{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:X6K4BOL7O5AD4QGOFGRD7O4IF6","short_pith_number":"pith:X6K4BOL7","canonical_record":{"source":{"id":"1211.5827","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2012-11-26T00:40:36Z","cross_cats_sorted":["physics.class-ph"],"title_canon_sha256":"7494fef7e94113678d09bac9fa175a736f764ee8fb148df990418f55f0c624bc","abstract_canon_sha256":"a461d35d8d1e485af164445db70d746d221b3b2bd718a433713fca2461459e4a"},"schema_version":"1.0"},"canonical_sha256":"bf95c0b97f77403e40ce29a23fbb882f8c565462e48cb086efb53f6f239eba2c","source":{"kind":"arxiv","id":"1211.5827","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.5827","created_at":"2026-05-18T03:40:01Z"},{"alias_kind":"arxiv_version","alias_value":"1211.5827v1","created_at":"2026-05-18T03:40:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.5827","created_at":"2026-05-18T03:40:01Z"},{"alias_kind":"pith_short_12","alias_value":"X6K4BOL7O5AD","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_16","alias_value":"X6K4BOL7O5AD4QGO","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_8","alias_value":"X6K4BOL7","created_at":"2026-05-18T12:27:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:X6K4BOL7O5AD4QGOFGRD7O4IF6","target":"record","payload":{"canonical_record":{"source":{"id":"1211.5827","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2012-11-26T00:40:36Z","cross_cats_sorted":["physics.class-ph"],"title_canon_sha256":"7494fef7e94113678d09bac9fa175a736f764ee8fb148df990418f55f0c624bc","abstract_canon_sha256":"a461d35d8d1e485af164445db70d746d221b3b2bd718a433713fca2461459e4a"},"schema_version":"1.0"},"canonical_sha256":"bf95c0b97f77403e40ce29a23fbb882f8c565462e48cb086efb53f6f239eba2c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:40:01.846844Z","signature_b64":"GVgWl8m5LTAanN4zzWl0lGf05E5HrYC1EA3lCM5agpWcbtrHNoAhNPh/Sfc7EprvdNq9eh+Uk9cs2OAgnLL1Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bf95c0b97f77403e40ce29a23fbb882f8c565462e48cb086efb53f6f239eba2c","last_reissued_at":"2026-05-18T03:40:01.846280Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:40:01.846280Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1211.5827","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:40:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qQEX4RHKMUR5VwKR4flj6c35KciWd6qzxEpsPVyq06GWy5cND/MFh5SWcutRPqzZTkORemUw/KBIT6q7LEgCBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T03:54:39.468572Z"},"content_sha256":"fc43311c6f53b384acaa4dc3b015dfe2ba8bd24c5bac6a4ec66e6d1375f814c9","schema_version":"1.0","event_id":"sha256:fc43311c6f53b384acaa4dc3b015dfe2ba8bd24c5bac6a4ec66e6d1375f814c9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:X6K4BOL7O5AD4QGOFGRD7O4IF6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Euler-Poincar\\'{e} equations for anelastic fluid flows","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.class-ph"],"primary_cat":"physics.flu-dyn","authors_text":"Darryl D. Holm","submitted_at":"2012-11-26T00:40:36Z","abstract_excerpt":"We show that the ideal (nondissipative) form of the dynamical equations for the Lipps-Hemler formulation of the anelastic fluid model follow as Euler-Poincar\\'{e} equations, obtained from a constrained Hamilton's principle expressed in the Eulerian fluid description. This establishes the mathematical framework for the following properties of these anelastic equations: the Kelvin-Noether circulation theorem, conservation of potential vorticity on fluid parcels, and the Lie-Poisson Hamiltonian formulation possessing conserved Casimirs, conserved domain integrated energy and an associated variati"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.5827","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:40:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rePLIbF2Xb6RNy+M4CiK4vKRwTWoNzfUM3JtJI1nJOO/4io+Gy+l157/TTn4IzjMhoeC0gsr5HBrHuvrR376DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T03:54:39.469181Z"},"content_sha256":"951320dd1942f4b8078d67346854cf92aecb1d037b4a72a2e888fd1a9a47f3ea","schema_version":"1.0","event_id":"sha256:951320dd1942f4b8078d67346854cf92aecb1d037b4a72a2e888fd1a9a47f3ea"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/X6K4BOL7O5AD4QGOFGRD7O4IF6/bundle.json","state_url":"https://pith.science/pith/X6K4BOL7O5AD4QGOFGRD7O4IF6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/X6K4BOL7O5AD4QGOFGRD7O4IF6/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-05T03:54:39Z","links":{"resolver":"https://pith.science/pith/X6K4BOL7O5AD4QGOFGRD7O4IF6","bundle":"https://pith.science/pith/X6K4BOL7O5AD4QGOFGRD7O4IF6/bundle.json","state":"https://pith.science/pith/X6K4BOL7O5AD4QGOFGRD7O4IF6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/X6K4BOL7O5AD4QGOFGRD7O4IF6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:X6K4BOL7O5AD4QGOFGRD7O4IF6","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":"a461d35d8d1e485af164445db70d746d221b3b2bd718a433713fca2461459e4a","cross_cats_sorted":["physics.class-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2012-11-26T00:40:36Z","title_canon_sha256":"7494fef7e94113678d09bac9fa175a736f764ee8fb148df990418f55f0c624bc"},"schema_version":"1.0","source":{"id":"1211.5827","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.5827","created_at":"2026-05-18T03:40:01Z"},{"alias_kind":"arxiv_version","alias_value":"1211.5827v1","created_at":"2026-05-18T03:40:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.5827","created_at":"2026-05-18T03:40:01Z"},{"alias_kind":"pith_short_12","alias_value":"X6K4BOL7O5AD","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_16","alias_value":"X6K4BOL7O5AD4QGO","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_8","alias_value":"X6K4BOL7","created_at":"2026-05-18T12:27:27Z"}],"graph_snapshots":[{"event_id":"sha256:951320dd1942f4b8078d67346854cf92aecb1d037b4a72a2e888fd1a9a47f3ea","target":"graph","created_at":"2026-05-18T03:40:01Z","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":"We show that the ideal (nondissipative) form of the dynamical equations for the Lipps-Hemler formulation of the anelastic fluid model follow as Euler-Poincar\\'{e} equations, obtained from a constrained Hamilton's principle expressed in the Eulerian fluid description. This establishes the mathematical framework for the following properties of these anelastic equations: the Kelvin-Noether circulation theorem, conservation of potential vorticity on fluid parcels, and the Lie-Poisson Hamiltonian formulation possessing conserved Casimirs, conserved domain integrated energy and an associated variati","authors_text":"Darryl D. Holm","cross_cats":["physics.class-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2012-11-26T00:40:36Z","title":"Euler-Poincar\\'{e} equations for anelastic fluid flows"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.5827","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:fc43311c6f53b384acaa4dc3b015dfe2ba8bd24c5bac6a4ec66e6d1375f814c9","target":"record","created_at":"2026-05-18T03:40:01Z","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":"a461d35d8d1e485af164445db70d746d221b3b2bd718a433713fca2461459e4a","cross_cats_sorted":["physics.class-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2012-11-26T00:40:36Z","title_canon_sha256":"7494fef7e94113678d09bac9fa175a736f764ee8fb148df990418f55f0c624bc"},"schema_version":"1.0","source":{"id":"1211.5827","kind":"arxiv","version":1}},"canonical_sha256":"bf95c0b97f77403e40ce29a23fbb882f8c565462e48cb086efb53f6f239eba2c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bf95c0b97f77403e40ce29a23fbb882f8c565462e48cb086efb53f6f239eba2c","first_computed_at":"2026-05-18T03:40:01.846280Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:40:01.846280Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GVgWl8m5LTAanN4zzWl0lGf05E5HrYC1EA3lCM5agpWcbtrHNoAhNPh/Sfc7EprvdNq9eh+Uk9cs2OAgnLL1Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:40:01.846844Z","signed_message":"canonical_sha256_bytes"},"source_id":"1211.5827","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fc43311c6f53b384acaa4dc3b015dfe2ba8bd24c5bac6a4ec66e6d1375f814c9","sha256:951320dd1942f4b8078d67346854cf92aecb1d037b4a72a2e888fd1a9a47f3ea"],"state_sha256":"62bce4e09137884a8554e3ad32bb23499ac39d57d9fe6e2ec4ff742e2c724f93"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"40aFKIqxY5X3R8oY3rjGaJJVJYxpgARELX3kEdDKRmau7j7O0mcYU9W8jZ9y9AfL3oENoW++5yXmW7tldYnOAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T03:54:39.472278Z","bundle_sha256":"847020bc0721536f749b12096167acca527067bf0ae5a2e74f8cc2123d679a03"}}