{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:4CEL4YDWBFDJYCITCMWLSBEHUQ","short_pith_number":"pith:4CEL4YDW","schema_version":"1.0","canonical_sha256":"e088be607609469c0913132cb90487a423335ba19f540458c72b2165a738e8bb","source":{"kind":"arxiv","id":"2206.12717","version":2},"attestation_state":"computed","paper":{"title":"Higher-order superintegrable momentum-dependent Hamiltonians on curved spaces from the classical Zernike system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","nlin.SI"],"primary_cat":"math-ph","authors_text":"Alfonso Blasco, Francisco J.Herranz, Ivan Gutierrez-Sagredo","submitted_at":"2022-06-25T19:04:13Z","abstract_excerpt":"We consider the classical momentum- or velocity-dependent two-dimensional Hamiltonian given by $$\\mathcal H_N = p_1^2 + p_2^2 +\\sum_{n=1}^N \\gamma_n(q_1 p_1 + q_2 p_2)^n ,$$ where $q_i$ and $p_i$ are generic canonical variables, $\\gamma_n$ are arbitrary coefficients, and $N\\in \\mathbb N$. For $N=2$, being both $\\gamma_1,\\gamma_2$ different from zero, this reduces to the classical Zernike system. We prove that $\\mathcal H_N$ always provides a superintegrable system (for any value of $\\gamma_n$ and $N$) by obtaining the corresponding constants of the motion explicitly, which turn out to be of hi"},"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":"2206.12717","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2022-06-25T19:04:13Z","cross_cats_sorted":["math.MP","nlin.SI"],"title_canon_sha256":"5aa4528ce4c1f8e30d073fa942c8b1fe9a64b5fdeda794fb7022ca1e7fea625d","abstract_canon_sha256":"e885218386765dc7e27d39c9e7c2f5894c906ff480b91bb753ed37d067ce0dd1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:30:43.314731Z","signature_b64":"96NMLn6XHSdeZ+by+QZLc/CSWtbZ3bvE1mMTic4g1KfSrmf9CduFG7yEEQaZ26ot2MijyW3zh/qpv+1VmdxIDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e088be607609469c0913132cb90487a423335ba19f540458c72b2165a738e8bb","last_reissued_at":"2026-07-05T05:30:43.314304Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:30:43.314304Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Higher-order superintegrable momentum-dependent Hamiltonians on curved spaces from the classical Zernike system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","nlin.SI"],"primary_cat":"math-ph","authors_text":"Alfonso Blasco, Francisco J.Herranz, Ivan Gutierrez-Sagredo","submitted_at":"2022-06-25T19:04:13Z","abstract_excerpt":"We consider the classical momentum- or velocity-dependent two-dimensional Hamiltonian given by $$\\mathcal H_N = p_1^2 + p_2^2 +\\sum_{n=1}^N \\gamma_n(q_1 p_1 + q_2 p_2)^n ,$$ where $q_i$ and $p_i$ are generic canonical variables, $\\gamma_n$ are arbitrary coefficients, and $N\\in \\mathbb N$. For $N=2$, being both $\\gamma_1,\\gamma_2$ different from zero, this reduces to the classical Zernike system. We prove that $\\mathcal H_N$ always provides a superintegrable system (for any value of $\\gamma_n$ and $N$) by obtaining the corresponding constants of the motion explicitly, which turn out to be of hi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2206.12717","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2206.12717/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2206.12717","created_at":"2026-07-05T05:30:43.314365+00:00"},{"alias_kind":"arxiv_version","alias_value":"2206.12717v2","created_at":"2026-07-05T05:30:43.314365+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2206.12717","created_at":"2026-07-05T05:30:43.314365+00:00"},{"alias_kind":"pith_short_12","alias_value":"4CEL4YDWBFDJ","created_at":"2026-07-05T05:30:43.314365+00:00"},{"alias_kind":"pith_short_16","alias_value":"4CEL4YDWBFDJYCIT","created_at":"2026-07-05T05:30:43.314365+00:00"},{"alias_kind":"pith_short_8","alias_value":"4CEL4YDW","created_at":"2026-07-05T05:30:43.314365+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2507.12051","citing_title":"Integrable systems from Poisson reductions of generalized Hamiltonian torus actions","ref_index":7,"is_internal_anchor":false},{"citing_arxiv_id":"2507.12051","citing_title":"Integrable systems from Poisson reductions of generalized Hamiltonian torus actions","ref_index":7,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/4CEL4YDWBFDJYCITCMWLSBEHUQ","json":"https://pith.science/pith/4CEL4YDWBFDJYCITCMWLSBEHUQ.json","graph_json":"https://pith.science/api/pith-number/4CEL4YDWBFDJYCITCMWLSBEHUQ/graph.json","events_json":"https://pith.science/api/pith-number/4CEL4YDWBFDJYCITCMWLSBEHUQ/events.json","paper":"https://pith.science/paper/4CEL4YDW"},"agent_actions":{"view_html":"https://pith.science/pith/4CEL4YDWBFDJYCITCMWLSBEHUQ","download_json":"https://pith.science/pith/4CEL4YDWBFDJYCITCMWLSBEHUQ.json","view_paper":"https://pith.science/paper/4CEL4YDW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2206.12717&json=true","fetch_graph":"https://pith.science/api/pith-number/4CEL4YDWBFDJYCITCMWLSBEHUQ/graph.json","fetch_events":"https://pith.science/api/pith-number/4CEL4YDWBFDJYCITCMWLSBEHUQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4CEL4YDWBFDJYCITCMWLSBEHUQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4CEL4YDWBFDJYCITCMWLSBEHUQ/action/storage_attestation","attest_author":"https://pith.science/pith/4CEL4YDWBFDJYCITCMWLSBEHUQ/action/author_attestation","sign_citation":"https://pith.science/pith/4CEL4YDWBFDJYCITCMWLSBEHUQ/action/citation_signature","submit_replication":"https://pith.science/pith/4CEL4YDWBFDJYCITCMWLSBEHUQ/action/replication_record"}},"created_at":"2026-07-05T05:30:43.314365+00:00","updated_at":"2026-07-05T05:30:43.314365+00:00"}