{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:LZTL5T4NLXUX7RFENBQB2S5DHX","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":"548c4e0743e7687d4ca4ba457f279c233a5c042ee8e8e2f25e1dba7904884160","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.OA","submitted_at":"2014-03-19T07:27:58Z","title_canon_sha256":"4f95abbaac596823386eaa1154a83b06f87a9cb682231fd6f7e02e8cb3863b2a"},"schema_version":"1.0","source":{"id":"1403.4718","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.4718","created_at":"2026-05-18T02:56:04Z"},{"alias_kind":"arxiv_version","alias_value":"1403.4718v1","created_at":"2026-05-18T02:56:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.4718","created_at":"2026-05-18T02:56:04Z"},{"alias_kind":"pith_short_12","alias_value":"LZTL5T4NLXUX","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_16","alias_value":"LZTL5T4NLXUX7RFE","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_8","alias_value":"LZTL5T4N","created_at":"2026-05-18T12:28:38Z"}],"graph_snapshots":[{"event_id":"sha256:4bd4822951547db6cc0cf172f7e1b771169722e55d43e62d00325ffdcac423a5","target":"graph","created_at":"2026-05-18T02:56:04Z","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 extend Dixmier's construction of singular traces (see \\cite{Dixmier}) to arbitrary fully symmetric operator ideals. In fact, we show that the set of Dixmier traces is weak$^*$ dense in the set of all fully symmetric traces (that is, those traces which respect Hardy-Littlewood submajorization). Our results complement and extend earlier work of Wodzicki \\cite{Wodzicki}.","authors_text":"D. Zanin, F. Sukochev","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.OA","submitted_at":"2014-03-19T07:27:58Z","title":"Dixmier traces are weak$^*$ dense in the set of all fully symmetric traces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.4718","kind":"arxiv","version":1},"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:f9d4381aab11b8a7e77054cb85a01c235a8863bd2adc19bc9cdeb82026d9c66e","target":"record","created_at":"2026-05-18T02:56:04Z","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":"548c4e0743e7687d4ca4ba457f279c233a5c042ee8e8e2f25e1dba7904884160","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.OA","submitted_at":"2014-03-19T07:27:58Z","title_canon_sha256":"4f95abbaac596823386eaa1154a83b06f87a9cb682231fd6f7e02e8cb3863b2a"},"schema_version":"1.0","source":{"id":"1403.4718","kind":"arxiv","version":1}},"canonical_sha256":"5e66becf8d5de97fc4a468601d4ba33de5f8c59881c165cf9768d7532d3abeb1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5e66becf8d5de97fc4a468601d4ba33de5f8c59881c165cf9768d7532d3abeb1","first_computed_at":"2026-05-18T02:56:04.610621Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:56:04.610621Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jOTzItcwbVmCOgD35wpGgNttzcxWCmOMVhSbh/s2l3LLXSTk0I3Hs1yojxH3s/dDFnioJrCV4KtzWX1JidcbDg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:56:04.611028Z","signed_message":"canonical_sha256_bytes"},"source_id":"1403.4718","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f9d4381aab11b8a7e77054cb85a01c235a8863bd2adc19bc9cdeb82026d9c66e","sha256:4bd4822951547db6cc0cf172f7e1b771169722e55d43e62d00325ffdcac423a5"],"state_sha256":"57479946a6ae7c077bf271dd77e4bba44ec2f1fe3245412af8e6cde6e0e4ab40"}