{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:UKOHNUYMXR5MYI3TH62RHV4P7X","short_pith_number":"pith:UKOHNUYM","schema_version":"1.0","canonical_sha256":"a29c76d30cbc7acc23733fb513d78ffdc98d9cf92f548b50ab373dadd028a61f","source":{"kind":"arxiv","id":"1409.5819","version":1},"attestation_state":"computed","paper":{"title":"Inverse problems for selfadjoint Schr\\\"odinger operators on the half line with compactly-supported potentials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Mehmet Unlu, Paul Sacks, Tuncay Aktosun","submitted_at":"2014-09-19T21:09:30Z","abstract_excerpt":"For a selfadjoint Schr\\\"odinger operator on the half line with a real-valued, integrable, and compactly-supported potential, it is investigated whether the boundary parameter at the origin and the potential can uniquely be determined by the scattering matrix or by the absolute value of the Jost function known at positive energies, without having the bound-state information. It is proved that, except in one special case where the scattering matrix has no bound states and its value is $+1$ at zero energy, the determination by the scattering matrix is unique. In the special case, it is shown that"},"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":"1409.5819","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2014-09-19T21:09:30Z","cross_cats_sorted":[],"title_canon_sha256":"8ccb7152b04fe85b65fb6008ea15ad4f6bb7826f2e9c6902ab0686964ca8ddff","abstract_canon_sha256":"1f350cfc479eddff2a096687d424eb2e5dba32b11e064601773dfb07e5f91f95"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:03:10.836178Z","signature_b64":"tlkixCGtxKPpVGVmhP5r9pdNBOwEL4MZFXR+QJiU/QVGsMeSxAK6+/w2jB8ztafDPTi4PsAMwR0imGg7WhAEDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a29c76d30cbc7acc23733fb513d78ffdc98d9cf92f548b50ab373dadd028a61f","last_reissued_at":"2026-05-18T01:03:10.835585Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:03:10.835585Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Inverse problems for selfadjoint Schr\\\"odinger operators on the half line with compactly-supported potentials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Mehmet Unlu, Paul Sacks, Tuncay Aktosun","submitted_at":"2014-09-19T21:09:30Z","abstract_excerpt":"For a selfadjoint Schr\\\"odinger operator on the half line with a real-valued, integrable, and compactly-supported potential, it is investigated whether the boundary parameter at the origin and the potential can uniquely be determined by the scattering matrix or by the absolute value of the Jost function known at positive energies, without having the bound-state information. It is proved that, except in one special case where the scattering matrix has no bound states and its value is $+1$ at zero energy, the determination by the scattering matrix is unique. In the special case, it is shown that"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.5819","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":"1409.5819","created_at":"2026-05-18T01:03:10.835684+00:00"},{"alias_kind":"arxiv_version","alias_value":"1409.5819v1","created_at":"2026-05-18T01:03:10.835684+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.5819","created_at":"2026-05-18T01:03:10.835684+00:00"},{"alias_kind":"pith_short_12","alias_value":"UKOHNUYMXR5M","created_at":"2026-05-18T12:28:52.271510+00:00"},{"alias_kind":"pith_short_16","alias_value":"UKOHNUYMXR5MYI3T","created_at":"2026-05-18T12:28:52.271510+00:00"},{"alias_kind":"pith_short_8","alias_value":"UKOHNUYM","created_at":"2026-05-18T12:28:52.271510+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/UKOHNUYMXR5MYI3TH62RHV4P7X","json":"https://pith.science/pith/UKOHNUYMXR5MYI3TH62RHV4P7X.json","graph_json":"https://pith.science/api/pith-number/UKOHNUYMXR5MYI3TH62RHV4P7X/graph.json","events_json":"https://pith.science/api/pith-number/UKOHNUYMXR5MYI3TH62RHV4P7X/events.json","paper":"https://pith.science/paper/UKOHNUYM"},"agent_actions":{"view_html":"https://pith.science/pith/UKOHNUYMXR5MYI3TH62RHV4P7X","download_json":"https://pith.science/pith/UKOHNUYMXR5MYI3TH62RHV4P7X.json","view_paper":"https://pith.science/paper/UKOHNUYM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1409.5819&json=true","fetch_graph":"https://pith.science/api/pith-number/UKOHNUYMXR5MYI3TH62RHV4P7X/graph.json","fetch_events":"https://pith.science/api/pith-number/UKOHNUYMXR5MYI3TH62RHV4P7X/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UKOHNUYMXR5MYI3TH62RHV4P7X/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UKOHNUYMXR5MYI3TH62RHV4P7X/action/storage_attestation","attest_author":"https://pith.science/pith/UKOHNUYMXR5MYI3TH62RHV4P7X/action/author_attestation","sign_citation":"https://pith.science/pith/UKOHNUYMXR5MYI3TH62RHV4P7X/action/citation_signature","submit_replication":"https://pith.science/pith/UKOHNUYMXR5MYI3TH62RHV4P7X/action/replication_record"}},"created_at":"2026-05-18T01:03:10.835684+00:00","updated_at":"2026-05-18T01:03:10.835684+00:00"}