":"2026-05-18T04:13:15Z","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":"16269bca9e24cc07eea751d2a3889a76a1d98064c9bec6091e37b061f8914405","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2010-12-23T14:29:20Z","title_canon_sha256":"7288d28d734a826e291242c7f7480be2437dac0e8f8de9636a7ec12ab0876c36"},"schema_version":"1.0","source":{"id":"1012.5216","kind":"arxiv","version":3}},"canonical_sha256":"5013b4490b481238bde8783d40ed46ed65a74fab5d8ddfdb6b5b8e51c11db467","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5013b4490b481238bde8783d40ed46ed65a74fab5d8ddfdb6b5b8e51c11db467","first_computed_at":"2026-05-18T04:13:15.971132Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:13:15.971132Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ru2QoECCYtl9Vvdk5/E0PgucTUCpPjzmYdtlSxEXifuATyqVI8dKpGhRBpU/eurrluFrGsQUaei3WSQzZOipBA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:13:15.971642Z","signed_message":"canonical_sha256_bytes"},"source_id":"1012.5216","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:56c46e780028f7c9ea863738e67d6dae953983d09e622993d2f4a3547051d74b","sha256:9c49327bdcd2783b85c0e45fb385959b6ad877346d2dd280b7b559f9acacd986"],"state_sha256":"9f196f74cf8d8fe7f62e5f39ba3fad3e91520534a0900df9ed4dfd2d78f5a4df"}