{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:5LEGCVKKLKIQUVRDYLGUO2Q3SS","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":"fbb2f5527e25dd05fc18c8f1a819e7cb2560beba3f8f060c96533ad8637da09b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2023-03-23T14:30:13Z","title_canon_sha256":"e370a433abec56bcae315b3b0da69e093dd1e78bb3c4aa3bad66e3e2179131a3"},"schema_version":"1.0","source":{"id":"2303.13298","kind":"arxiv","version":6}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2303.13298","created_at":"2026-05-20T00:01:31Z"},{"alias_kind":"arxiv_version","alias_value":"2303.13298v6","created_at":"2026-05-20T00:01:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2303.13298","created_at":"2026-05-20T00:01:31Z"},{"alias_kind":"pith_short_12","alias_value":"5LEGCVKKLKIQ","created_at":"2026-05-20T00:01:31Z"},{"alias_kind":"pith_short_16","alias_value":"5LEGCVKKLKIQUVRD","created_at":"2026-05-20T00:01:31Z"},{"alias_kind":"pith_short_8","alias_value":"5LEGCVKK","created_at":"2026-05-20T00:01:31Z"}],"graph_snapshots":[{"event_id":"sha256:6de55275bfd9255f6a61c6e06e2e4e17f026d1323a92157855866dda880dd56a","target":"graph","created_at":"2026-05-20T00:01:31Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2303.13298/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The paper establishes the Krein and Koplienko trace formulas for multivariable operator functions on symmetrically normed ideals of bounded operators. Results are proved for self-adjoint and maximal dissipative operators. They cover both ideals with normal and singular traces. The admissible function classes considered in the trace formulas include both analytic and non-analytic scalar functions. Results are illustrated with examples.","authors_text":"Alexandr Usachev, Arup Chattopadhyay, Chandan Pradhan, Saikat Giri","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2023-03-23T14:30:13Z","title":"Trace formulas in higher dimensions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2303.13298","kind":"arxiv","version":6},"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":"sha256:6236b89e961f69c9d7b5c0a95f88d1eef116e27b01830ee97e9d831bfebc98a4","target":"record","created_at":"2026-05-20T00:01:31Z","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":"fbb2f5527e25dd05fc18c8f1a819e7cb2560beba3f8f060c96533ad8637da09b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2023-03-23T14:30:13Z","title_canon_sha256":"e370a433abec56bcae315b3b0da69e093dd1e78bb3c4aa3bad66e3e2179131a3"},"schema_version":"1.0","source":{"id":"2303.13298","kind":"arxiv","version":6}},"canonical_sha256":"eac861554a5a910a5623c2cd476a1b949d5a626f43a0beb41eb1febd8772b250","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eac861554a5a910a5623c2cd476a1b949d5a626f43a0beb41eb1febd8772b250","first_computed_at":"2026-05-20T00:01:31.869215Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T00:01:31.869215Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pP7HsITLujqukMzdBXJjM/51IF2NEL483FPK9GCvpUM27PTUnghSsMH7DXDUtoa9zmwSulhwmgy1isckSzf/CQ==","signature_status":"signed_v1","signed_at":"2026-05-20T00:01:31.870013Z","signed_message":"canonical_sha256_bytes"},"source_id":"2303.13298","source_kind":"arxiv","source_version":6}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6236b89e961f69c9d7b5c0a95f88d1eef116e27b01830ee97e9d831bfebc98a4","sha256:6de55275bfd9255f6a61c6e06e2e4e17f026d1323a92157855866dda880dd56a"],"state_sha256":"c29fac5e7d37cfd73c97396f770788ca4af0c761dcefe0b752c516ead2eb277d"}