{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:HJD6PZ4HYCNKSWBTHRF3W4YG5X","short_pith_number":"pith:HJD6PZ4H","canonical_record":{"source":{"id":"1412.5237","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-12-17T01:23:45Z","cross_cats_sorted":["math.NA"],"title_canon_sha256":"bb4847bc99d2a7580bbd2eaf9a03e0dd9fac445d746b78616301947e3f3262f2","abstract_canon_sha256":"de8b5f24b50febc76554a965c6c76bfb45ea7b52cf4836f09b1d09ba075993c4"},"schema_version":"1.0"},"canonical_sha256":"3a47e7e787c09aa958333c4bbb7306edfc6358191c8b4050d6796a5a7aa3bc2c","source":{"kind":"arxiv","id":"1412.5237","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.5237","created_at":"2026-05-18T01:27:05Z"},{"alias_kind":"arxiv_version","alias_value":"1412.5237v1","created_at":"2026-05-18T01:27:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.5237","created_at":"2026-05-18T01:27:05Z"},{"alias_kind":"pith_short_12","alias_value":"HJD6PZ4HYCNK","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_16","alias_value":"HJD6PZ4HYCNKSWBT","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_8","alias_value":"HJD6PZ4H","created_at":"2026-05-18T12:28:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:HJD6PZ4HYCNKSWBTHRF3W4YG5X","target":"record","payload":{"canonical_record":{"source":{"id":"1412.5237","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-12-17T01:23:45Z","cross_cats_sorted":["math.NA"],"title_canon_sha256":"bb4847bc99d2a7580bbd2eaf9a03e0dd9fac445d746b78616301947e3f3262f2","abstract_canon_sha256":"de8b5f24b50febc76554a965c6c76bfb45ea7b52cf4836f09b1d09ba075993c4"},"schema_version":"1.0"},"canonical_sha256":"3a47e7e787c09aa958333c4bbb7306edfc6358191c8b4050d6796a5a7aa3bc2c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:27:05.472013Z","signature_b64":"VBqyXmIfepm2LoxbP7mi8enMkF2JPkEt+yHrgOi/NzW4lPI8vSx6gqVBLx2OVCU7h9OuR3hQnx0VKiw9BGafCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3a47e7e787c09aa958333c4bbb7306edfc6358191c8b4050d6796a5a7aa3bc2c","last_reissued_at":"2026-05-18T01:27:05.471335Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:27:05.471335Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1412.5237","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:27:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OYVZbGq0hmLehp7uQ6omyQ3I4PIlGUsYf6tFi47et5qwEX++tXR0H4Bz+pMsxWc4oXSvp6xoOByXMWy1saHIAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T07:51:26.356657Z"},"content_sha256":"1084ce94764e6aaae29dd8129189e29bb0961c0e8dd1a3a8f852af3929efbdb2","schema_version":"1.0","event_id":"sha256:1084ce94764e6aaae29dd8129189e29bb0961c0e8dd1a3a8f852af3929efbdb2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:HJD6PZ4HYCNKSWBTHRF3W4YG5X","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Liouville transformation, analytic approximation of transmutation operators and solution of spectral problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NA"],"primary_cat":"math.CA","authors_text":"Samy Morelos, Sergii M. Torba, Vladislav V. Kravchenko","submitted_at":"2014-12-17T01:23:45Z","abstract_excerpt":"A method for solving spectral problems for the Sturm-Liouville equation $(pv^{\\prime})^{\\prime}-qv+\\lambda rv=0$ based on the approximation of the Delsarte transmutation operators combined with the Liouville transformation is presented. The problem of numerical approximation of solutions and of eigendata is reduced to approximation of a pair of functions depending on the coefficients $p$, $q$ and $r$ by a finite linear combination of certain specially constructed functions related to generalized wave polynomials introduced in arXiv:1208.5984, arXiv:1208.6166. The method allows one to compute b"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.5237","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:27:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"g0KSKABDa6Ghzr0W6NFZ12O7npeUvzsXe/eQyBOhv4kH7rhdhKqj62I/C3AMMoFzkT5p4WvUyLVjhYala0rNAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T07:51:26.357007Z"},"content_sha256":"58c9401bb49cab7f7b227ffb938da8d7346c7d3f83b1d92793e8267122a2bb16","schema_version":"1.0","event_id":"sha256:58c9401bb49cab7f7b227ffb938da8d7346c7d3f83b1d92793e8267122a2bb16"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HJD6PZ4HYCNKSWBTHRF3W4YG5X/bundle.json","state_url":"https://pith.science/pith/HJD