{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:35GOFQ6WJCCEKHUOX6ROYDWNQA","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":"39abca6ce6c1325a7d29677e1503d93bbac71d5ca6df3dc5c3f1ca71fd95db77","cross_cats_sorted":["cs.NA"],"license":"","primary_cat":"math.NA","submitted_at":"2005-01-26T12:51:33Z","title_canon_sha256":"a345604c1fd4051ee4c6f0381d1b9f3f6c204e7b2da839b09e33b630e0f448d7"},"schema_version":"1.0","source":{"id":"math/0501468","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0501468","created_at":"2026-06-03T22:06:16Z"},{"alias_kind":"arxiv_version","alias_value":"math/0501468v2","created_at":"2026-06-03T22:06:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0501468","created_at":"2026-06-03T22:06:16Z"},{"alias_kind":"pith_short_12","alias_value":"35GOFQ6WJCCE","created_at":"2026-06-03T22:06:16Z"},{"alias_kind":"pith_short_16","alias_value":"35GOFQ6WJCCEKHUO","created_at":"2026-06-03T22:06:16Z"},{"alias_kind":"pith_short_8","alias_value":"35GOFQ6W","created_at":"2026-06-03T22:06:16Z"}],"graph_snapshots":[{"event_id":"sha256:6ec0ea30bcc73d85f871443d16ba7fa8050015e27906c24149903ff70304dc4c","target":"graph","created_at":"2026-06-03T22:06:16Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/math/0501468/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Given a fluid equation with reduced Lagrangian $l$ which is a functional of velocity $\\MM{u}$ and advected density $D$ given in Eulerian coordinates, we give a general method for semidiscretising the equations to give a canonical Hamiltonian system; this system may then be integrated in time using a symplectic integrator. The method is Lagrangian, with the variables being a set of Lagrangian particle positions and their associated momenta. The canonical equations obtained yield a discrete form of Euler-Poincar\\'e equations for $l$ when projected onto the grid, with a new form of discrete calcu","authors_text":"Colin Cotter","cross_cats":["cs.NA"],"headline":"","license":"","primary_cat":"math.NA","submitted_at":"2005-01-26T12:51:33Z","title":"A General Approach for Producing Hamiltonian Numerical Schemes for Fluid Equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0501468","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":"sha256:3783b6c168b3c2abd11be389a261ef57935eef12b9e6ba4d3135b40d593ab414","target":"record","created_at":"2026-06-03T22:06:16Z","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":"39abca6ce6c1325a7d29677e1503d93bbac71d5ca6df3dc5c3f1ca71fd95db77","cross_cats_sorted":["cs.NA"],"license":"","primary_cat":"math.NA","submitted_at":"2005-01-26T12:51:33Z","title_canon_sha256":"a345604c1fd4051ee4c6f0381d1b9f3f6c204e7b2da839b09e33b630e0f448d7"},"schema_version":"1.0","source":{"id":"math/0501468","kind":"arxiv","version":2}},"canonical_sha256":"df4ce2c3d64884451e8ebfa2ec0ecd800a90db2994aaf0a6034f6b67a94823bf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"df4ce2c3d64884451e8ebfa2ec0ecd800a90db2994aaf0a6034f6b67a94823bf","first_computed_at":"2026-06-03T22:06:16.188743Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-03T22:06:16.188743Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/qOC6JobHWyKx1swPZcz2Zft5jAo/yq9R81ObiPpAP32fGFR9VOq1BMXi7c/KbcZViJhjuBW89u7MFnmcppjDg==","signature_status":"signed_v1","signed_at":"2026-06-03T22:06:16.189163Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0501468","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3783b6c168b3c2abd11be389a261ef57935eef12b9e6ba4d3135b40d593ab414","sha256:6ec0ea30bcc73d85f871443d16ba7fa8050015e27906c24149903ff70304dc4c"],"state_sha256":"0c2e95d11666271f660dc53f865f3bc44181b82fa944d92b7de8bf46e73678fb"}