{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:6G4KNSONYNRHU3NCU7CDQVLKFV","short_pith_number":"pith:6G4KNSON","schema_version":"1.0","canonical_sha256":"f1b8a6c9cdc3627a6da2a7c438556a2d43a4296397286ef334f97eb126917071","source":{"kind":"arxiv","id":"1210.8227","version":1},"attestation_state":"computed","paper":{"title":"Higher order spectral shift for contractions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SP"],"primary_cat":"math.FA","authors_text":"Anna Skripka, Denis Potapov, Fedor Sukochev","submitted_at":"2012-10-31T04:17:52Z","abstract_excerpt":"We derive strong estimates for Schatten norms of operator derivatives along paths of contractions and apply them to prove existence of higher order spectral shift functions for pairs of contractions."},"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":"1210.8227","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-10-31T04:17:52Z","cross_cats_sorted":["math.SP"],"title_canon_sha256":"d5a9ead48eb008ea8f08f3bc3b68521938d90942c5744443600729882078e3bd","abstract_canon_sha256":"098f19b3c031a55fc9e351ff4951e65e1ae7c27002f3049f720b24c2476744b5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:57:53.196796Z","signature_b64":"SyDzqVuHdpF3G9vd9rfchJwy6MPHtNSBdjsWMD61+Mjdodca6M7xK+LkNU0Le/8j6DLMUOuDrReb+MIIcZkLDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f1b8a6c9cdc3627a6da2a7c438556a2d43a4296397286ef334f97eb126917071","last_reissued_at":"2026-05-18T02:57:53.196260Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:57:53.196260Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Higher order spectral shift for contractions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SP"],"primary_cat":"math.FA","authors_text":"Anna Skripka, Denis Potapov, Fedor Sukochev","submitted_at":"2012-10-31T04:17:52Z","abstract_excerpt":"We derive strong estimates for Schatten norms of operator derivatives along paths of contractions and apply them to prove existence of higher order spectral shift functions for pairs of contractions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.8227","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":"1210.8227","created_at":"2026-05-18T02:57:53.196338+00:00"},{"alias_kind":"arxiv_version","alias_value":"1210.8227v1","created_at":"2026-05-18T02:57:53.196338+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.8227","created_at":"2026-05-18T02:57:53.196338+00:00"},{"alias_kind":"pith_short_12","alias_value":"6G4KNSONYNRH","created_at":"2026-05-18T12:26:56.085431+00:00"},{"alias_kind":"pith_short_16","alias_value":"6G4KNSONYNRHU3NC","created_at":"2026-05-18T12:26:56.085431+00:00"},{"alias_kind":"pith_short_8","alias_value":"6G4KNSON","created_at":"2026-05-18T12:26:56.085431+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/6G4KNSONYNRHU3NCU7CDQVLKFV","json":"https://pith.science/pith/6G4KNSONYNRHU3NCU7CDQVLKFV.json","graph_json":"https://pith.science/api/pith-number/6G4KNSONYNRHU3NCU7CDQVLKFV/graph.json","events_json":"https://pith.science/api/pith-number/6G4KNSONYNRHU3NCU7CDQVLKFV/events.json","paper":"https://pith.science/paper/6G4KNSON"},"agent_actions":{"view_html":"https://pith.science/pith/6G4KNSONYNRHU3NCU7CDQVLKFV","download_json":"https://pith.science/pith/6G4KNSONYNRHU3NCU7CDQVLKFV.json","view_paper":"https://pith.science/paper/6G4KNSON","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1210.8227&json=true","fetch_graph":"https://pith.science/api/pith-number/6G4KNSONYNRHU3NCU7CDQVLKFV/graph.json","fetch_events":"https://pith.science/api/pith-number/6G4KNSONYNRHU3NCU7CDQVLKFV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6G4KNSONYNRHU3NCU7CDQVLKFV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6G4KNSONYNRHU3NCU7CDQVLKFV/action/storage_attestation","attest_author":"https://pith.science/pith/6G4KNSONYNRHU3NCU7CDQVLKFV/action/author_attestation","sign_citation":"https://pith.science/pith/6G4KNSONYNRHU3NCU7CDQVLKFV/action/citation_signature","submit_replication":"https://pith.science/pith/6G4KNSONYNRHU3NCU7CDQVLKFV/action/replication_record"}},"created_at":"2026-05-18T02:57:53.196338+00:00","updated_at":"2026-05-18T02:57:53.196338+00:00"}