{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:BOLOTXQGGLP76KTE2B3YSPX462","short_pith_number":"pith:BOLOTXQG","schema_version":"1.0","canonical_sha256":"0b96e9de0632dfff2a64d077893efcf6871d90e509ed9468b2952a7f2ba9413c","source":{"kind":"arxiv","id":"1505.03645","version":1},"attestation_state":"computed","paper":{"title":"The existence and location of eigenvalues of the one particle discrete Schroedinger operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.SP","authors_text":"Ender Ozdemir, Saidakhmat N. Lakaev","submitted_at":"2015-05-14T08:14:15Z","abstract_excerpt":"We consider a quantum particle moving in the one dimensional lattice Z and interacting with a indefinite sign external field v. We prove that the associated discrete Schroedinger operator H can have one or two eigenvalues, situated as below the bottom of the essential spectrum, as well as above its top. Moreover, we show that the operator H can have two eigenvalues outside of the essential spectrum such that one of them is situated below the bottom of the essential spectrum, and other one above its top."},"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":"1505.03645","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2015-05-14T08:14:15Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"8e69bebf5d34ce6924f25a8cdb94a38a7fd8db3a299718d338693cbc02d0b6fb","abstract_canon_sha256":"5bbd683038e9327fc275cf557567c0b79560f82f5df31e000b90a4f8c194fc48"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:09:53.445790Z","signature_b64":"KQq63jz5ty6mJ0oDwGB007zGZ0odiX6pQ+YHw4UcTvy26YKvMTkW6pFG3IHWX2eeSM15Zyq0sQUwcB5zl3D3Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0b96e9de0632dfff2a64d077893efcf6871d90e509ed9468b2952a7f2ba9413c","last_reissued_at":"2026-05-18T02:09:53.445121Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:09:53.445121Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The existence and location of eigenvalues of the one particle discrete Schroedinger operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.SP","authors_text":"Ender Ozdemir, Saidakhmat N. Lakaev","submitted_at":"2015-05-14T08:14:15Z","abstract_excerpt":"We consider a quantum particle moving in the one dimensional lattice Z and interacting with a indefinite sign external field v. We prove that the associated discrete Schroedinger operator H can have one or two eigenvalues, situated as below the bottom of the essential spectrum, as well as above its top. Moreover, we show that the operator H can have two eigenvalues outside of the essential spectrum such that one of them is situated below the bottom of the essential spectrum, and other one above its top."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.03645","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":""},"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":"1505.03645","created_at":"2026-05-18T02:09:53.445212+00:00"},{"alias_kind":"arxiv_version","alias_value":"1505.03645v1","created_at":"2026-05-18T02:09:53.445212+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.03645","created_at":"2026-05-18T02:09:53.445212+00:00"},{"alias_kind":"pith_short_12","alias_value":"BOLOTXQGGLP7","created_at":"2026-05-18T12:29:14.074870+00:00"},{"alias_kind":"pith_short_16","alias_value":"BOLOTXQGGLP76KTE","created_at":"2026-05-18T12:29:14.074870+00:00"},{"alias_kind":"pith_short_8","alias_value":"BOLOTXQG","created_at":"2026-05-18T12:29:14.074870+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/BOLOTXQGGLP76KTE2B3YSPX462","json":"https://pith.science/pith/BOLOTXQGGLP76KTE2B3YSPX462.json","graph_json":"https://pith.science/api/pith-number/BOLOTXQGGLP76KTE2B3YSPX462/graph.json","events_json":"https://pith.science/api/pith-number/BOLOTXQGGLP76KTE2B3YSPX462/events.json","paper":"https://pith.science/paper/BOLOTXQG"},"agent_actions":{"view_html":"https://pith.science/pith/BOLOTXQGGLP76KTE2B3YSPX462","download_json":"https://pith.science/pith/BOLOTXQGGLP76KTE2B3YSPX462.json","view_paper":"https://pith.science/paper/BOLOTXQG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1505.03645&json=true","fetch_graph":"https://pith.science/api/pith-number/BOLOTXQGGLP76KTE2B3YSPX462/graph.json","fetch_events":"https://pith.science/api/pith-number/BOLOTXQGGLP76KTE2B3YSPX462/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BOLOTXQGGLP76KTE2B3YSPX462/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BOLOTXQGGLP76KTE2B3YSPX462/action/storage_attestation","attest_author":"https://pith.science/pith/BOLOTXQGGLP76KTE2B3YSPX462/action/author_attestation","sign_citation":"https://pith.science/pith/BOLOTXQGGLP76KTE2B3YSPX462/action/citation_signature","submit_replication":"https://pith.science/pith/BOLOTXQGGLP76KTE2B3YSPX462/action/replication_record"}},"created_at":"2026-05-18T02:09:53.445212+00:00","updated_at":"2026-05-18T02:09:53.445212+00:00"}