{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:JGQ3FIFD3XPPWZIVHEDTKZBSBO","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":"170936a6303334e8ab8f51e0a2cfe0a623cba81ee7942b6604d9b96b26d97473","cross_cats_sorted":["math.DG"],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"nlin.SI","submitted_at":"2015-06-29T15:14:40Z","title_canon_sha256":"b33a65789ba0014f0edb2206f65f218c462bfc7275360394f32093effa99dceb"},"schema_version":"1.0","source":{"id":"1506.08675","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.08675","created_at":"2026-05-18T00:33:27Z"},{"alias_kind":"arxiv_version","alias_value":"1506.08675v2","created_at":"2026-05-18T00:33:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.08675","created_at":"2026-05-18T00:33:27Z"},{"alias_kind":"pith_short_12","alias_value":"JGQ3FIFD3XPP","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"JGQ3FIFD3XPPWZIV","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"JGQ3FIFD","created_at":"2026-05-18T12:29:27Z"}],"graph_snapshots":[{"event_id":"sha256:f3592e201222c839f54cdbfbd14de8eeb6b5d9dd3825b451a2c813896b8f07f4","target":"graph","created_at":"2026-05-18T00:33:27Z","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":"Bi-Hamiltonian structures are of great importance in the theory of integrable Hamiltonian systems. The notion of compatibility of symplectic structures is a key aspect of bi-Hamiltonian systems. Because of this, a few different notions of compatibility have been introduced. In this paper we show that, under some additional assumptions, compatibility in the sense of Magri implies a notion of compatibility due to Fass\\`o and Ratiu, that we dub bi-affine compatibility. We present two proofs of this fact. The first one uses the uniqueness of the connection parallelizing all the Hamiltonian vector ","authors_text":"Manuele Santoprete","cross_cats":["math.DG"],"headline":"","license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"nlin.SI","submitted_at":"2015-06-29T15:14:40Z","title":"On the Relationship between Two Notions of Compatibility for Bi-Hamiltonian Systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.08675","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":"sha256:8fd3cf2a37e0b3f76da64a8f4fbca435e6babb5b58595b45653b0d8bb1640f13","target":"record","created_at":"2026-05-18T00:33:27Z","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":"170936a6303334e8ab8f51e0a2cfe0a623cba81ee7942b6604d9b96b26d97473","cross_cats_sorted":["math.DG"],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"nlin.SI","submitted_at":"2015-06-29T15:14:40Z","title_canon_sha256":"b33a65789ba0014f0edb2206f65f218c462bfc7275360394f32093effa99dceb"},"schema_version":"1.0","source":{"id":"1506.08675","kind":"arxiv","version":2}},"canonical_sha256":"49a1b2a0a3dddefb651539073564320ba1c986e9b33dd4d5604b6e8af96e226f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"49a1b2a0a3dddefb651539073564320ba1c986e9b33dd4d5604b6e8af96e226f","first_computed_at":"2026-05-18T00:33:27.914012Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:33:27.914012Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SMyDMb19rWp2Axk1wRGCOAn6ix1BMv8TwhRnjEUuZjRYZqp8Tx6gptVgPT3Xg41z3reKMzo5ATjKhB8JrS8TAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:33:27.914784Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.08675","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8fd3cf2a37e0b3f76da64a8f4fbca435e6babb5b58595b45653b0d8bb1640f13","sha256:f3592e201222c839f54cdbfbd14de8eeb6b5d9dd3825b451a2c813896b8f07f4"],"state_sha256":"2fe3f7206cd725ed09ee72602da203962fb872abee9464abf8907ebfc7d23320"}