{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:422W2LWL33G5TRNWW36TLJQQF4","short_pith_number":"pith:422W2LWL","schema_version":"1.0","canonical_sha256":"e6b56d2ecbdecdd9c5b6b6fd35a6102f2e4b2603d470bdb519cef457a3b99df3","source":{"kind":"arxiv","id":"2405.19364","version":1},"attestation_state":"computed","paper":{"title":"Essential Self-Adjointness of Semi-Bounded Schrodinger Operators on Birth-Death Chains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Sean Ku","submitted_at":"2024-05-24T22:25:44Z","abstract_excerpt":"We study the essential self-adjointness of semi-bounded Schr\\\"{o}dinger operators on birth-death chains. First, we offer a general characterization which originates from studying a second order linear recurrence with variational coefficients which comes from the Schr\\\"{o}dinger operator. As this characterization is algebraically complicated, we present an additional theorem discussing the failure of essential self-adjointness. Finally, we study two specific cases of solutions to equations involving the Schr\\\"{o}dinger operator over birth-death chains and derive explicit formulas in these cases"},"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":"2405.19364","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2024-05-24T22:25:44Z","cross_cats_sorted":[],"title_canon_sha256":"581d5d505e54eb3b30d844ffd51779447095c96949f8021038e5dc4d014fbe59","abstract_canon_sha256":"6feb1e49d851b1661a4bd79b6ce25c5474e7ff3653dbee47bb53b7b7e13f3696"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:25:06.741756Z","signature_b64":"CnX11ODnD6wciy1f4OFwbay+GpuuWGueh9zG3o/JfOL/sx65OXpiHYdxDLRlTcYeBhoyHVzEHzUp8jbR2oLABA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e6b56d2ecbdecdd9c5b6b6fd35a6102f2e4b2603d470bdb519cef457a3b99df3","last_reissued_at":"2026-07-05T08:25:06.741202Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:25:06.741202Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Essential Self-Adjointness of Semi-Bounded Schrodinger Operators on Birth-Death Chains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Sean Ku","submitted_at":"2024-05-24T22:25:44Z","abstract_excerpt":"We study the essential self-adjointness of semi-bounded Schr\\\"{o}dinger operators on birth-death chains. First, we offer a general characterization which originates from studying a second order linear recurrence with variational coefficients which comes from the Schr\\\"{o}dinger operator. As this characterization is algebraically complicated, we present an additional theorem discussing the failure of essential self-adjointness. Finally, we study two specific cases of solutions to equations involving the Schr\\\"{o}dinger operator over birth-death chains and derive explicit formulas in these cases"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.19364","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/2405.19364/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":"2405.19364","created_at":"2026-07-05T08:25:06.741258+00:00"},{"alias_kind":"arxiv_version","alias_value":"2405.19364v1","created_at":"2026-07-05T08:25:06.741258+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2405.19364","created_at":"2026-07-05T08:25:06.741258+00:00"},{"alias_kind":"pith_short_12","alias_value":"422W2LWL33G5","created_at":"2026-07-05T08:25:06.741258+00:00"},{"alias_kind":"pith_short_16","alias_value":"422W2LWL33G5TRNW","created_at":"2026-07-05T08:25:06.741258+00:00"},{"alias_kind":"pith_short_8","alias_value":"422W2LWL","created_at":"2026-07-05T08:25:06.741258+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/422W2LWL33G5TRNWW36TLJQQF4","json":"https://pith.science/pith/422W2LWL33G5TRNWW36TLJQQF4.json","graph_json":"https://pith.science/api/pith-number/422W2LWL33G5TRNWW36TLJQQF4/graph.json","events_json":"https://pith.science/api/pith-number/422W2LWL33G5TRNWW36TLJQQF4/events.json","paper":"https://pith.science/paper/422W2LWL"},"agent_actions":{"view_html":"https://pith.science/pith/422W2LWL33G5TRNWW36TLJQQF4","download_json":"https://pith.science/pith/422W2LWL33G5TRNWW36TLJQQF4.json","view_paper":"https://pith.science/paper/422W2LWL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2405.19364&json=true","fetch_graph":"https://pith.science/api/pith-number/422W2LWL33G5TRNWW36TLJQQF4/graph.json","fetch_events":"https://pith.science/api/pith-number/422W2LWL33G5TRNWW36TLJQQF4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/422W2LWL33G5TRNWW36TLJQQF4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/422W2LWL33G5TRNWW36TLJQQF4/action/storage_attestation","attest_author":"https://pith.science/pith/422W2LWL33G5TRNWW36TLJQQF4/action/author_attestation","sign_citation":"https://pith.science/pith/422W2LWL33G5TRNWW36TLJQQF4/action/citation_signature","submit_replication":"https://pith.science/pith/422W2LWL33G5TRNWW36TLJQQF4/action/replication_record"}},"created_at":"2026-07-05T08:25:06.741258+00:00","updated_at":"2026-07-05T08:25:06.741258+00:00"}