{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2008:YPMWRVBTUGVIKJ2M2ZFOSEETCC","short_pith_number":"pith:YPMWRVBT","schema_version":"1.0","canonical_sha256":"c3d968d433a1aa85274cd64ae9109310b69aeb83d3c664252a1fb8095c50c02b","source":{"kind":"arxiv","id":"0811.4488","version":1},"attestation_state":"computed","paper":{"title":"Spectral parameter power series for Sturm-Liouville problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"R. Michael Porter, Vladislav V. Kravchenko","submitted_at":"2008-11-28T16:17:32Z","abstract_excerpt":"We consider a recently discovered representation for the general solution of the Sturm-Liouville equation as a spectral parameter power series (SPPS). The coefficients of the power series are given in terms of a particular solution of the Sturm-Liouville equation with the zero spectral parameter. We show that, among other possible applications, this provides a new and efficient numerical method for solving initial value and boundary value problems. Moreover, due to its convenient form the representation lends itself to numerical solution of spectral Sturm-Liouville problems, effectively by cal"},"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":"0811.4488","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2008-11-28T16:17:32Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"035b7ba73452d5431173a40524b3e4c8bbf2c0dde1667aabf8d1d03200f53ed7","abstract_canon_sha256":"20c5018c4a820f02d4ebd7f48ae86ef4de2d69d04c937b977e2f1c2bbfcffd65"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:08:12.790384Z","signature_b64":"I4dU5R62v4btYZcf7M7AKLGgkak/dJWX/p7FkvSHZhUFSDmR+2z6zVkxlkMArseqR8/mCC1rKf54WZrOWZw0BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c3d968d433a1aa85274cd64ae9109310b69aeb83d3c664252a1fb8095c50c02b","last_reissued_at":"2026-05-18T04:08:12.789965Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:08:12.789965Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Spectral parameter power series for Sturm-Liouville problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"R. Michael Porter, Vladislav V. Kravchenko","submitted_at":"2008-11-28T16:17:32Z","abstract_excerpt":"We consider a recently discovered representation for the general solution of the Sturm-Liouville equation as a spectral parameter power series (SPPS). The coefficients of the power series are given in terms of a particular solution of the Sturm-Liouville equation with the zero spectral parameter. We show that, among other possible applications, this provides a new and efficient numerical method for solving initial value and boundary value problems. Moreover, due to its convenient form the representation lends itself to numerical solution of spectral Sturm-Liouville problems, effectively by cal"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0811.4488","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":"0811.4488","created_at":"2026-05-18T04:08:12.790025+00:00"},{"alias_kind":"arxiv_version","alias_value":"0811.4488v1","created_at":"2026-05-18T04:08:12.790025+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0811.4488","created_at":"2026-05-18T04:08:12.790025+00:00"},{"alias_kind":"pith_short_12","alias_value":"YPMWRVBTUGVI","created_at":"2026-05-18T12:25:58.018023+00:00"},{"alias_kind":"pith_short_16","alias_value":"YPMWRVBTUGVIKJ2M","created_at":"2026-05-18T12:25:58.018023+00:00"},{"alias_kind":"pith_short_8","alias_value":"YPMWRVBT","created_at":"2026-05-18T12:25:58.018023+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/YPMWRVBTUGVIKJ2M2ZFOSEETCC","json":"https://pith.science/pith/YPMWRVBTUGVIKJ2M2ZFOSEETCC.json","graph_json":"https://pith.science/api/pith-number/YPMWRVBTUGVIKJ2M2ZFOSEETCC/graph.json","events_json":"https://pith.science/api/pith-number/YPMWRVBTUGVIKJ2M2ZFOSEETCC/events.json","paper":"https://pith.science/paper/YPMWRVBT"},"agent_actions":{"view_html":"https://pith.science/pith/YPMWRVBTUGVIKJ2M2ZFOSEETCC","download_json":"https://pith.science/pith/YPMWRVBTUGVIKJ2M2ZFOSEETCC.json","view_paper":"https://pith.science/paper/YPMWRVBT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0811.4488&json=true","fetch_graph":"https://pith.science/api/pith-number/YPMWRVBTUGVIKJ2M2ZFOSEETCC/graph.json","fetch_events":"https://pith.science/api/pith-number/YPMWRVBTUGVIKJ2M2ZFOSEETCC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YPMWRVBTUGVIKJ2M2ZFOSEETCC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YPMWRVBTUGVIKJ2M2ZFOSEETCC/action/storage_attestation","attest_author":"https://pith.science/pith/YPMWRVBTUGVIKJ2M2ZFOSEETCC/action/author_attestation","sign_citation":"https://pith.science/pith/YPMWRVBTUGVIKJ2M2ZFOSEETCC/action/citation_signature","submit_replication":"https://pith.science/pith/YPMWRVBTUGVIKJ2M2ZFOSEETCC/action/replication_record"}},"created_at":"2026-05-18T04:08:12.790025+00:00","updated_at":"2026-05-18T04:08:12.790025+00:00"}