{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2008:LMKHXMJEHUOWXRFKRR5HYXWJZT","short_pith_number":"pith:LMKHXMJE","schema_version":"1.0","canonical_sha256":"5b147bb1243d1d6bc4aa8c7a7c5ec9ccc5230ae95fcdb0f68112c9fb5bcdd6f6","source":{"kind":"arxiv","id":"0809.0135","version":2},"attestation_state":"computed","paper":{"title":"On Hamiltonian potentials with quartic polynomial normal variational equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Camilo Vargas Contreras, David Blazquez-Sanz, Primitivo B. Acosta-Humanez","submitted_at":"2008-08-31T16:29:07Z","abstract_excerpt":"In this paper we prove that there exists only one family of classical Hamiltonian systems of two degrees of freedom with invariant plane $\\Gamma=\\{q_2=p_2=0\\}$ whose normal variational equation around integral curves in $\\Gamma$ is generically a Hill-Schr\\\"odinger equation with quartic polynomial potential. In particular, by means of the Morales-Ramis theory, these Hamiltonian systems are non-integrable through rational first integrals."},"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":"0809.0135","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2008-08-31T16:29:07Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"15cb22a89e0c318345b8814a3d4105e367e68ba65a9c7508a68dac653f58b43d","abstract_canon_sha256":"a1edd05914d6156a683abbbc22512ad6e353e4c7989fb9323a0c68fe4f923aa3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:01:23.885304Z","signature_b64":"TKxuVXe08hPxzWeMguecjct1t03l/n7taESjHmGiA3/FijgszZZGVVakmCaMJiIqrsjWugFLhhUwssmRS2XKBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5b147bb1243d1d6bc4aa8c7a7c5ec9ccc5230ae95fcdb0f68112c9fb5bcdd6f6","last_reissued_at":"2026-05-18T04:01:23.884582Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:01:23.884582Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Hamiltonian potentials with quartic polynomial normal variational equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Camilo Vargas Contreras, David Blazquez-Sanz, Primitivo B. Acosta-Humanez","submitted_at":"2008-08-31T16:29:07Z","abstract_excerpt":"In this paper we prove that there exists only one family of classical Hamiltonian systems of two degrees of freedom with invariant plane $\\Gamma=\\{q_2=p_2=0\\}$ whose normal variational equation around integral curves in $\\Gamma$ is generically a Hill-Schr\\\"odinger equation with quartic polynomial potential. In particular, by means of the Morales-Ramis theory, these Hamiltonian systems are non-integrable through rational first integrals."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0809.0135","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":"0809.0135","created_at":"2026-05-18T04:01:23.884695+00:00"},{"alias_kind":"arxiv_version","alias_value":"0809.0135v2","created_at":"2026-05-18T04:01:23.884695+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0809.0135","created_at":"2026-05-18T04:01:23.884695+00:00"},{"alias_kind":"pith_short_12","alias_value":"LMKHXMJEHUOW","created_at":"2026-05-18T12:25:57.157939+00:00"},{"alias_kind":"pith_short_16","alias_value":"LMKHXMJEHUOWXRFK","created_at":"2026-05-18T12:25:57.157939+00:00"},{"alias_kind":"pith_short_8","alias_value":"LMKHXMJE","created_at":"2026-05-18T12:25:57.157939+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/LMKHXMJEHUOWXRFKRR5HYXWJZT","json":"https://pith.science/pith/LMKHXMJEHUOWXRFKRR5HYXWJZT.json","graph_json":"https://pith.science/api/pith-number/LMKHXMJEHUOWXRFKRR5HYXWJZT/graph.json","events_json":"https://pith.science/api/pith-number/LMKHXMJEHUOWXRFKRR5HYXWJZT/events.json","paper":"https://pith.science/paper/LMKHXMJE"},"agent_actions":{"view_html":"https://pith.science/pith/LMKHXMJEHUOWXRFKRR5HYXWJZT","download_json":"https://pith.science/pith/LMKHXMJEHUOWXRFKRR5HYXWJZT.json","view_paper":"https://pith.science/paper/LMKHXMJE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0809.0135&json=true","fetch_graph":"https://pith.science/api/pith-number/LMKHXMJEHUOWXRFKRR5HYXWJZT/graph.json","fetch_events":"https://pith.science/api/pith-number/LMKHXMJEHUOWXRFKRR5HYXWJZT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LMKHXMJEHUOWXRFKRR5HYXWJZT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LMKHXMJEHUOWXRFKRR5HYXWJZT/action/storage_attestation","attest_author":"https://pith.science/pith/LMKHXMJEHUOWXRFKRR5HYXWJZT/action/author_attestation","sign_citation":"https://pith.science/pith/LMKHXMJEHUOWXRFKRR5HYXWJZT/action/citation_signature","submit_replication":"https://pith.science/pith/LMKHXMJEHUOWXRFKRR5HYXWJZT/action/replication_record"}},"created_at":"2026-05-18T04:01:23.884695+00:00","updated_at":"2026-05-18T04:01:23.884695+00:00"}