{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:JLOLGMFVMDGQKB3PCU67JVCO7L","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":"ea6b1713adb05c7fc483ad120d9a3451b27e74099ff9cb68203d7c48ac15b582","cross_cats_sorted":["math.AP","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-12-26T19:52:35Z","title_canon_sha256":"8680a7d1378d7eb6386015ea7e38bccefc66f1609f7b936973c04f6ee6d06f8b"},"schema_version":"1.0","source":{"id":"1812.10513","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.10513","created_at":"2026-05-17T23:57:20Z"},{"alias_kind":"arxiv_version","alias_value":"1812.10513v1","created_at":"2026-05-17T23:57:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.10513","created_at":"2026-05-17T23:57:20Z"},{"alias_kind":"pith_short_12","alias_value":"JLOLGMFVMDGQ","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_16","alias_value":"JLOLGMFVMDGQKB3P","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_8","alias_value":"JLOLGMFV","created_at":"2026-05-18T12:32:31Z"}],"graph_snapshots":[{"event_id":"sha256:f1a44d286d769e1f254511815b9543c5a16e3f74d5f8b1cee55796688795dd58","target":"graph","created_at":"2026-05-17T23:57:20Z","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":"The representations of the kernels of the transmutation operator and of its inverse relating the one-dimensional Schr\\\"odinger operator with the second derivative are obtained in terms of the eigenfunctions of a corresponding Sturm-Liouville problem. Since both series converge slowly and in general only in a certain distributional sense we find a way to improve these expansions and make them convergent uniformly and absolutely by adding and subtracting corresponding terms. A numerical illustration of the obtained results is given.","authors_text":"Kira V. Khmelnytskaya, Sergii M. Torba, Vladislav V. Kravchenko","cross_cats":["math.AP","math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-12-26T19:52:35Z","title":"A representation of the transmutation kernels for the Schr\\\"odinger operator in terms of eigenfunctions and applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.10513","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:ed163b965e114771b693c27697612636dd332a3d7e27afae28f9676d7680412e","target":"record","created_at":"2026-05-17T23:57:20Z","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":"ea6b1713adb05c7fc483ad120d9a3451b27e74099ff9cb68203d7c48ac15b582","cross_cats_sorted":["math.AP","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-12-26T19:52:35Z","title_canon_sha256":"8680a7d1378d7eb6386015ea7e38bccefc66f1609f7b936973c04f6ee6d06f8b"},"schema_version":"1.0","source":{"id":"1812.10513","kind":"arxiv","version":1}},"canonical_sha256":"4adcb330b560cd05076f153df4d44efacb6848bb953bc1b758620ca460c7d4ea","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4adcb330b560cd05076f153df4d44efacb6848bb953bc1b758620ca460c7d4ea","first_computed_at":"2026-05-17T23:57:20.852281Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:57:20.852281Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OlKXhjw1N0YML6yKNHkbw15zZClrlASvpfULsG5636U68WaKrfNYvNRsqi+ekrsdFjkOL/lLsXnQbFEhxCfsDw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:57:20.853056Z","signed_message":"canonical_sha256_bytes"},"source_id":"1812.10513","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ed163b965e114771b693c27697612636dd332a3d7e27afae28f9676d7680412e","sha256:f1a44d286d769e1f254511815b9543c5a16e3f74d5f8b1cee55796688795dd58"],"state_sha256":"757d70aff15ee9d5efbad8509ad07d50c9d3132d795e965de1cc424b770602ab"}