{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:HG3WDFQWFS7JSWSNE6UNB4C4KK","short_pith_number":"pith:HG3WDFQW","schema_version":"1.0","canonical_sha256":"39b76196162cbe995a4d27a8d0f05c529a85756a4122b5b6b99dde454a5c915c","source":{"kind":"arxiv","id":"1409.0139","version":2},"attestation_state":"computed","paper":{"title":"The inverse spectral problem for indefinite strings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Aleksey Kostenko, Jonathan Eckhardt","submitted_at":"2014-08-30T17:50:43Z","abstract_excerpt":"Motivated by the study of certain nonlinear wave equations (in particular, the Camassa-Holm equation), we introduce a new class of generalized indefinite strings associated with differential equations of the form \\[-u\"=z\\,u\\,\\omega+z^2u\\,\\upsilon\\] on an interval $[0,L)$, where $\\omega$ is a real-valued distribution in $H^{-1}_{\\mathrm{loc}}[0,L)$, $\\upsilon$ is a non-negative Borel measure on $[0,L)$ and $z$ is a complex spectral parameter. Apart from developing basic spectral theory for these kinds of spectral problems, our main result is an indefinite analogue of M. G. Krein's celebrated so"},"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":"1409.0139","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2014-08-30T17:50:43Z","cross_cats_sorted":[],"title_canon_sha256":"fc0ef3e7f7974facdd6044b214819919d384552d5548497d1534f9392ba77a8a","abstract_canon_sha256":"421324d5f367723016de4750ec3e65026e48f57a2fd81aabd0a0c296e6e65493"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:14:29.663239Z","signature_b64":"kw3hZE2FL+ZZPIDjnoKJ6/TaR9SCntwn2bw9KmQAZIABCScI094irMsX9X4mcevCi5dmDVTKIv2WqMN5GKTiDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"39b76196162cbe995a4d27a8d0f05c529a85756a4122b5b6b99dde454a5c915c","last_reissued_at":"2026-05-18T01:14:29.662549Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:14:29.662549Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The inverse spectral problem for indefinite strings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Aleksey Kostenko, Jonathan Eckhardt","submitted_at":"2014-08-30T17:50:43Z","abstract_excerpt":"Motivated by the study of certain nonlinear wave equations (in particular, the Camassa-Holm equation), we introduce a new class of generalized indefinite strings associated with differential equations of the form \\[-u\"=z\\,u\\,\\omega+z^2u\\,\\upsilon\\] on an interval $[0,L)$, where $\\omega$ is a real-valued distribution in $H^{-1}_{\\mathrm{loc}}[0,L)$, $\\upsilon$ is a non-negative Borel measure on $[0,L)$ and $z$ is a complex spectral parameter. Apart from developing basic spectral theory for these kinds of spectral problems, our main result is an indefinite analogue of M. G. Krein's celebrated so"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.0139","kind":"arxiv","version":2},"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":"1409.0139","created_at":"2026-05-18T01:14:29.662669+00:00"},{"alias_kind":"arxiv_version","alias_value":"1409.0139v2","created_at":"2026-05-18T01:14:29.662669+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.0139","created_at":"2026-05-18T01:14:29.662669+00:00"},{"alias_kind":"pith_short_12","alias_value":"HG3WDFQWFS7J","created_at":"2026-05-18T12:28:30.664211+00:00"},{"alias_kind":"pith_short_16","alias_value":"HG3WDFQWFS7JSWSN","created_at":"2026-05-18T12:28:30.664211+00:00"},{"alias_kind":"pith_short_8","alias_value":"HG3WDFQW","created_at":"2026-05-18T12:28:30.664211+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/HG3WDFQWFS7JSWSNE6UNB4C4KK","json":"https://pith.science/pith/HG3WDFQWFS7JSWSNE6UNB4C4KK.json","graph_json":"https://pith.science/api/pith-number/HG3WDFQWFS7JSWSNE6UNB4C4KK/graph.json","events_json":"https://pith.science/api/pith-number/HG3WDFQWFS7JSWSNE6UNB4C4KK/events.json","paper":"https://pith.science/paper/HG3WDFQW"},"agent_actions":{"view_html":"https://pith.science/pith/HG3WDFQWFS7JSWSNE6UNB4C4KK","download_json":"https://pith.science/pith/HG3WDFQWFS7JSWSNE6UNB4C4KK.json","view_paper":"https://pith.science/paper/HG3WDFQW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1409.0139&json=true","fetch_graph":"https://pith.science/api/pith-number/HG3WDFQWFS7JSWSNE6UNB4C4KK/graph.json","fetch_events":"https://pith.science/api/pith-number/HG3WDFQWFS7JSWSNE6UNB4C4KK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HG3WDFQWFS7JSWSNE6UNB4C4KK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HG3WDFQWFS7JSWSNE6UNB4C4KK/action/storage_attestation","attest_author":"https://pith.science/pith/HG3WDFQWFS7JSWSNE6UNB4C4KK/action/author_attestation","sign_citation":"https://pith.science/pith/HG3WDFQWFS7JSWSNE6UNB4C4KK/action/citation_signature","submit_replication":"https://pith.science/pith/HG3WDFQWFS7JSWSNE6UNB4C4KK/action/replication_record"}},"created_at":"2026-05-18T01:14:29.662669+00:00","updated_at":"2026-05-18T01:14:29.662669+00:00"}