{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:PI4OQ52SNKADLA2K4PFKWZO7Z4","short_pith_number":"pith:PI4OQ52S","schema_version":"1.0","canonical_sha256":"7a38e877526a8035834ae3caab65dfcf2f7985568c5284ce1808e6f22bbfbbfe","source":{"kind":"arxiv","id":"1908.07876","version":1},"attestation_state":"computed","paper":{"title":"On an optimal potential of Schr\\\"odinger operator with prescribed $m$ eigenvalue","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.SP"],"primary_cat":"math.AP","authors_text":"Nurmukhamet Valeev, Yavdat Ilyasov","submitted_at":"2019-08-21T13:56:53Z","abstract_excerpt":"The purpose of this paper is twofold: firstly, we present a new type of relationship between inverse problems and nonlinear differential equations. Secondly, we introduce a new type of inverse spectral problem, posed as follows: for a priori given potential $V_0$ find the closest function $\\hat{V}$ such that $m$ eigenvalues of one-dimensional space Schrodinger operator with potential $\\hat{V}$ would coincide with the given values $ E_1 $, $ \\ldots $, $ E_m \\in \\mathbb {R} $. In our main result, we prove the existence of a solution to this problem, and more importantly, we show that such a solu"},"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":"1908.07876","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-08-21T13:56:53Z","cross_cats_sorted":["math-ph","math.MP","math.SP"],"title_canon_sha256":"1eb581622efc277a01cef9577198f2f232b1f83da8c2555815fb8dc81695eb82","abstract_canon_sha256":"2939e24d64fd07f72301fd90e0d5fc50fea8a6f2bb2a13856e79af8412288172"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T23:59:02.029463Z","signature_b64":"Kx/2lA2DqcsmOr+LzFAcuwD9PyKetct/XkIBnrHRE3oxEIQJY/45DaWmBHa7tvtkb3Wpozr7zd/KMx94o24hDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7a38e877526a8035834ae3caab65dfcf2f7985568c5284ce1808e6f22bbfbbfe","last_reissued_at":"2026-07-04T23:59:02.029021Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T23:59:02.029021Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On an optimal potential of Schr\\\"odinger operator with prescribed $m$ eigenvalue","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.SP"],"primary_cat":"math.AP","authors_text":"Nurmukhamet Valeev, Yavdat Ilyasov","submitted_at":"2019-08-21T13:56:53Z","abstract_excerpt":"The purpose of this paper is twofold: firstly, we present a new type of relationship between inverse problems and nonlinear differential equations. Secondly, we introduce a new type of inverse spectral problem, posed as follows: for a priori given potential $V_0$ find the closest function $\\hat{V}$ such that $m$ eigenvalues of one-dimensional space Schrodinger operator with potential $\\hat{V}$ would coincide with the given values $ E_1 $, $ \\ldots $, $ E_m \\in \\mathbb {R} $. In our main result, we prove the existence of a solution to this problem, and more importantly, we show that such a solu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.07876","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/1908.07876/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":"1908.07876","created_at":"2026-07-04T23:59:02.029090+00:00"},{"alias_kind":"arxiv_version","alias_value":"1908.07876v1","created_at":"2026-07-04T23:59:02.029090+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.07876","created_at":"2026-07-04T23:59:02.029090+00:00"},{"alias_kind":"pith_short_12","alias_value":"PI4OQ52SNKAD","created_at":"2026-07-04T23:59:02.029090+00:00"},{"alias_kind":"pith_short_16","alias_value":"PI4OQ52SNKADLA2K","created_at":"2026-07-04T23:59:02.029090+00:00"},{"alias_kind":"pith_short_8","alias_value":"PI4OQ52S","created_at":"2026-07-04T23:59:02.029090+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/PI4OQ52SNKADLA2K4PFKWZO7Z4","json":"https://pith.science/pith/PI4OQ52SNKADLA2K4PFKWZO7Z4.json","graph_json":"https://pith.science/api/pith-number/PI4OQ52SNKADLA2K4PFKWZO7Z4/graph.json","events_json":"https://pith.science/api/pith-number/PI4OQ52SNKADLA2K4PFKWZO7Z4/events.json","paper":"https://pith.science/paper/PI4OQ52S"},"agent_actions":{"view_html":"https://pith.science/pith/PI4OQ52SNKADLA2K4PFKWZO7Z4","download_json":"https://pith.science/pith/PI4OQ52SNKADLA2K4PFKWZO7Z4.json","view_paper":"https://pith.science/paper/PI4OQ52S","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1908.07876&json=true","fetch_graph":"https://pith.science/api/pith-number/PI4OQ52SNKADLA2K4PFKWZO7Z4/graph.json","fetch_events":"https://pith.science/api/pith-number/PI4OQ52SNKADLA2K4PFKWZO7Z4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PI4OQ52SNKADLA2K4PFKWZO7Z4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PI4OQ52SNKADLA2K4PFKWZO7Z4/action/storage_attestation","attest_author":"https://pith.science/pith/PI4OQ52SNKADLA2K4PFKWZO7Z4/action/author_attestation","sign_citation":"https://pith.science/pith/PI4OQ52SNKADLA2K4PFKWZO7Z4/action/citation_signature","submit_replication":"https://pith.science/pith/PI4OQ52SNKADLA2K4PFKWZO7Z4/action/replication_record"}},"created_at":"2026-07-04T23:59:02.029090+00:00","updated_at":"2026-07-04T23:59:02.029090+00:00"}