{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:ZLLXLKAN53M2TVYWAVQCPTFX65","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":"ab2ea24b016fbbba7303d07ea54aa715c2912efb9b285e267f92ba967b90a9ea","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2011-04-28T16:31:57Z","title_canon_sha256":"f8aca5a70fa8ccce0c50f372090c810c284b0f43354763f65acc5a9de86dd256"},"schema_version":"1.0","source":{"id":"1104.5439","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.5439","created_at":"2026-05-18T04:23:21Z"},{"alias_kind":"arxiv_version","alias_value":"1104.5439v1","created_at":"2026-05-18T04:23:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.5439","created_at":"2026-05-18T04:23:21Z"},{"alias_kind":"pith_short_12","alias_value":"ZLLXLKAN53M2","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"ZLLXLKAN53M2TVYW","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"ZLLXLKAN","created_at":"2026-05-18T12:26:47Z"}],"graph_snapshots":[{"event_id":"sha256:812229399157870dd14fb8584d4cb752759d7073e8263acb841e8fa20ccfe9dc","target":"graph","created_at":"2026-05-18T04:23:21Z","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"},"paper":{"abstract_excerpt":"An operator $H=H_{0}+V$ where $H_{0}=i^{-N} \\partial^{N}$ ($N$ is arbitrary) and $V$ is a differential operator of order $N-1$ with coefficients decaying sufficiently rapidly at infinity is considered in the space $L^2(\\Bbb R)$. The goal of the paper is to find an expression for the trace of the difference of the resolvents $(H-z)^{-1}$ and $(H_{0}-z)^{-1}$ in terms of the Wronskian of appropriate solutions to the differential equation $Hu=zu$. This also leads to a representation for the perturbation determinant of the pair $H_{0}, H$.","authors_text":"D. R. Yafaev, J. Ostensson","cross_cats":["math.CA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2011-04-28T16:31:57Z","title":"A trace formula for differential operators of arbitrary order"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.5439","kind":"arxiv","version":1},"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:dfd1ecafa4cff5d1810589ca516f095523401a88c9189ca12312371c8d5a88d6","target":"record","created_at":"2026-05-18T04:23:21Z","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":"ab2ea24b016fbbba7303d07ea54aa715c2912efb9b285e267f92ba967b90a9ea","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2011-04-28T16:31:57Z","title_canon_sha256":"f8aca5a70fa8ccce0c50f372090c810c284b0f43354763f65acc5a9de86dd256"},"schema_version":"1.0","source":{"id":"1104.5439","kind":"arxiv","version":1}},"canonical_sha256":"cad775a80deed9a9d716056027ccb7f76bebe03e965928fe7f0cb0191649e16c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cad775a80deed9a9d716056027ccb7f76bebe03e965928fe7f0cb0191649e16c","first_computed_at":"2026-05-18T04:23:21.467119Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:23:21.467119Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vIPLgKzmqw3CKgAPyorq4iLJWSR3jsbn5NOkg1fW0QQGnzqlwHbqS9NKflISFdcm23lQedbZkFjLtrjLTYR3Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:23:21.467724Z","signed_message":"canonical_sha256_bytes"},"source_id":"1104.5439","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dfd1ecafa4cff5d1810589ca516f095523401a88c9189ca12312371c8d5a88d6","sha256:812229399157870dd14fb8584d4cb752759d7073e8263acb841e8fa20ccfe9dc"],"state_sha256":"169762a1ef75555eb5c7b6045dbfb2f5eaf26193739299f9d4666fec79af2d17"}