{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:N7JUT6ZRLKJGNGYADD7O4A22LU","short_pith_number":"pith:N7JUT6ZR","schema_version":"1.0","canonical_sha256":"6fd349fb315a92669b0018feee035a5d1715f5b931753d50ab06e1b679547bc6","source":{"kind":"arxiv","id":"1603.01052","version":2},"attestation_state":"computed","paper":{"title":"Spectral analysis of non-self-adjoint Jacobi operator associated with Jacobian elliptic functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.FA","math.MP"],"primary_cat":"math.SP","authors_text":"Franti\\v{s}ek \\v{S}tampach, Petr Siegl","submitted_at":"2016-03-03T11:00:29Z","abstract_excerpt":"We perform the spectral analysis of a family of Jacobi operators $J(\\alpha)$ depending on a complex parameter $\\alpha$. If $|\\alpha|\\neq1$ the spectrum of $J(\\alpha)$ is discrete and formulas for eigenvalues and eigenvectors are established in terms of elliptic integrals and Jacobian elliptic functions. If $|\\alpha|=1$, $\\alpha \\neq \\pm 1$, the essential spectrum of $J(\\alpha)$ covers the entire complex plane. In addition, a formula for the Weyl $m$-function as well as the asymptotic expansions of solutions of the difference equation corresponding to $J(\\alpha)$ are obtained. Finally, the comp"},"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":"1603.01052","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2016-03-03T11:00:29Z","cross_cats_sorted":["math-ph","math.FA","math.MP"],"title_canon_sha256":"83e4302e666858679f7c29ecff54e3c688c3b857ea66e5e652593c077ea583fb","abstract_canon_sha256":"ad201e100c73be28b14b0d044f3c817e9ba6855a3fc5ab37087df9367c4d0a54"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:51:28.340675Z","signature_b64":"Svmzim1U6z2/OqLA+7bdZi/91aPnG5pkLl76rTiT2GXoexGxohlSMTRrWFN27ByG6aUKJmKInh06JIEOHhBJCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6fd349fb315a92669b0018feee035a5d1715f5b931753d50ab06e1b679547bc6","last_reissued_at":"2026-05-18T00:51:28.339979Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:51:28.339979Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Spectral analysis of non-self-adjoint Jacobi operator associated with Jacobian elliptic functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.FA","math.MP"],"primary_cat":"math.SP","authors_text":"Franti\\v{s}ek \\v{S}tampach, Petr Siegl","submitted_at":"2016-03-03T11:00:29Z","abstract_excerpt":"We perform the spectral analysis of a family of Jacobi operators $J(\\alpha)$ depending on a complex parameter $\\alpha$. If $|\\alpha|\\neq1$ the spectrum of $J(\\alpha)$ is discrete and formulas for eigenvalues and eigenvectors are established in terms of elliptic integrals and Jacobian elliptic functions. If $|\\alpha|=1$, $\\alpha \\neq \\pm 1$, the essential spectrum of $J(\\alpha)$ covers the entire complex plane. In addition, a formula for the Weyl $m$-function as well as the asymptotic expansions of solutions of the difference equation corresponding to $J(\\alpha)$ are obtained. Finally, the comp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.01052","kind":"arxiv","version":2},"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":"1603.01052","created_at":"2026-05-18T00:51:28.340075+00:00"},{"alias_kind":"arxiv_version","alias_value":"1603.01052v2","created_at":"2026-05-18T00:51:28.340075+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.01052","created_at":"2026-05-18T00:51:28.340075+00:00"},{"alias_kind":"pith_short_12","alias_value":"N7JUT6ZRLKJG","created_at":"2026-05-18T12:30:32.724797+00:00"},{"alias_kind":"pith_short_16","alias_value":"N7JUT6ZRLKJGNGYA","created_at":"2026-05-18T12:30:32.724797+00:00"},{"alias_kind":"pith_short_8","alias_value":"N7JUT6ZR","created_at":"2026-05-18T12:30:32.724797+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/N7JUT6ZRLKJGNGYADD7O4A22LU","json":"https://pith.science/pith/N7JUT6ZRLKJGNGYADD7O4A22LU.json","graph_json":"https://pith.science/api/pith-number/N7JUT6ZRLKJGNGYADD7O4A22LU/graph.json","events_json":"https://pith.science/api/pith-number/N7JUT6ZRLKJGNGYADD7O4A22LU/events.json","paper":"https://pith.science/paper/N7JUT6ZR"},"agent_actions":{"view_html":"https://pith.science/pith/N7JUT6ZRLKJGNGYADD7O4A22LU","download_json":"https://pith.science/pith/N7JUT6ZRLKJGNGYADD7O4A22LU.json","view_paper":"https://pith.science/paper/N7JUT6ZR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1603.01052&json=true","fetch_graph":"https://pith.science/api/pith-number/N7JUT6ZRLKJGNGYADD7O4A22LU/graph.json","fetch_events":"https://pith.science/api/pith-number/N7JUT6ZRLKJGNGYADD7O4A22LU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/N7JUT6ZRLKJGNGYADD7O4A22LU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/N7JUT6ZRLKJGNGYADD7O4A22LU/action/storage_attestation","attest_author":"https://pith.science/pith/N7JUT6ZRLKJGNGYADD7O4A22LU/action/author_attestation","sign_citation":"https://pith.science/pith/N7JUT6ZRLKJGNGYADD7O4A22LU/action/citation_signature","submit_replication":"https://pith.science/pith/N7JUT6ZRLKJGNGYADD7O4A22LU/action/replication_record"}},"created_at":"2026-05-18T00:51:28.340075+00:00","updated_at":"2026-05-18T00:51:28.340075+00:00"}