6PZ4HYCNKSWBTHRF3W4YG5X/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HJD6PZ4HYCNKSWBTHRF3W4YG5X/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-23T07:51:26Z","links":{"resolver":"https://pith.science/pith/HJD6PZ4HYCNKSWBTHRF3W4YG5X","bundle":"https://pith.science/pith/HJD6PZ4HYCNKSWBTHRF3W4YG5X/bundle.json","state":"https://pith.science/pith/HJD6PZ4HYCNKSWBTHRF3W4YG5X/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HJD6PZ4HYCNKSWBTHRF3W4YG5X/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:HJD6PZ4HYCNKSWBTHRF3W4YG5X","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":"de8b5f24b50febc76554a965c6c76bfb45ea7b52cf4836f09b1d09ba075993c4","cross_cats_sorted":["math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-12-17T01:23:45Z","title_canon_sha256":"bb4847bc99d2a7580bbd2eaf9a03e0dd9fac445d746b78616301947e3f3262f2"},"schema_version":"1.0","source":{"id":"1412.5237","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.5237","created_at":"2026-05-18T01:27:05Z"},{"alias_kind":"arxiv_version","alias_value":"1412.5237v1","created_at":"2026-05-18T01:27:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.5237","created_at":"2026-05-18T01:27:05Z"},{"alias_kind":"pith_short_12","alias_value":"HJD6PZ4HYCNK","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_16","alias_value":"HJD6PZ4HYCNKSWBT","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_8","alias_value":"HJD6PZ4H","created_at":"2026-05-18T12:28:30Z"}],"graph_snapshots":[{"event_id":"sha256:58c9401bb49cab7f7b227ffb938da8d7346c7d3f83b1d92793e8267122a2bb16","target":"graph","created_at":"2026-05-18T01:27:05Z","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":"A method for solving spectral problems for the Sturm-Liouville equation $(pv^{\\prime})^{\\prime}-qv+\\lambda rv=0$ based on the approximation of the Delsarte transmutation operators combined with the Liouville transformation is presented. The problem of numerical approximation of solutions and of eigendata is reduced to approximation of a pair of functions depending on the coefficients $p$, $q$ and $r$ by a finite linear combination of certain specially constructed functions related to generalized wave polynomials introduced in arXiv:1208.5984, arXiv:1208.6166. The method allows one to compute b","authors_text":"Samy Morelos, Sergii M. Torba, Vladislav V. Kravchenko","cross_cats":["math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-12-17T01:23:45Z","title":"Liouville transformation, analytic approximation of transmutation operators and solution of spectral problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.5237","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":"sha256:1084ce94764e6aaae29dd8129189e29bb0961c0e8dd1a3a8f852af3929efbdb2","target":"record","created_at":"2026-05-18T01:27:05Z","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":"de8b5f24b50febc76554a965c6c76bfb45ea7b52cf4836f09b1d09ba075993c4","cross_cats_sorted":["math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-12-17T01:23:45Z","title_canon_sha256":"bb4847bc99d2a7580bbd2eaf9a03e0dd9fac445d746b78616301947e3f3262f2"},"schema_version":"1.0","source":{"id":"1412.5237","kind":"arxiv","version":1}},"canonical_sha256":"3a47e7e787c09aa958333c4bbb7306edfc6358191c8b4050d6796a5a7aa3bc2c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3a47e7e787c09aa958333c4bbb7306edfc6358191c8b4050d6796a5a7aa3bc2c","first_computed_at":"2026-05-18T01:27:05.471335Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:27:05.471335Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VBqyXmIfepm2LoxbP7mi8enMkF2JPkEt+yHrgOi/NzW4lPI8vSx6gqVBLx2OVCU7h9OuR3hQnx0VKiw9BGafCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:27:05.472013Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.5237","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1084ce94764e6aaae29dd8129189e29bb0961c0e8dd1a3a8f852af3929efbdb2","sha256:58c9401bb49cab7f7b227ffb938da8d7346c7d3f83b1d92793e8267122a2bb16"],"state_sha256":"9a12b2ffe1632848916694fa9bdb15335f1fe58ed3cd0ccca42c0d748d2cc3ac"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SZwBnRIarn1BS8fNKMjAlJS+TCuJk32peaNXNn9sz5XlrAHzK9UGz3Q6VSTwgYAeT2jUJUCWmbrgEDhBIFxfBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T07:51:26.359255Z","bundle_sha256":"caf34bc3376acf88596d3c85123ef5282f59190e21379ab72dd855aac9743314"}}