{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:AB4AXQBNTEW4HDEKPE4TQ3GAKR","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":"1877e0bed55b26aed32e347ac55cf1fe6d122e33f5ca86656fd3cd0973c7f13a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-09-14T11:19:56Z","title_canon_sha256":"46c5022e69a5dd6cd8730863ac205bd9dde122c75778a7ed7136545bf4bfa62d"},"schema_version":"1.0","source":{"id":"1709.04705","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.04705","created_at":"2026-05-18T00:35:10Z"},{"alias_kind":"arxiv_version","alias_value":"1709.04705v1","created_at":"2026-05-18T00:35:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.04705","created_at":"2026-05-18T00:35:10Z"},{"alias_kind":"pith_short_12","alias_value":"AB4AXQBNTEW4","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_16","alias_value":"AB4AXQBNTEW4HDEK","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_8","alias_value":"AB4AXQBN","created_at":"2026-05-18T12:31:05Z"}],"graph_snapshots":[{"event_id":"sha256:4c04b728f3d829a593bcabf29eaf92aca0fea33a89fd1fd4501ce8f57c630973","target":"graph","created_at":"2026-05-18T00:35:10Z","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":"It is well known that functions in involution with respect to Poisson brackets have a privileged role in the theory of completely integrable systems. Finding functionally independent functions in involution with a given function $h$ on a Poisson manifold is a fundamental problem of this theory and is very useful for the explicit integration of the equations of motion defined by $h$. In this paper, we present our results on the study of the inverse, so to speak, problem. By developing a technique analogous to that presented in P. Damianou and F. Petalidou, Poisson brackets with prescribed Casim","authors_text":"Fani Petalidou","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-09-14T11:19:56Z","title":"Poisson brackets with prescribed family of functions in involution"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.04705","kind":"arxiv","version":1},"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":"sha256:09b8480ef02a141e24b527fec056fb584a3f752fbe2604a068c61c67a3e34fb5","target":"record","created_at":"2026-05-18T00:35:10Z","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":"1877e0bed55b26aed32e347ac55cf1fe6d122e33f5ca86656fd3cd0973c7f13a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-09-14T11:19:56Z","title_canon_sha256":"46c5022e69a5dd6cd8730863ac205bd9dde122c75778a7ed7136545bf4bfa62d"},"schema_version":"1.0","source":{"id":"1709.04705","kind":"arxiv","version":1}},"canonical_sha256":"00780bc02d992dc38c8a7939386cc054633f683e6f34ba368aaa281a0972a56f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"00780bc02d992dc38c8a7939386cc054633f683e6f34ba368aaa281a0972a56f","first_computed_at":"2026-05-18T00:35:10.372240Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:35:10.372240Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3Gqui9UXJMxTKnxHf7UAY/k6/mIAoCcJQWRe1nQw+m/5wW+Lz1HH93k9t6vQ5imUFSTA+/NEact+SCv1pijhCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:35:10.372670Z","signed_message":"canonical_sha256_bytes"},"source_id":"1709.04705","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:09b8480ef02a141e24b527fec056fb584a3f752fbe2604a068c61c67a3e34fb5","sha256:4c04b728f3d829a593bcabf29eaf92aca0fea33a89fd1fd4501ce8f57c630973"],"state_sha256":"df5a5a9eaa0aa13f246a45e3ac90aa79b634d054c85d352fd4e19bd5d6907a0a"}