{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2005:E4UBSRFMOHMOEDUVB73WZSY4FU","short_pith_number":"pith:E4UBSRFM","schema_version":"1.0","canonical_sha256":"27281944ac71d8e20e950ff76ccb1c2d162a1196d0390322a571c9c956a8b8e7","source":{"kind":"arxiv","id":"math-ph/0512001","version":1},"attestation_state":"computed","paper":{"title":"The Borg-Marchenko Theorem with a Continuous Spectrum","license":"","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Ricardo Weder, Tuncay Aktosun","submitted_at":"2005-12-01T00:34:36Z","abstract_excerpt":"The Schr\\\"odinger equation is considered on the half line with a selfadjoint boundary condition when the potential is real valued, integrable, and has a finite first moment. It is proved that the potential and the two boundary conditions are uniquely determined by a set of spectral data containing the discrete eigenvalues for a boundary condition at the origin, the continuous part of the spectral measure for that boundary condition, and a subset of the discrete eigenvalues for a different boundary condition. This result provides a generalization of the celebrated uniqueness theorem of Borg and"},"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":"math-ph/0512001","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math-ph","submitted_at":"2005-12-01T00:34:36Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"662e3136f1d5b3ac6071e0e02c255065675415425b756738c7abb167abd605f9","abstract_canon_sha256":"609de3d0bb7d13c49bfd60e99c974b5549ff6fb994700227caa9402fb9062b20"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:52:11.491163Z","signature_b64":"i4I6iHJxof3TAGG06u94BPuKF8z8X/lE1CKdnBoNx+LWCGiUNG8Hm7vU/K+YQ4bFRyddogWagdW4ME0c5h68Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"27281944ac71d8e20e950ff76ccb1c2d162a1196d0390322a571c9c956a8b8e7","last_reissued_at":"2026-07-04T14:52:11.490645Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:52:11.490645Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Borg-Marchenko Theorem with a Continuous Spectrum","license":"","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Ricardo Weder, Tuncay Aktosun","submitted_at":"2005-12-01T00:34:36Z","abstract_excerpt":"The Schr\\\"odinger equation is considered on the half line with a selfadjoint boundary condition when the potential is real valued, integrable, and has a finite first moment. It is proved that the potential and the two boundary conditions are uniquely determined by a set of spectral data containing the discrete eigenvalues for a boundary condition at the origin, the continuous part of the spectral measure for that boundary condition, and a subset of the discrete eigenvalues for a different boundary condition. This result provides a generalization of the celebrated uniqueness theorem of Borg and"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0512001","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math-ph/0512001/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"math-ph/0512001","created_at":"2026-07-04T14:52:11.490709+00:00"},{"alias_kind":"arxiv_version","alias_value":"math-ph/0512001v1","created_at":"2026-07-04T14:52:11.490709+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/0512001","created_at":"2026-07-04T14:52:11.490709+00:00"},{"alias_kind":"pith_short_12","alias_value":"E4UBSRFMOHMO","created_at":"2026-07-04T14:52:11.490709+00:00"},{"alias_kind":"pith_short_16","alias_value":"E4UBSRFMOHMOEDUV","created_at":"2026-07-04T14:52:11.490709+00:00"},{"alias_kind":"pith_short_8","alias_value":"E4UBSRFM","created_at":"2026-07-04T14:52:11.490709+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/E4UBSRFMOHMOEDUVB73WZSY4FU","json":"https://pith.science/pith/E4UBSRFMOHMOEDUVB73WZSY4FU.json","graph_json":"https://pith.science/api/pith-number/E4UBSRFMOHMOEDUVB73WZSY4FU/graph.json","events_json":"https://pith.science/api/pith-number/E4UBSRFMOHMOEDUVB73WZSY4FU/events.json","paper":"https://pith.science/paper/E4UBSRFM"},"agent_actions":{"view_html":"https://pith.science/pith/E4UBSRFMOHMOEDUVB73WZSY4FU","download_json":"https://pith.science/pith/E4UBSRFMOHMOEDUVB73WZSY4FU.json","view_paper":"https://pith.science/paper/E4UBSRFM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math-ph/0512001&json=true","fetch_graph":"https://pith.science/api/pith-number/E4UBSRFMOHMOEDUVB73WZSY4FU/graph.json","fetch_events":"https://pith.science/api/pith-number/E4UBSRFMOHMOEDUVB73WZSY4FU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/E4UBSRFMOHMOEDUVB73WZSY4FU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/E4UBSRFMOHMOEDUVB73WZSY4FU/action/storage_attestation","attest_author":"https://pith.science/pith/E4UBSRFMOHMOEDUVB73WZSY4FU/action/author_attestation","sign_citation":"https://pith.science/pith/E4UBSRFMOHMOEDUVB73WZSY4FU/action/citation_signature","submit_replication":"https://pith.science/pith/E4UBSRFMOHMOEDUVB73WZSY4FU/action/replication_record"}},"created_at":"2026-07-04T14:52:11.490709+00:00","updated_at":"2026-07-04T14:52:11.490709+00:00"}