{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2001:SPF76RPVSOM6ODI7XKLS36KPVZ","short_pith_number":"pith:SPF76RPV","schema_version":"1.0","canonical_sha256":"93cbff45f59399e70d1fba972df94fae491bc5d30f02b05adb59371044fc92c6","source":{"kind":"arxiv","id":"math-ph/0111045","version":1},"attestation_state":"computed","paper":{"title":"Commensurate Harmonic Oscillators: Classical Symmetries","license":"","headline":"","cross_cats":["math.GR","math.MP","quant-ph"],"primary_cat":"math-ph","authors_text":"Jean-Pierre Amiet, Stefan Weigert","submitted_at":"2001-11-22T12:16:11Z","abstract_excerpt":"The symmetry properties of a classical N-dimensional harmonic oscillator with rational frequency ratios are studied from a global point of view. A commensurate oscillator possesses the same number of globally defined constants of motion as an isotropic oscillator. In both cases invariant phase-space functions form the algebra su(N) with respect to the Poisson bracket. In the isotropic case, the phase-space flows generated by the invariants can be integrated globally to a set of finite transformations isomorphic to the group SU(N). For a commensurate oscillator, however, the group SU(N) of symm"},"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/0111045","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math-ph","submitted_at":"2001-11-22T12:16:11Z","cross_cats_sorted":["math.GR","math.MP","quant-ph"],"title_canon_sha256":"06bc971d1de29a77bef412b3d9c58e8644a7969d6a227f97ed1fa9a65af1fd47","abstract_canon_sha256":"73d2eb80d658d80c8c25c610f260b05e4ad0544bd36a3ba9d7b3698b87d91880"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:38:34.400577Z","signature_b64":"dCMrKquqtZvAD6JS03VqrMdWupqkhcoYbmnaeGMkF59F0nrZMfUmZBFcasA8J6petOQtal+jVBlpO1xQnjPGAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"93cbff45f59399e70d1fba972df94fae491bc5d30f02b05adb59371044fc92c6","last_reissued_at":"2026-05-18T01:38:34.400041Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:38:34.400041Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Commensurate Harmonic Oscillators: Classical Symmetries","license":"","headline":"","cross_cats":["math.GR","math.MP","quant-ph"],"primary_cat":"math-ph","authors_text":"Jean-Pierre Amiet, Stefan Weigert","submitted_at":"2001-11-22T12:16:11Z","abstract_excerpt":"The symmetry properties of a classical N-dimensional harmonic oscillator with rational frequency ratios are studied from a global point of view. A commensurate oscillator possesses the same number of globally defined constants of motion as an isotropic oscillator. In both cases invariant phase-space functions form the algebra su(N) with respect to the Poisson bracket. In the isotropic case, the phase-space flows generated by the invariants can be integrated globally to a set of finite transformations isomorphic to the group SU(N). For a commensurate oscillator, however, the group SU(N) of symm"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0111045","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":"math-ph/0111045","created_at":"2026-05-18T01:38:34.400106+00:00"},{"alias_kind":"arxiv_version","alias_value":"math-ph/0111045v1","created_at":"2026-05-18T01:38:34.400106+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/0111045","created_at":"2026-05-18T01:38:34.400106+00:00"},{"alias_kind":"pith_short_12","alias_value":"SPF76RPVSOM6","created_at":"2026-05-18T12:25:50.845339+00:00"},{"alias_kind":"pith_short_16","alias_value":"SPF76RPVSOM6ODI7","created_at":"2026-05-18T12:25:50.845339+00:00"},{"alias_kind":"pith_short_8","alias_value":"SPF76RPV","created_at":"2026-05-18T12:25:50.845339+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/SPF76RPVSOM6ODI7XKLS36KPVZ","json":"https://pith.science/pith/SPF76RPVSOM6ODI7XKLS36KPVZ.json","graph_json":"https://pith.science/api/pith-number/SPF76RPVSOM6ODI7XKLS36KPVZ/graph.json","events_json":"https://pith.science/api/pith-number/SPF76RPVSOM6ODI7XKLS36KPVZ/events.json","paper":"https://pith.science/paper/SPF76RPV"},"agent_actions":{"view_html":"https://pith.science/pith/SPF76RPVSOM6ODI7XKLS36KPVZ","download_json":"https://pith.science/pith/SPF76RPVSOM6ODI7XKLS36KPVZ.json","view_paper":"https://pith.science/paper/SPF76RPV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math-ph/0111045&json=true","fetch_graph":"https://pith.science/api/pith-number/SPF76RPVSOM6ODI7XKLS36KPVZ/graph.json","fetch_events":"https://pith.science/api/pith-number/SPF76RPVSOM6ODI7XKLS36KPVZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SPF76RPVSOM6ODI7XKLS36KPVZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SPF76RPVSOM6ODI7XKLS36KPVZ/action/storage_attestation","attest_author":"https://pith.science/pith/SPF76RPVSOM6ODI7XKLS36KPVZ/action/author_attestation","sign_citation":"https://pith.science/pith/SPF76RPVSOM6ODI7XKLS36KPVZ/action/citation_signature","submit_replication":"https://pith.science/pith/SPF76RPVSOM6ODI7XKLS36KPVZ/action/replication_record"}},"created_at":"2026-05-18T01:38:34.400106+00:00","updated_at":"2026-05-18T01:38:34.400106+00:00"}