{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:Z7P424BZ3SYVRVGRNHL6IBSC5Q","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":"8dff1053e0a45286b98ad435b455cbbfc1a65e50cb2c5954191c35c7b13193ce","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2019-08-15T02:11:14Z","title_canon_sha256":"d297c9120cb565b1004650bbc072ac203f9d3e90ff47ac07b08c448c853dbdc4"},"schema_version":"1.0","source":{"id":"1908.05392","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.05392","created_at":"2026-07-04T23:56:51Z"},{"alias_kind":"arxiv_version","alias_value":"1908.05392v1","created_at":"2026-07-04T23:56:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.05392","created_at":"2026-07-04T23:56:51Z"},{"alias_kind":"pith_short_12","alias_value":"Z7P424BZ3SYV","created_at":"2026-07-04T23:56:51Z"},{"alias_kind":"pith_short_16","alias_value":"Z7P424BZ3SYVRVGR","created_at":"2026-07-04T23:56:51Z"},{"alias_kind":"pith_short_8","alias_value":"Z7P424BZ","created_at":"2026-07-04T23:56:51Z"}],"graph_snapshots":[{"event_id":"sha256:0f0d99eb2530e48b22e8ab5ab84016853ccdd62a6cd6f4408434535c3bd4615b","target":"graph","created_at":"2026-07-04T23:56:51Z","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/1908.05392/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We derive explicit Krein resolvent identities for generally singular Sturm-Liouville operators in terms of boundary condition bases and the Lagrange bracket. As an application of the resolvent identities obtained, we compute the trace of the resolvent difference of a pair of self-adjoint realizations of the Bessel expression $-d^2/dx^2+(\\nu^2-(1/4))x^{-2}$ on $(0,\\infty)$ for values of the parameter $\\nu\\in[0,1)$ and use the resulting trace formula to explicitly determine the spectral shift function for the pair.","authors_text":"Don Rung, Gregory Michajlyszyn, Justin Hanbin Kim, Roger Nichols, S. Blake Allan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2019-08-15T02:11:14Z","title":"Explicit Krein Resolvent Identities for Singular Sturm-Liouville Operators with Applications to Bessel Operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.05392","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":"sha256:63d972669d02868030e469ac1570a6e12fc5746c1d6cfd90ac8bc4bd0af86498","target":"record","created_at":"2026-07-04T23:56:51Z","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":"8dff1053e0a45286b98ad435b455cbbfc1a65e50cb2c5954191c35c7b13193ce","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2019-08-15T02:11:14Z","title_canon_sha256":"d297c9120cb565b1004650bbc072ac203f9d3e90ff47ac07b08c448c853dbdc4"},"schema_version":"1.0","source":{"id":"1908.05392","kind":"arxiv","version":1}},"canonical_sha256":"cfdfcd7039dcb158d4d169d7e40642ec1c47671be3e2d0b5a301a4bf611acf18","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cfdfcd7039dcb158d4d169d7e40642ec1c47671be3e2d0b5a301a4bf611acf18","first_computed_at":"2026-07-04T23:56:51.048478Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T23:56:51.048478Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ykbn+HrJGSfRNwyVVnQtq5zErSQlOSNhCr0mELgdgvcmdNEUj2PGQJcRgnkFiYy31EPmrG733tZV2ieWrFFgDg==","signature_status":"signed_v1","signed_at":"2026-07-04T23:56:51.048862Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.05392","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:63d972669d02868030e469ac1570a6e12fc5746c1d6cfd90ac8bc4bd0af86498","sha256:0f0d99eb2530e48b22e8ab5ab84016853ccdd62a6cd6f4408434535c3bd4615b"],"state_sha256":"c86e7b7bc043ad45a3a2a14d3a72985e573c93dede26b61aaba90d62f5633dd7"}