{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:3DNTBP4V25XNIBRR6KBVYK2AQ7","short_pith_number":"pith:3DNTBP4V","schema_version":"1.0","canonical_sha256":"d8db30bf95d76ed40631f2835c2b4087e3a4552a3e6f12c79dc4f0819334ecf6","source":{"kind":"arxiv","id":"1411.2033","version":2},"attestation_state":"computed","paper":{"title":"An integrable Henon-Heiles system on the sphere and the hyperbolic plane","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"nlin.SI","authors_text":"Alfonso Blasco, Angel Ballesteros, Fabio Musso, Francisco J. Herranz","submitted_at":"2014-11-07T21:11:01Z","abstract_excerpt":"We construct a constant curvature analogue on the two-dimensional sphere ${\\mathbf S}^2$ and the hyperbolic space ${\\mathbf H}^2$ of the integrable H\\'enon-Heiles Hamiltonian $\\mathcal{H}$ given by $$ \\mathcal{H}=\\dfrac{1}{2}(p_{1}^{2}+p_{2}^{2})+ \\Omega \\left( q_{1}^{2}+ 4 q_{2}^{2}\\right) +\\alpha \\left( q_{1}^{2}q_{2}+2 q_{2}^{3}\\right) , $$ where $\\Omega$ and $\\alpha$ are real constants. The curved integrable Hamiltonian $\\mathcal{H}_\\kappa$ so obtained depends on a parameter $\\kappa$ which is just the curvature of the underlying space, and is such that the Euclidean H\\'enon-Heiles system $"},"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":"1411.2033","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2014-11-07T21:11:01Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"5f26cae2959b4ddb7e1df0ddf5ff9f3e099a336d237a4f86f8954c021c18c872","abstract_canon_sha256":"10650ba480a1eb37b70d3824809e139d748a059bb56aee12619b3840c17598d5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:31:21.404635Z","signature_b64":"tnmOqxRN/7l/upoAsAJWOM+Ytuit8t1Az1QFU/p66PpOY2PP7DIYfg+9wQ/yUuz+P3U85djur3fe3tpyg9O0Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d8db30bf95d76ed40631f2835c2b4087e3a4552a3e6f12c79dc4f0819334ecf6","last_reissued_at":"2026-05-18T01:31:21.403972Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:31:21.403972Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An integrable Henon-Heiles system on the sphere and the hyperbolic plane","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"nlin.SI","authors_text":"Alfonso Blasco, Angel Ballesteros, Fabio Musso, Francisco J. Herranz","submitted_at":"2014-11-07T21:11:01Z","abstract_excerpt":"We construct a constant curvature analogue on the two-dimensional sphere ${\\mathbf S}^2$ and the hyperbolic space ${\\mathbf H}^2$ of the integrable H\\'enon-Heiles Hamiltonian $\\mathcal{H}$ given by $$ \\mathcal{H}=\\dfrac{1}{2}(p_{1}^{2}+p_{2}^{2})+ \\Omega \\left( q_{1}^{2}+ 4 q_{2}^{2}\\right) +\\alpha \\left( q_{1}^{2}q_{2}+2 q_{2}^{3}\\right) , $$ where $\\Omega$ and $\\alpha$ are real constants. The curved integrable Hamiltonian $\\mathcal{H}_\\kappa$ so obtained depends on a parameter $\\kappa$ which is just the curvature of the underlying space, and is such that the Euclidean H\\'enon-Heiles system $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.2033","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":"1411.2033","created_at":"2026-05-18T01:31:21.404073+00:00"},{"alias_kind":"arxiv_version","alias_value":"1411.2033v2","created_at":"2026-05-18T01:31:21.404073+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.2033","created_at":"2026-05-18T01:31:21.404073+00:00"},{"alias_kind":"pith_short_12","alias_value":"3DNTBP4V25XN","created_at":"2026-05-18T12:28:11.866339+00:00"},{"alias_kind":"pith_short_16","alias_value":"3DNTBP4V25XNIBRR","created_at":"2026-05-18T12:28:11.866339+00:00"},{"alias_kind":"pith_short_8","alias_value":"3DNTBP4V","created_at":"2026-05-18T12:28:11.866339+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/3DNTBP4V25XNIBRR6KBVYK2AQ7","json":"https://pith.science/pith/3DNTBP4V25XNIBRR6KBVYK2AQ7.json","graph_json":"https://pith.science/api/pith-number/3DNTBP4V25XNIBRR6KBVYK2AQ7/graph.json","events_json":"https://pith.science/api/pith-number/3DNTBP4V25XNIBRR6KBVYK2AQ7/events.json","paper":"https://pith.science/paper/3DNTBP4V"},"agent_actions":{"view_html":"https://pith.science/pith/3DNTBP4V25XNIBRR6KBVYK2AQ7","download_json":"https://pith.science/pith/3DNTBP4V25XNIBRR6KBVYK2AQ7.json","view_paper":"https://pith.science/paper/3DNTBP4V","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1411.2033&json=true","fetch_graph":"https://pith.science/api/pith-number/3DNTBP4V25XNIBRR6KBVYK2AQ7/graph.json","fetch_events":"https://pith.science/api/pith-number/3DNTBP4V25XNIBRR6KBVYK2AQ7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3DNTBP4V25XNIBRR6KBVYK2AQ7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3DNTBP4V25XNIBRR6KBVYK2AQ7/action/storage_attestation","attest_author":"https://pith.science/pith/3DNTBP4V25XNIBRR6KBVYK2AQ7/action/author_attestation","sign_citation":"https://pith.science/pith/3DNTBP4V25XNIBRR6KBVYK2AQ7/action/citation_signature","submit_replication":"https://pith.science/pith/3DNTBP4V25XNIBRR6KBVYK2AQ7/action/replication_record"}},"created_at":"2026-05-18T01:31:21.404073+00:00","updated_at":"2026-05-18T01:31:21.404073+00:00"}