{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:MMUF6UTVWHFGHLEZYESNYX5URB","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":"efbdbff505439e302bf206faa54df8102be94887f4e02df67eb93760fe3d0b1f","cross_cats_sorted":["math.DS","math.MP","physics.flu-dyn","physics.plasm-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-08-30T14:52:10Z","title_canon_sha256":"1e68bdec95508bf1b9089bc12956907630a347e13646d7a280bf56ce03c867c5"},"schema_version":"1.0","source":{"id":"1208.6193","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.6193","created_at":"2026-05-18T03:46:46Z"},{"alias_kind":"arxiv_version","alias_value":"1208.6193v1","created_at":"2026-05-18T03:46:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.6193","created_at":"2026-05-18T03:46:46Z"},{"alias_kind":"pith_short_12","alias_value":"MMUF6UTVWHFG","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"MMUF6UTVWHFGHLEZ","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"MMUF6UTV","created_at":"2026-05-18T12:27:14Z"}],"graph_snapshots":[{"event_id":"sha256:e0a604a67b9afbab29af7433b015703b86bb45bdbdab91fe1daaed947295661f","target":"graph","created_at":"2026-05-18T03:46:46Z","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":"The dynamics of gradient and Hamiltonian flows with particular application to flows on adjoint orbits of a Lie group and the extension of this setting to flows on a loop group are discussed. Different types of gradient flows that arise from different metrics including the so-called normal metric on adjoint orbits of a Lie group and the K\\\"ahler metric are compared. It is discussed how a K\\\"ahler metric can arise from a complex structure induced by the Hilbert transform. Hybrid and metriplectic flows that arise when one has both Hamiltonian and gradient components are examined. A class of metri","authors_text":"Anthony M. Bloch, Philip J. Morrison, Tudor S. Ratiu","cross_cats":["math.DS","math.MP","physics.flu-dyn","physics.plasm-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-08-30T14:52:10Z","title":"Gradient flows in the normal and K\\\"ahler metrics and triple bracket generated metriplectic systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.6193","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:f1610e938181786cc22f3ca2b2b8536ff64763cd50f97f4f14c7c8477d6005d1","target":"record","created_at":"2026-05-18T03:46:46Z","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":"efbdbff505439e302bf206faa54df8102be94887f4e02df67eb93760fe3d0b1f","cross_cats_sorted":["math.DS","math.MP","physics.flu-dyn","physics.plasm-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-08-30T14:52:10Z","title_canon_sha256":"1e68bdec95508bf1b9089bc12956907630a347e13646d7a280bf56ce03c867c5"},"schema_version":"1.0","source":{"id":"1208.6193","kind":"arxiv","version":1}},"canonical_sha256":"63285f5275b1ca63ac99c124dc5fb4884af261ade92f936b939e962711918c80","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"63285f5275b1ca63ac99c124dc5fb4884af261ade92f936b939e962711918c80","first_computed_at":"2026-05-18T03:46:46.220772Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:46:46.220772Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KAiScD6WM+sBqkfn7S9G4IfZ7FeI923lji30yN2/sl/Z8ITunKmwz33bczKfYZM2uZePs48dGkIBlGcU7jC/Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:46:46.221546Z","signed_message":"canonical_sha256_bytes"},"source_id":"1208.6193","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f1610e938181786cc22f3ca2b2b8536ff64763cd50f97f4f14c7c8477d6005d1","sha256:e0a604a67b9afbab29af7433b015703b86bb45bdbdab91fe1daaed947295661f"],"state_sha256":"514a4870f3323ee8d31a52864ce0d95867c280895a8c9d057ff77d7226f0c65f"}