{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:H5NDEPJ3IESMBOE5YBNZBFBINW","short_pith_number":"pith:H5NDEPJ3","schema_version":"1.0","canonical_sha256":"3f5a323d3b4124c0b89dc05b9094286d988887756ec3609f8c92ef705efe6a32","source":{"kind":"arxiv","id":"2411.16426","version":2},"attestation_state":"computed","paper":{"title":"Trace formulas for $\\mathcal{S}^p$-perturbations and extension of Koplienko-Neidhardt trace formulas","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Arup Chattopadhyay, Chandan Pradhan, Cl\\'ement Coine, Saikat Giri","submitted_at":"2024-11-25T14:28:47Z","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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2411.16426","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2024-11-25T14:28:47Z","cross_cats_sorted":[],"title_canon_sha256":"83d03a31e17d73d42897cb8d41a10881e1ccf241d3f77e9b3adeb781b2d57a04","abstract_canon_sha256":"14c128b62a542e8a8f20b59d0e6359b1d2040ffd46a79bd67e3e7e9b3b9d2298"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:42:33.490689Z","signature_b64":"mwYYfOop8oWuYa+y+UBUYvN95I6fzHYo20Mhkd00WrTKdDnWtYTzCy6vmP4iTaCW0/yRGQSAJAnZQPaJRI/sCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3f5a323d3b4124c0b89dc05b9094286d988887756ec3609f8c92ef705efe6a32","last_reissued_at":"2026-07-05T09:42:33.490178Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:42:33.490178Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Trace formulas for $\\mathcal{S}^p$-perturbations and extension of Koplienko-Neidhardt trace formulas","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Arup Chattopadhyay, Chandan Pradhan, Cl\\'ement Coine, Saikat Giri","submitted_at":"2024-11-25T14:28:47Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.16426","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2411.16426/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2411.16426","created_at":"2026-07-05T09:42:33.490242+00:00"},{"alias_kind":"arxiv_version","alias_value":"2411.16426v2","created_at":"2026-07-05T09:42:33.490242+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.16426","created_at":"2026-07-05T09:42:33.490242+00:00"},{"alias_kind":"pith_short_12","alias_value":"H5NDEPJ3IESM","created_at":"2026-07-05T09:42:33.490242+00:00"},{"alias_kind":"pith_short_16","alias_value":"H5NDEPJ3IESMBOE5","created_at":"2026-07-05T09:42:33.490242+00:00"},{"alias_kind":"pith_short_8","alias_value":"H5NDEPJ3","created_at":"2026-07-05T09:42:33.490242+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/H5NDEPJ3IESMBOE5YBNZBFBINW","json":"https://pith.science/pith/H5NDEPJ3IESMBOE5YBNZBFBINW.json","graph_json":"https://pith.science/api/pith-number/H5NDEPJ3IESMBOE5YBNZBFBINW/graph.json","events_json":"https://pith.science/api/pith-number/H5NDEPJ3IESMBOE5YBNZBFBINW/events.json","paper":"https://pith.science/paper/H5NDEPJ3"},"agent_actions":{"view_html":"https://pith.science/pith/H5NDEPJ3IESMBOE5YBNZBFBINW","download_json":"https://pith.science/pith/H5NDEPJ3IESMBOE5YBNZBFBINW.json","view_paper":"https://pith.science/paper/H5NDEPJ3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2411.16426&json=true","fetch_graph":"https://pith.science/api/pith-number/H5NDEPJ3IESMBOE5YBNZBFBINW/graph.json","fetch_events":"https://pith.science/api/pith-number/H5NDEPJ3IESMBOE5YBNZBFBINW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/H5NDEPJ3IESMBOE5YBNZBFBINW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/H5NDEPJ3IESMBOE5YBNZBFBINW/action/storage_attestation","attest_author":"https://pith.science/pith/H5NDEPJ3IESMBOE5YBNZBFBINW/action/author_attestation","sign_citation":"https://pith.science/pith/H5NDEPJ3IESMBOE5YBNZBFBINW/action/citation_signature","submit_replication":"https://pith.science/pith/H5NDEPJ3IESMBOE5YBNZBFBINW/action/replication_record"}},"created_at":"2026-07-05T09:42:33.490242+00:00","updated_at":"2026-07-05T09:42:33.490242+00:00"}