{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:JPG73OW6NQBW7LAUJLC47K5VSO","short_pith_number":"pith:JPG73OW6","schema_version":"1.0","canonical_sha256":"4bcdfdbade6c036fac144ac5cfabb593a40e0fe70bde9bc9d8cd10b69b6a32fd","source":{"kind":"arxiv","id":"2505.23332","version":1},"attestation_state":"computed","paper":{"title":"The boundary control approach to the Titchmarsh-Weyl $m-$function","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["math.SP"],"primary_cat":"math.AP","authors_text":"A.V. Rybkin, S.A. Avdonin, V.S. Mikhaylov","submitted_at":"2025-05-29T10:45:39Z","abstract_excerpt":"We link the Boundary Control Theory and the Titchmarsh-Weyl Theory. This provides a natural interpretation of the $A-$amplitude due to Simon and yields a new efficient method to evaluate the Titchmarsh-Weyl $m-$function associated with the Schr\\\"{o}dinger operator $H=-\\partial _{x}^{2}+q\\left( x\\right) $ on $L_{2}\\left( 0,\\infty \\right) $ with Dirichlet boundary condition at $x=0.$"},"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":"2505.23332","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.AP","submitted_at":"2025-05-29T10:45:39Z","cross_cats_sorted":["math.SP"],"title_canon_sha256":"73ca7df6a3f22b8aa6be40d1971ae409f03019e1cfecf890b28671d89114d1a6","abstract_canon_sha256":"48e891d6b5eb676ec00d6ff4a329cb6ad5b035903dd5b8eac2ef2294633dfe93"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:11:59.739433Z","signature_b64":"I4b/NmgXq4aywPISSLKKB6QxNvkqapCAhCpXopQDTOz8naClZ48xaUSCjel12VEyAW7EgY5AocAuBnOHw13sCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4bcdfdbade6c036fac144ac5cfabb593a40e0fe70bde9bc9d8cd10b69b6a32fd","last_reissued_at":"2026-07-05T11:11:59.738910Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:11:59.738910Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The boundary control approach to the Titchmarsh-Weyl $m-$function","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["math.SP"],"primary_cat":"math.AP","authors_text":"A.V. Rybkin, S.A. Avdonin, V.S. Mikhaylov","submitted_at":"2025-05-29T10:45:39Z","abstract_excerpt":"We link the Boundary Control Theory and the Titchmarsh-Weyl Theory. This provides a natural interpretation of the $A-$amplitude due to Simon and yields a new efficient method to evaluate the Titchmarsh-Weyl $m-$function associated with the Schr\\\"{o}dinger operator $H=-\\partial _{x}^{2}+q\\left( x\\right) $ on $L_{2}\\left( 0,\\infty \\right) $ with Dirichlet boundary condition at $x=0.$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.23332","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/2505.23332/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":"2505.23332","created_at":"2026-07-05T11:11:59.738966+00:00"},{"alias_kind":"arxiv_version","alias_value":"2505.23332v1","created_at":"2026-07-05T11:11:59.738966+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.23332","created_at":"2026-07-05T11:11:59.738966+00:00"},{"alias_kind":"pith_short_12","alias_value":"JPG73OW6NQBW","created_at":"2026-07-05T11:11:59.738966+00:00"},{"alias_kind":"pith_short_16","alias_value":"JPG73OW6NQBW7LAU","created_at":"2026-07-05T11:11:59.738966+00:00"},{"alias_kind":"pith_short_8","alias_value":"JPG73OW6","created_at":"2026-07-05T11:11:59.738966+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/JPG73OW6NQBW7LAUJLC47K5VSO","json":"https://pith.science/pith/JPG73OW6NQBW7LAUJLC47K5VSO.json","graph_json":"https://pith.science/api/pith-number/JPG73OW6NQBW7LAUJLC47K5VSO/graph.json","events_json":"https://pith.science/api/pith-number/JPG73OW6NQBW7LAUJLC47K5VSO/events.json","paper":"https://pith.science/paper/JPG73OW6"},"agent_actions":{"view_html":"https://pith.science/pith/JPG73OW6NQBW7LAUJLC47K5VSO","download_json":"https://pith.science/pith/JPG73OW6NQBW7LAUJLC47K5VSO.json","view_paper":"https://pith.science/paper/JPG73OW6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2505.23332&json=true","fetch_graph":"https://pith.science/api/pith-number/JPG73OW6NQBW7LAUJLC47K5VSO/graph.json","fetch_events":"https://pith.science/api/pith-number/JPG73OW6NQBW7LAUJLC47K5VSO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JPG73OW6NQBW7LAUJLC47K5VSO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JPG73OW6NQBW7LAUJLC47K5VSO/action/storage_attestation","attest_author":"https://pith.science/pith/JPG73OW6NQBW7LAUJLC47K5VSO/action/author_attestation","sign_citation":"https://pith.science/pith/JPG73OW6NQBW7LAUJLC47K5VSO/action/citation_signature","submit_replication":"https://pith.science/pith/JPG73OW6NQBW7LAUJLC47K5VSO/action/replication_record"}},"created_at":"2026-07-05T11:11:59.738966+00:00","updated_at":"2026-07-05T11:11:59.738966+00:00"}