{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2002:UUFLT4YZHEDF55X2BHY4GFSO37","short_pith_number":"pith:UUFLT4YZ","schema_version":"1.0","canonical_sha256":"a50ab9f31939065ef6fa09f1c3164edff9794752305c35a5ccc45e62dd722e33","source":{"kind":"arxiv","id":"math-ph/0207038","version":6},"attestation_state":"computed","paper":{"title":"The discretised harmonic oscillator: Mathieu functions and a new class of generalised Hermite polynomials","license":"","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"M. Aunola","submitted_at":"2002-07-26T12:27:25Z","abstract_excerpt":"We present a general, asymptotical solution for the discretised harmonic oscillator. The corresponding Schr\\\"odinger equation is canonically conjugate to the Mathieu differential equation, the Schr\\\"odinger equation of the quantum pendulum. Thus, in addition to giving an explicit solution for the Hamiltonian of an isolated Josephon junction or a superconducting single-electron transistor (SSET), we obtain an asymptotical representation of Mathieu functions. We solve the discretised harmonic oscillator by transforming the infinite-dimensional matrix-eigenvalue problem into an infinite set of al"},"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":"math-ph/0207038","kind":"arxiv","version":6},"metadata":{"license":"","primary_cat":"math-ph","submitted_at":"2002-07-26T12:27:25Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"b53f0eac038f6c8c8f14435c2910a42dfe2352c9ee86b7b62328ef20b6dbaa1f","abstract_canon_sha256":"1f0c51122966d7d341682b41535962ea655b084c26241df99762e29c0ff55def"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:38:34.127985Z","signature_b64":"R6llcJHy6spm8/m6k8nZdYkXKJcvvkc4R7moT+89BkBU5CUqUX/9klCBV1FsitdbbGwtHYD/+fjmW6BGheYHAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a50ab9f31939065ef6fa09f1c3164edff9794752305c35a5ccc45e62dd722e33","last_reissued_at":"2026-05-18T01:38:34.127406Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:38:34.127406Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The discretised harmonic oscillator: Mathieu functions and a new class of generalised Hermite polynomials","license":"","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"M. Aunola","submitted_at":"2002-07-26T12:27:25Z","abstract_excerpt":"We present a general, asymptotical solution for the discretised harmonic oscillator. The corresponding Schr\\\"odinger equation is canonically conjugate to the Mathieu differential equation, the Schr\\\"odinger equation of the quantum pendulum. Thus, in addition to giving an explicit solution for the Hamiltonian of an isolated Josephon junction or a superconducting single-electron transistor (SSET), we obtain an asymptotical representation of Mathieu functions. We solve the discretised harmonic oscillator by transforming the infinite-dimensional matrix-eigenvalue problem into an infinite set of al"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0207038","kind":"arxiv","version":6},"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":"math-ph/0207038","created_at":"2026-05-18T01:38:34.127487+00:00"},{"alias_kind":"arxiv_version","alias_value":"math-ph/0207038v6","created_at":"2026-05-18T01:38:34.127487+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/0207038","created_at":"2026-05-18T01:38:34.127487+00:00"},{"alias_kind":"pith_short_12","alias_value":"UUFLT4YZHEDF","created_at":"2026-05-18T12:25:51.375804+00:00"},{"alias_kind":"pith_short_16","alias_value":"UUFLT4YZHEDF55X2","created_at":"2026-05-18T12:25:51.375804+00:00"},{"alias_kind":"pith_short_8","alias_value":"UUFLT4YZ","created_at":"2026-05-18T12:25:51.375804+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/UUFLT4YZHEDF55X2BHY4GFSO37","json":"https://pith.science/pith/UUFLT4YZHEDF55X2BHY4GFSO37.json","graph_json":"https://pith.science/api/pith-number/UUFLT4YZHEDF55X2BHY4GFSO37/graph.json","events_json":"https://pith.science/api/pith-number/UUFLT4YZHEDF55X2BHY4GFSO37/events.json","paper":"https://pith.science/paper/UUFLT4YZ"},"agent_actions":{"view_html":"https://pith.science/pith/UUFLT4YZHEDF55X2BHY4GFSO37","download_json":"https://pith.science/pith/UUFLT4YZHEDF55X2BHY4GFSO37.json","view_paper":"https://pith.science/paper/UUFLT4YZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math-ph/0207038&json=true","fetch_graph":"https://pith.science/api/pith-number/UUFLT4YZHEDF55X2BHY4GFSO37/graph.json","fetch_events":"https://pith.science/api/pith-number/UUFLT4YZHEDF55X2BHY4GFSO37/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UUFLT4YZHEDF55X2BHY4GFSO37/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UUFLT4YZHEDF55X2BHY4GFSO37/action/storage_attestation","attest_author":"https://pith.science/pith/UUFLT4YZHEDF55X2BHY4GFSO37/action/author_attestation","sign_citation":"https://pith.science/pith/UUFLT4YZHEDF55X2BHY4GFSO37/action/citation_signature","submit_replication":"https://pith.science/pith/UUFLT4YZHEDF55X2BHY4GFSO37/action/replication_record"}},"created_at":"2026-05-18T01:38:34.127487+00:00","updated_at":"2026-05-18T01:38:34.127487+00:00"}