{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:TEO2O4FIRIX4XEYBQJXA2J3VPN","short_pith_number":"pith:TEO2O4FI","schema_version":"1.0","canonical_sha256":"991da770a88a2fcb9301826e0d27757b7ddfc0481583ce82b9f168e6332d51b8","source":{"kind":"arxiv","id":"1504.01817","version":1},"attestation_state":"computed","paper":{"title":"Eigenvalue problem of Sturm-Liouville systems with separated boundary conditions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.FA"],"primary_cat":"math.SP","authors_text":"Penghui Wang, Xijun Hu","submitted_at":"2015-04-08T03:14:32Z","abstract_excerpt":"Let $\\lambda_j$ be the $j$-th eigenvalue of Sturm-Liouville systems with separated boundary conditions, we build up the Hill-type formula, which represent $\\prod\\limits_{j}(1-\\lambda_j^{-1})$ as a determinant of finite matrix. This is the first attack on such a formula under non-periodic type boundary conditions. Consequently, we get the Krein-type trace formula based on the Hill-type formula, which express $\\sum\\limits_{j}{1\\over \\lambda_j^m}$ as trace of finite matrices. The trace formula can be used to estimate the conjugate point alone a geodesic in Riemannian manifold and to get some infi"},"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":"1504.01817","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2015-04-08T03:14:32Z","cross_cats_sorted":["math.DS","math.FA"],"title_canon_sha256":"37936502ddf2483ab1d84e85babc6657fe9eb34d62e36ac054319729d3a880c6","abstract_canon_sha256":"1884b1d639e3e497e68d37eda401421e5c2cf6130d887989872d78ca72757ec1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:19:18.203352Z","signature_b64":"joaeyjJtTGzmATVbM4FAtMhPnVqMEFPfeIcF9TSnbZU46k/jAmN8US03tT5wBPb1p9reHHcpVsrMO+j9I+CQAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"991da770a88a2fcb9301826e0d27757b7ddfc0481583ce82b9f168e6332d51b8","last_reissued_at":"2026-05-18T02:19:18.202649Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:19:18.202649Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Eigenvalue problem of Sturm-Liouville systems with separated boundary conditions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.FA"],"primary_cat":"math.SP","authors_text":"Penghui Wang, Xijun Hu","submitted_at":"2015-04-08T03:14:32Z","abstract_excerpt":"Let $\\lambda_j$ be the $j$-th eigenvalue of Sturm-Liouville systems with separated boundary conditions, we build up the Hill-type formula, which represent $\\prod\\limits_{j}(1-\\lambda_j^{-1})$ as a determinant of finite matrix. This is the first attack on such a formula under non-periodic type boundary conditions. Consequently, we get the Krein-type trace formula based on the Hill-type formula, which express $\\sum\\limits_{j}{1\\over \\lambda_j^m}$ as trace of finite matrices. The trace formula can be used to estimate the conjugate point alone a geodesic in Riemannian manifold and to get some infi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.01817","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":"1504.01817","created_at":"2026-05-18T02:19:18.202756+00:00"},{"alias_kind":"arxiv_version","alias_value":"1504.01817v1","created_at":"2026-05-18T02:19:18.202756+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.01817","created_at":"2026-05-18T02:19:18.202756+00:00"},{"alias_kind":"pith_short_12","alias_value":"TEO2O4FIRIX4","created_at":"2026-05-18T12:29:42.218222+00:00"},{"alias_kind":"pith_short_16","alias_value":"TEO2O4FIRIX4XEYB","created_at":"2026-05-18T12:29:42.218222+00:00"},{"alias_kind":"pith_short_8","alias_value":"TEO2O4FI","created_at":"2026-05-18T12:29:42.218222+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/TEO2O4FIRIX4XEYBQJXA2J3VPN","json":"https://pith.science/pith/TEO2O4FIRIX4XEYBQJXA2J3VPN.json","graph_json":"https://pith.science/api/pith-number/TEO2O4FIRIX4XEYBQJXA2J3VPN/graph.json","events_json":"https://pith.science/api/pith-number/TEO2O4FIRIX4XEYBQJXA2J3VPN/events.json","paper":"https://pith.science/paper/TEO2O4FI"},"agent_actions":{"view_html":"https://pith.science/pith/TEO2O4FIRIX4XEYBQJXA2J3VPN","download_json":"https://pith.science/pith/TEO2O4FIRIX4XEYBQJXA2J3VPN.json","view_paper":"https://pith.science/paper/TEO2O4FI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1504.01817&json=true","fetch_graph":"https://pith.science/api/pith-number/TEO2O4FIRIX4XEYBQJXA2J3VPN/graph.json","fetch_events":"https://pith.science/api/pith-number/TEO2O4FIRIX4XEYBQJXA2J3VPN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TEO2O4FIRIX4XEYBQJXA2J3VPN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TEO2O4FIRIX4XEYBQJXA2J3VPN/action/storage_attestation","attest_author":"https://pith.science/pith/TEO2O4FIRIX4XEYBQJXA2J3VPN/action/author_attestation","sign_citation":"https://pith.science/pith/TEO2O4FIRIX4XEYBQJXA2J3VPN/action/citation_signature","submit_replication":"https://pith.science/pith/TEO2O4FIRIX4XEYBQJXA2J3VPN/action/replication_record"}},"created_at":"2026-05-18T02:19:18.202756+00:00","updated_at":"2026-05-18T02:19:18.202756+00:00"}