{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:VU6XNNMHZPAVDWGEA7YMWMMC57","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":"b84aadd7c5e773212ef2658d604425dbf4a3d58a9d95cd3921618bb3a7f23ed9","cross_cats_sorted":["math-ph","math.MP","math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-09-18T16:01:59Z","title_canon_sha256":"022c788158bf40267ec88733b78aed927649688c1bf63fff6a5d9a14354602db"},"schema_version":"1.0","source":{"id":"1209.4003","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.4003","created_at":"2026-05-18T03:45:22Z"},{"alias_kind":"arxiv_version","alias_value":"1209.4003v1","created_at":"2026-05-18T03:45:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.4003","created_at":"2026-05-18T03:45:22Z"},{"alias_kind":"pith_short_12","alias_value":"VU6XNNMHZPAV","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_16","alias_value":"VU6XNNMHZPAVDWGE","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_8","alias_value":"VU6XNNMH","created_at":"2026-05-18T12:27:25Z"}],"graph_snapshots":[{"event_id":"sha256:c39e77778d22eb6bf4d19d787a03c725a8ea4eceab8e531b6b63ffb0a0f42dc9","target":"graph","created_at":"2026-05-18T03:45:22Z","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":"In this paper we introduce poly-Poisson structures as a higher-order extension of Poisson structures. It is shown that any poly-Poisson structure is endowed with a polysymplectic foliation. It is also proved that if a Lie group acts polysymplectically on a polysymplectic manifold then, under certain regularity conditions, the reduced space is a poly-Poisson manifold. In addition, some interesting examples of poly-Poisson manifolds are discussed.","authors_text":"D. Iglesias-Ponte, J.C. Marrero, M. Vaquero","cross_cats":["math-ph","math.MP","math.SG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-09-18T16:01:59Z","title":"Poly-Poisson structures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.4003","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":"sha256:4d9d0bc7ca87c93e1c310f4c4593f65205012a231016a0414a0de254ec6af879","target":"record","created_at":"2026-05-18T03:45:22Z","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":"b84aadd7c5e773212ef2658d604425dbf4a3d58a9d95cd3921618bb3a7f23ed9","cross_cats_sorted":["math-ph","math.MP","math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-09-18T16:01:59Z","title_canon_sha256":"022c788158bf40267ec88733b78aed927649688c1bf63fff6a5d9a14354602db"},"schema_version":"1.0","source":{"id":"1209.4003","kind":"arxiv","version":1}},"canonical_sha256":"ad3d76b587cbc151d8c407f0cb3182efd92fe2b1712815a98971d0c3c6d241d1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ad3d76b587cbc151d8c407f0cb3182efd92fe2b1712815a98971d0c3c6d241d1","first_computed_at":"2026-05-18T03:45:22.045888Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:45:22.045888Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kAnQURZDxTH2osNhzhfvVcGE2Wk8fqvUTwH96H2Z+TJuqtwXfcZ5jgjEcbWfn9MmMc5lvf2+GRMr0XgAMDu2BA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:45:22.046583Z","signed_message":"canonical_sha256_bytes"},"source_id":"1209.4003","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4d9d0bc7ca87c93e1c310f4c4593f65205012a231016a0414a0de254ec6af879","sha256:c39e77778d22eb6bf4d19d787a03c725a8ea4eceab8e531b6b63ffb0a0f42dc9"],"state_sha256":"209b51bf841241b241852536dfe96b692096bf3543f7e51b3479506ea2a05949"}