{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:KKLLZCQEI6QMQOX2WBBYHTNNII","short_pith_number":"pith:KKLLZCQE","schema_version":"1.0","canonical_sha256":"5296bc8a0447a0c83afab04383cdad4228212bd39b582b137281972921c7b6a6","source":{"kind":"arxiv","id":"1204.0167","version":1},"attestation_state":"computed","paper":{"title":"Koplienko Trace Formula","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Arup Chattopadhyay, Kalyan B. Sinha","submitted_at":"2012-04-01T05:16:25Z","abstract_excerpt":"Koplienko gave a trace formula for perturbations of self-adjoint operators by operators of Hilbert-Schmidt class $\\mathcal{B}_2(\\mathcal{H})$. Recently Gesztesy, Pushnitski and Simon gave an alternative proof of the trace formula when the operators involved are bounded. In this article, we give a still another proof and extend the formula for unbounded case by reducing the problem to a finite dimensional one as in the proof of Krein trace formula by Voiculescu, Sinha and Mohapatra."},"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":"1204.0167","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-04-01T05:16:25Z","cross_cats_sorted":[],"title_canon_sha256":"2a3b9f815b34bc2c6024875009b81aa1650824401fdfc0700991527e656e4fa9","abstract_canon_sha256":"2dedfeba6655bbc045d0e1dcd1b8437d113f4190bad0842d63b0e5e3c6ae79cf"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:58:50.173003Z","signature_b64":"uvF4lLZkC2E68DJeE/VgEAZKLoaXHWax0HMTzj7xzzgfMpXNV3frNYNrNUk7YTogYFcm/WQ1BVK8agOeOvrlAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5296bc8a0447a0c83afab04383cdad4228212bd39b582b137281972921c7b6a6","last_reissued_at":"2026-05-18T03:58:50.172295Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:58:50.172295Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Koplienko Trace Formula","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Arup Chattopadhyay, Kalyan B. Sinha","submitted_at":"2012-04-01T05:16:25Z","abstract_excerpt":"Koplienko gave a trace formula for perturbations of self-adjoint operators by operators of Hilbert-Schmidt class $\\mathcal{B}_2(\\mathcal{H})$. Recently Gesztesy, Pushnitski and Simon gave an alternative proof of the trace formula when the operators involved are bounded. In this article, we give a still another proof and extend the formula for unbounded case by reducing the problem to a finite dimensional one as in the proof of Krein trace formula by Voiculescu, Sinha and Mohapatra."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.0167","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"1204.0167","created_at":"2026-05-18T03:58:50.172412+00:00"},{"alias_kind":"arxiv_version","alias_value":"1204.0167v1","created_at":"2026-05-18T03:58:50.172412+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.0167","created_at":"2026-05-18T03:58:50.172412+00:00"},{"alias_kind":"pith_short_12","alias_value":"KKLLZCQEI6QM","created_at":"2026-05-18T12:27:11.947152+00:00"},{"alias_kind":"pith_short_16","alias_value":"KKLLZCQEI6QMQOX2","created_at":"2026-05-18T12:27:11.947152+00:00"},{"alias_kind":"pith_short_8","alias_value":"KKLLZCQE","created_at":"2026-05-18T12:27:11.947152+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/KKLLZCQEI6QMQOX2WBBYHTNNII","json":"https://pith.science/pith/KKLLZCQEI6QMQOX2WBBYHTNNII.json","graph_json":"https://pith.science/api/pith-number/KKLLZCQEI6QMQOX2WBBYHTNNII/graph.json","events_json":"https://pith.science/api/pith-number/KKLLZCQEI6QMQOX2WBBYHTNNII/events.json","paper":"https://pith.science/paper/KKLLZCQE"},"agent_actions":{"view_html":"https://pith.science/pith/KKLLZCQEI6QMQOX2WBBYHTNNII","download_json":"https://pith.science/pith/KKLLZCQEI6QMQOX2WBBYHTNNII.json","view_paper":"https://pith.science/paper/KKLLZCQE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1204.0167&json=true","fetch_graph":"https://pith.science/api/pith-number/KKLLZCQEI6QMQOX2WBBYHTNNII/graph.json","fetch_events":"https://pith.science/api/pith-number/KKLLZCQEI6QMQOX2WBBYHTNNII/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KKLLZCQEI6QMQOX2WBBYHTNNII/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KKLLZCQEI6QMQOX2WBBYHTNNII/action/storage_attestation","attest_author":"https://pith.science/pith/KKLLZCQEI6QMQOX2WBBYHTNNII/action/author_attestation","sign_citation":"https://pith.science/pith/KKLLZCQEI6QMQOX2WBBYHTNNII/action/citation_signature","submit_replication":"https://pith.science/pith/KKLLZCQEI6QMQOX2WBBYHTNNII/action/replication_record"}},"created_at":"2026-05-18T03:58:50.172412+00:00","updated_at":"2026-05-18T03:58:50.172412+00:00"}