{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2005:35GOFQ6WJCCEKHUOX6ROYDWNQA","short_pith_number":"pith:35GOFQ6W","schema_version":"1.0","canonical_sha256":"df4ce2c3d64884451e8ebfa2ec0ecd800a90db2994aaf0a6034f6b67a94823bf","source":{"kind":"arxiv","id":"math/0501468","version":2},"attestation_state":"computed","paper":{"title":"A General Approach for Producing Hamiltonian Numerical Schemes for Fluid Equations","license":"","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Colin Cotter","submitted_at":"2005-01-26T12:51:33Z","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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"math/0501468","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.NA","submitted_at":"2005-01-26T12:51:33Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"a345604c1fd4051ee4c6f0381d1b9f3f6c204e7b2da839b09e33b630e0f448d7","abstract_canon_sha256":"39abca6ce6c1325a7d29677e1503d93bbac71d5ca6df3dc5c3f1ca71fd95db77"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-03T22:06:16.189163Z","signature_b64":"/qOC6JobHWyKx1swPZcz2Zft5jAo/yq9R81ObiPpAP32fGFR9VOq1BMXi7c/KbcZViJhjuBW89u7MFnmcppjDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"df4ce2c3d64884451e8ebfa2ec0ecd800a90db2994aaf0a6034f6b67a94823bf","last_reissued_at":"2026-06-03T22:06:16.188743Z","signature_status":"signed_v1","first_computed_at":"2026-06-03T22:06:16.188743Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A General Approach for Producing Hamiltonian Numerical Schemes for Fluid Equations","license":"","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Colin Cotter","submitted_at":"2005-01-26T12:51:33Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0501468","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math/0501468/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"math/0501468","created_at":"2026-06-03T22:06:16.188807+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0501468v2","created_at":"2026-06-03T22:06:16.188807+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0501468","created_at":"2026-06-03T22:06:16.188807+00:00"},{"alias_kind":"pith_short_12","alias_value":"35GOFQ6WJCCE","created_at":"2026-06-03T22:06:16.188807+00:00"},{"alias_kind":"pith_short_16","alias_value":"35GOFQ6WJCCEKHUO","created_at":"2026-06-03T22:06:16.188807+00:00"},{"alias_kind":"pith_short_8","alias_value":"35GOFQ6W","created_at":"2026-06-03T22:06:16.188807+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/35GOFQ6WJCCEKHUOX6ROYDWNQA","json":"https://pith.science/pith/35GOFQ6WJCCEKHUOX6ROYDWNQA.json","graph_json":"https://pith.science/api/pith-number/35GOFQ6WJCCEKHUOX6ROYDWNQA/graph.json","events_json":"https://pith.science/api/pith-number/35GOFQ6WJCCEKHUOX6ROYDWNQA/events.json","paper":"https://pith.science/paper/35GOFQ6W"},"agent_actions":{"view_html":"https://pith.science/pith/35GOFQ6WJCCEKHUOX6ROYDWNQA","download_json":"https://pith.science/pith/35GOFQ6WJCCEKHUOX6ROYDWNQA.json","view_paper":"https://pith.science/paper/35GOFQ6W","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0501468&json=true","fetch_graph":"https://pith.science/api/pith-number/35GOFQ6WJCCEKHUOX6ROYDWNQA/graph.json","fetch_events":"https://pith.science/api/pith-number/35GOFQ6WJCCEKHUOX6ROYDWNQA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/35GOFQ6WJCCEKHUOX6ROYDWNQA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/35GOFQ6WJCCEKHUOX6ROYDWNQA/action/storage_attestation","attest_author":"https://pith.science/pith/35GOFQ6WJCCEKHUOX6ROYDWNQA/action/author_attestation","sign_citation":"https://pith.science/pith/35GOFQ6WJCCEKHUOX6ROYDWNQA/action/citation_signature","submit_replication":"https://pith.science/pith/35GOFQ6WJCCEKHUOX6ROYDWNQA/action/replication_record"}},"created_at":"2026-06-03T22:06:16.188807+00:00","updated_at":"2026-06-03T22:06:16.188807+00:00"}