{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:7XM3YAOHVDYUM5OOZMOCSUMS66","short_pith_number":"pith:7XM3YAOH","schema_version":"1.0","canonical_sha256":"fdd9bc01c7a8f14675cecb1c295192f7a2e6101356a0a89c31c2721eeb080942","source":{"kind":"arxiv","id":"1802.00831","version":1},"attestation_state":"computed","paper":{"title":"Commuting planar polynomial vector fields for conservative Newton systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC","math.CA","math.RA"],"primary_cat":"math.DS","authors_text":"Alexey Ovchinnikov, Joel Nagloo, Peter Thompson","submitted_at":"2018-02-02T19:54:33Z","abstract_excerpt":"We study the problem of characterizing polynomial vector fields that commute with a given polynomial vector field on a plane. It is a classical result that one can write down solution formulas for an ODE that corresponds to a planar vector field that possesses a linearly independent commuting vector field. This problem is also central to the question of linearizability of vector fields. Let $f \\in K[x]$, where $K$ is a field of characteristic zero, and $d$ the derivation that corresponds to the differential equation $\\ddot x = f(x)$ in a standard way. Let also $H$ be the Hamiltonian polynomial"},"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":"1802.00831","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-02-02T19:54:33Z","cross_cats_sorted":["math.AC","math.CA","math.RA"],"title_canon_sha256":"d7c76fd0bc29c06381096e6e2cb4a1a29f82c0a8ca297b06f908cb0186bfb9f9","abstract_canon_sha256":"607e196a5309435fe98d6b5fdd9ddc8432e5f0f7971751fdc4de43d71f0115d7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:51:35.256655Z","signature_b64":"14vcCa3andKRXrXiEnhZzPHqtwSVxfb6vrD6/6xazRcNLiX3eztrZECaSQiK9F4DviKyRLIR02RqhbDQb/+qDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fdd9bc01c7a8f14675cecb1c295192f7a2e6101356a0a89c31c2721eeb080942","last_reissued_at":"2026-07-05T01:51:35.256302Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:51:35.256302Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Commuting planar polynomial vector fields for conservative Newton systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC","math.CA","math.RA"],"primary_cat":"math.DS","authors_text":"Alexey Ovchinnikov, Joel Nagloo, Peter Thompson","submitted_at":"2018-02-02T19:54:33Z","abstract_excerpt":"We study the problem of characterizing polynomial vector fields that commute with a given polynomial vector field on a plane. It is a classical result that one can write down solution formulas for an ODE that corresponds to a planar vector field that possesses a linearly independent commuting vector field. This problem is also central to the question of linearizability of vector fields. Let $f \\in K[x]$, where $K$ is a field of characteristic zero, and $d$ the derivation that corresponds to the differential equation $\\ddot x = f(x)$ in a standard way. Let also $H$ be the Hamiltonian polynomial"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.00831","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1802.00831/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":"1802.00831","created_at":"2026-07-05T01:51:35.256368+00:00"},{"alias_kind":"arxiv_version","alias_value":"1802.00831v1","created_at":"2026-07-05T01:51:35.256368+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.00831","created_at":"2026-07-05T01:51:35.256368+00:00"},{"alias_kind":"pith_short_12","alias_value":"7XM3YAOHVDYU","created_at":"2026-07-05T01:51:35.256368+00:00"},{"alias_kind":"pith_short_16","alias_value":"7XM3YAOHVDYUM5OO","created_at":"2026-07-05T01:51:35.256368+00:00"},{"alias_kind":"pith_short_8","alias_value":"7XM3YAOH","created_at":"2026-07-05T01:51:35.256368+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/7XM3YAOHVDYUM5OOZMOCSUMS66","json":"https://pith.science/pith/7XM3YAOHVDYUM5OOZMOCSUMS66.json","graph_json":"https://pith.science/api/pith-number/7XM3YAOHVDYUM5OOZMOCSUMS66/graph.json","events_json":"https://pith.science/api/pith-number/7XM3YAOHVDYUM5OOZMOCSUMS66/events.json","paper":"https://pith.science/paper/7XM3YAOH"},"agent_actions":{"view_html":"https://pith.science/pith/7XM3YAOHVDYUM5OOZMOCSUMS66","download_json":"https://pith.science/pith/7XM3YAOHVDYUM5OOZMOCSUMS66.json","view_paper":"https://pith.science/paper/7XM3YAOH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1802.00831&json=true","fetch_graph":"https://pith.science/api/pith-number/7XM3YAOHVDYUM5OOZMOCSUMS66/graph.json","fetch_events":"https://pith.science/api/pith-number/7XM3YAOHVDYUM5OOZMOCSUMS66/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7XM3YAOHVDYUM5OOZMOCSUMS66/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7XM3YAOHVDYUM5OOZMOCSUMS66/action/storage_attestation","attest_author":"https://pith.science/pith/7XM3YAOHVDYUM5OOZMOCSUMS66/action/author_attestation","sign_citation":"https://pith.science/pith/7XM3YAOHVDYUM5OOZMOCSUMS66/action/citation_signature","submit_replication":"https://pith.science/pith/7XM3YAOHVDYUM5OOZMOCSUMS66/action/replication_record"}},"created_at":"2026-07-05T01:51:35.256368+00:00","updated_at":"2026-07-05T01:51:35.256368+00:00"}