{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:5Z3RJF6XSKYEIY2VU3JYQI3MWI","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":"8e0ad358c8c47bdfd891b353b32d04c4c219a1082b70dcb2beb3bb0c4500586c","cross_cats_sorted":["math.CT","math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2014-10-02T08:41:02Z","title_canon_sha256":"961cf7e114688023112c2600c69fb5b68d6f493ffc993fb2536acfed0516fef6"},"schema_version":"1.0","source":{"id":"1410.0483","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.0483","created_at":"2026-05-17T23:47:49Z"},{"alias_kind":"arxiv_version","alias_value":"1410.0483v3","created_at":"2026-05-17T23:47:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.0483","created_at":"2026-05-17T23:47:49Z"},{"alias_kind":"pith_short_12","alias_value":"5Z3RJF6XSKYE","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_16","alias_value":"5Z3RJF6XSKYEIY2V","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_8","alias_value":"5Z3RJF6X","created_at":"2026-05-18T12:28:16Z"}],"graph_snapshots":[{"event_id":"sha256:59a534fab6b3dd55341aac597bc68d43ac4a0d29e1cb69b0780c86cf1991c74d","target":"graph","created_at":"2026-05-17T23:47:49Z","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 Cuntz semigroup of a C*-algebra is an important invariant in the structure and classification theory of C*-algebras. It captures more information than K-theory but is often more delicate to handle. We systematically study the lattice and category theoretic aspects of Cuntz semigroups.\n  Given a C*-algebra $A$, its (concrete) Cuntz semigroup $Cu(A)$ is an object in the category $Cu$ of (abstract) Cuntz semigroups, as introduced by Coward, Elliott and Ivanescu. To clarify the distinction between concrete and abstract Cuntz semigroups, we will call the latter $Cu$-semigroups.\n  We establish t","authors_text":"Francesc Perera, Hannes Thiel, Ramon Antoine","cross_cats":["math.CT","math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2014-10-02T08:41:02Z","title":"Tensor products and regularity properties of Cuntz semigroups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.0483","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:a2cbc7a3e8bc7b64b2e4da8e44ce3b11f48cbe8bedb2943b49b19689db32f864","target":"record","created_at":"2026-05-17T23:47:49Z","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":"8e0ad358c8c47bdfd891b353b32d04c4c219a1082b70dcb2beb3bb0c4500586c","cross_cats_sorted":["math.CT","math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2014-10-02T08:41:02Z","title_canon_sha256":"961cf7e114688023112c2600c69fb5b68d6f493ffc993fb2536acfed0516fef6"},"schema_version":"1.0","source":{"id":"1410.0483","kind":"arxiv","version":3}},"canonical_sha256":"ee771497d792b0446355a6d388236cb20f06b1f0ca2a5463cec8630c7fcb9a17","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ee771497d792b0446355a6d388236cb20f06b1f0ca2a5463cec8630c7fcb9a17","first_computed_at":"2026-05-17T23:47:49.523383Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:47:49.523383Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ypPFRoK707LYYWSrSOwZd6wBpnB5E7xYAj4e5DEPA3onTfBEMISxNvCDLNBDQ0/Q03H+XPaQnHxl6HHRmXNMDg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:47:49.523922Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.0483","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a2cbc7a3e8bc7b64b2e4da8e44ce3b11f48cbe8bedb2943b49b19689db32f864","sha256:59a534fab6b3dd55341aac597bc68d43ac4a0d29e1cb69b0780c86cf1991c74d"],"state_sha256":"b8f74561b0b63ff0b0d06366e0970c7d02c6e091ea58d1135f0f77b5e0c1fe7c"}