{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:CEJQJQF3PJ72RGKKY2R44DGNKQ","short_pith_number":"pith:CEJQJQF3","schema_version":"1.0","canonical_sha256":"111304c0bb7a7fa8994ac6a3ce0ccd54225444f7fb79226e01b36c295794a09d","source":{"kind":"arxiv","id":"1605.00393","version":1},"attestation_state":"computed","paper":{"title":"Spectral analysis of two doubly infinite Jacobi matrices with exponential entries","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Franti\\v{s}ek \\v{S}tampach, Mourad E. H. Ismail","submitted_at":"2016-05-02T08:49:11Z","abstract_excerpt":"We provide a complete spectral analysis of all self-adjoint operators acting on $\\ell^{2}(\\mathbb{Z})$ which are associated with two doubly infinite Jacobi matrices with entries given by $$ q^{-n+1}\\delta_{m,n-1}+q^{-n}\\delta_{m,n+1} $$ and $$ \\delta_{m,n-1}+\\alpha q^{-n}\\delta_{m,n}+\\delta_{m,n+1}, $$ respectively, where $q\\in(0,1)$ and $\\alpha\\in\\mathbb{R}$. As an application, we derive orthogonality relations for the Ramanujan entire function and the third Jackson $q$-Bessel function."},"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":"1605.00393","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2016-05-02T08:49:11Z","cross_cats_sorted":[],"title_canon_sha256":"86de6e0b74fc61bf410babbb64a5866401f2d006244dd711334376cba72dddd6","abstract_canon_sha256":"1b47689bec65bcf5933785eb0d1dee625025ae212864afe78191ab6fb4d0e1eb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:15:55.939674Z","signature_b64":"7sITsN/9bHxDjt8V29IaNHtzVnhms8wqMZv5unnyf3eLHCvQhQjuik7jXnweNIeW3PeKOnoQ9ItJOD7UoijdAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"111304c0bb7a7fa8994ac6a3ce0ccd54225444f7fb79226e01b36c295794a09d","last_reissued_at":"2026-05-18T01:15:55.939031Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:15:55.939031Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Spectral analysis of two doubly infinite Jacobi matrices with exponential entries","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Franti\\v{s}ek \\v{S}tampach, Mourad E. H. Ismail","submitted_at":"2016-05-02T08:49:11Z","abstract_excerpt":"We provide a complete spectral analysis of all self-adjoint operators acting on $\\ell^{2}(\\mathbb{Z})$ which are associated with two doubly infinite Jacobi matrices with entries given by $$ q^{-n+1}\\delta_{m,n-1}+q^{-n}\\delta_{m,n+1} $$ and $$ \\delta_{m,n-1}+\\alpha q^{-n}\\delta_{m,n}+\\delta_{m,n+1}, $$ respectively, where $q\\in(0,1)$ and $\\alpha\\in\\mathbb{R}$. As an application, we derive orthogonality relations for the Ramanujan entire function and the third Jackson $q$-Bessel function."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.00393","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":"1605.00393","created_at":"2026-05-18T01:15:55.939127+00:00"},{"alias_kind":"arxiv_version","alias_value":"1605.00393v1","created_at":"2026-05-18T01:15:55.939127+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.00393","created_at":"2026-05-18T01:15:55.939127+00:00"},{"alias_kind":"pith_short_12","alias_value":"CEJQJQF3PJ72","created_at":"2026-05-18T12:30:09.641336+00:00"},{"alias_kind":"pith_short_16","alias_value":"CEJQJQF3PJ72RGKK","created_at":"2026-05-18T12:30:09.641336+00:00"},{"alias_kind":"pith_short_8","alias_value":"CEJQJQF3","created_at":"2026-05-18T12:30:09.641336+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/CEJQJQF3PJ72RGKKY2R44DGNKQ","json":"https://pith.science/pith/CEJQJQF3PJ72RGKKY2R44DGNKQ.json","graph_json":"https://pith.science/api/pith-number/CEJQJQF3PJ72RGKKY2R44DGNKQ/graph.json","events_json":"https://pith.science/api/pith-number/CEJQJQF3PJ72RGKKY2R44DGNKQ/events.json","paper":"https://pith.science/paper/CEJQJQF3"},"agent_actions":{"view_html":"https://pith.science/pith/CEJQJQF3PJ72RGKKY2R44DGNKQ","download_json":"https://pith.science/pith/CEJQJQF3PJ72RGKKY2R44DGNKQ.json","view_paper":"https://pith.science/paper/CEJQJQF3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1605.00393&json=true","fetch_graph":"https://pith.science/api/pith-number/CEJQJQF3PJ72RGKKY2R44DGNKQ/graph.json","fetch_events":"https://pith.science/api/pith-number/CEJQJQF3PJ72RGKKY2R44DGNKQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CEJQJQF3PJ72RGKKY2R44DGNKQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CEJQJQF3PJ72RGKKY2R44DGNKQ/action/storage_attestation","attest_author":"https://pith.science/pith/CEJQJQF3PJ72RGKKY2R44DGNKQ/action/author_attestation","sign_citation":"https://pith.science/pith/CEJQJQF3PJ72RGKKY2R44DGNKQ/action/citation_signature","submit_replication":"https://pith.science/pith/CEJQJQF3PJ72RGKKY2R44DGNKQ/action/replication_record"}},"created_at":"2026-05-18T01:15:55.939127+00:00","updated_at":"2026-05-18T01:15:55.939127+00:00"}