{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:TKO5RW5HMCTX2CGBQTZMEI4E52","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"9813a533fab06720f9dd9d819d759eb50433a4d30e187d953afaecbc9cc2177f","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-09-20T12:05:11Z","title_canon_sha256":"41d5d8a7786b98a3c53bfa46b0f912ddb168ce2d0849615bb5502f4c1122cef8"},"schema_version":"1.0","source":{"id":"1109.4274","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.4274","created_at":"2026-05-18T03:59:36Z"},{"alias_kind":"arxiv_version","alias_value":"1109.4274v2","created_at":"2026-05-18T03:59:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.4274","created_at":"2026-05-18T03:59:36Z"},{"alias_kind":"pith_short_12","alias_value":"TKO5RW5HMCTX","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"TKO5RW5HMCTX2CGB","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"TKO5RW5H","created_at":"2026-05-18T12:26:42Z"}],"graph_snapshots":[{"event_id":"sha256:6fc76af723fb404eaa4568fd7729adc074e8c37a359e168f704b6ba994740642","target":"graph","created_at":"2026-05-18T03:59:36Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"This is a continuation of the work initiated in a previous paper on so-called driven cofactor systems, which are partially decoupling second-order differential equations of a special kind. The main purpose in that paper was to obtain an intrinsic, geometrical characterization of such systems, and to explain the basic underlying concepts in a brief note. In the present paper we address the more intricate part of the theory. It involves in the first place understanding all details of an algorithmic construction of quadratic integrals and their involutivity. It secondly requires explaining the su","authors_text":"G. Waeyaert, W. Sarlet","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-09-20T12:05:11Z","title":"Driven cofactor systems and Hamilton-Jacobi separability"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.4274","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:236ddd584abfd9da640bf05248e58ef677195181fcdefe79f19378f1b38803a2","target":"record","created_at":"2026-05-18T03:59:36Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"9813a533fab06720f9dd9d819d759eb50433a4d30e187d953afaecbc9cc2177f","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-09-20T12:05:11Z","title_canon_sha256":"41d5d8a7786b98a3c53bfa46b0f912ddb168ce2d0849615bb5502f4c1122cef8"},"schema_version":"1.0","source":{"id":"1109.4274","kind":"arxiv","version":2}},"canonical_sha256":"9a9dd8dba760a77d08c184f2c22384ee87cdd68728f42c77a4d5dc7c9acafcdc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9a9dd8dba760a77d08c184f2c22384ee87cdd68728f42c77a4d5dc7c9acafcdc","first_computed_at":"2026-05-18T03:59:36.577814Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:59:36.577814Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8nv4UM9zuhqvzhJr3yaEh1qGFyjFuW2DkHk1Gysv1arD3H+jumJ2i1PltTjhrz0qpl075u9y2WiaJOEUSmf4AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:59:36.578271Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.4274","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:236ddd584abfd9da640bf05248e58ef677195181fcdefe79f19378f1b38803a2","sha256:6fc76af723fb404eaa4568fd7729adc074e8c37a359e168f704b6ba994740642"],"state_sha256":"66e404bd06d5108aa7e3a237a1c115d6d9e3d7014e69ea14765876531206f19e"}