{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:H5NDEPJ3IESMBOE5YBNZBFBINW","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":"14c128b62a542e8a8f20b59d0e6359b1d2040ffd46a79bd67e3e7e9b3b9d2298","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2024-11-25T14:28:47Z","title_canon_sha256":"83d03a31e17d73d42897cb8d41a10881e1ccf241d3f77e9b3adeb781b2d57a04"},"schema_version":"1.0","source":{"id":"2411.16426","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.16426","created_at":"2026-07-05T09:42:33Z"},{"alias_kind":"arxiv_version","alias_value":"2411.16426v2","created_at":"2026-07-05T09:42:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.16426","created_at":"2026-07-05T09:42:33Z"},{"alias_kind":"pith_short_12","alias_value":"H5NDEPJ3IESM","created_at":"2026-07-05T09:42:33Z"},{"alias_kind":"pith_short_16","alias_value":"H5NDEPJ3IESMBOE5","created_at":"2026-07-05T09:42:33Z"},{"alias_kind":"pith_short_8","alias_value":"H5NDEPJ3","created_at":"2026-07-05T09:42:33Z"}],"graph_snapshots":[{"event_id":"sha256:0ce443f49f9863783cf07955fab90b562e5b008ce3663bb32570f14f76bcc1ba","target":"graph","created_at":"2026-07-05T09:42:33Z","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/2411.16426/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we extend the class of admissible functions for the trace formula of the second order in the self-adjoint, unitary, and contraction cases for a perturbation in the Hilbert-Schmidt class $\\mathcal{S}^2(\\mathcal{H})$ by assuming a certain factorization of the divided difference $f^{[2]}$. This class is the natural one to ensure that the second order Taylor remainder is a trace class operator. It encompasses all the classes of functions for which the trace formula was previously known. Secondly, for a Schatten $\\mathcal{S}^p$-perturbation, $1<p<\\infty$, we prove general modified tr","authors_text":"Arup Chattopadhyay, Chandan Pradhan, Cl\\'ement Coine, Saikat Giri","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2024-11-25T14:28:47Z","title":"Trace formulas for $\\mathcal{S}^p$-perturbations and extension of Koplienko-Neidhardt trace formulas"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.16426","kind":"arxiv","version":2},"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":"sha256:71f2c5937f6ae7ea1a6b7dff99d986a21525c4effe0e875c49a06c04606913cb","target":"record","created_at":"2026-07-05T09:42:33Z","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":"14c128b62a542e8a8f20b59d0e6359b1d2040ffd46a79bd67e3e7e9b3b9d2298","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2024-11-25T14:28:47Z","title_canon_sha256":"83d03a31e17d73d42897cb8d41a10881e1ccf241d3f77e9b3adeb781b2d57a04"},"schema_version":"1.0","source":{"id":"2411.16426","kind":"arxiv","version":2}},"canonical_sha256":"3f5a323d3b4124c0b89dc05b9094286d988887756ec3609f8c92ef705efe6a32","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3f5a323d3b4124c0b89dc05b9094286d988887756ec3609f8c92ef705efe6a32","first_computed_at":"2026-07-05T09:42:33.490178Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:42:33.490178Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mwYYfOop8oWuYa+y+UBUYvN95I6fzHYo20Mhkd00WrTKdDnWtYTzCy6vmP4iTaCW0/yRGQSAJAnZQPaJRI/sCg==","signature_status":"signed_v1","signed_at":"2026-07-05T09:42:33.490689Z","signed_message":"canonical_sha256_bytes"},"source_id":"2411.16426","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:71f2c5937f6ae7ea1a6b7dff99d986a21525c4effe0e875c49a06c04606913cb","sha256:0ce443f49f9863783cf07955fab90b562e5b008ce3663bb32570f14f76bcc1ba"],"state_sha256":"ba9b89e6d2f7173312165858dcaad65c4638eb62de6ffaad2eddbb2135cf1d26"}