{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:PBYTPWBYMY2G7LYITVR6SMPD7U","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":"1255f2245d07f10c6ed93695bce826b311364d7ed8e815ec1a6bca37c4cd9de7","cross_cats_sorted":["math.DG","math.MP"],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math-ph","submitted_at":"2014-08-13T14:41:08Z","title_canon_sha256":"76b01373f2ca2d000a0302c71043e4b9e236faa5dee50ae730deb663bcc8d502"},"schema_version":"1.0","source":{"id":"1408.3019","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.3019","created_at":"2026-05-18T02:28:22Z"},{"alias_kind":"arxiv_version","alias_value":"1408.3019v2","created_at":"2026-05-18T02:28:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.3019","created_at":"2026-05-18T02:28:22Z"},{"alias_kind":"pith_short_12","alias_value":"PBYTPWBYMY2G","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_16","alias_value":"PBYTPWBYMY2G7LYI","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_8","alias_value":"PBYTPWBY","created_at":"2026-05-18T12:28:43Z"}],"graph_snapshots":[{"event_id":"sha256:077de29ab65855011f8bd6202d33a28a86d0ef94f178cd45d0e38a3d6137db39","target":"graph","created_at":"2026-05-18T02:28:22Z","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 study the Euler-Lagrange equations for a parameter dependent $G$-invariant Lagrangian on a homogeneous $G$-space. We consider the pullback of the parameter dependent Lagrangian to the Lie group $G$, emphasizing the special invariance properties of the associated Euler-Poincar\\'e equations with advected parameters.","authors_text":"Cornelia Vizman","cross_cats":["math.DG","math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math-ph","submitted_at":"2014-08-13T14:41:08Z","title":"Lagrangian Reduction on Homogeneous Spaces with Advected Parameters"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.3019","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:b5b58a9393ea193238e9f24c92785985d88a72201cdfe66c0e007d765cac8ed1","target":"record","created_at":"2026-05-18T02:28:22Z","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":"1255f2245d07f10c6ed93695bce826b311364d7ed8e815ec1a6bca37c4cd9de7","cross_cats_sorted":["math.DG","math.MP"],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math-ph","submitted_at":"2014-08-13T14:41:08Z","title_canon_sha256":"76b01373f2ca2d000a0302c71043e4b9e236faa5dee50ae730deb663bcc8d502"},"schema_version":"1.0","source":{"id":"1408.3019","kind":"arxiv","version":2}},"canonical_sha256":"787137d83866346faf089d63e931e3fd31f3b4ea9ac2e4a5e6b4ca89aee81e6a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"787137d83866346faf089d63e931e3fd31f3b4ea9ac2e4a5e6b4ca89aee81e6a","first_computed_at":"2026-05-18T02:28:22.820218Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:28:22.820218Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/FFvWj/IM1h83/B3UXz9tEY+QMZPrc1rWFRbvnrpYnMWIF22Fxsrhqc6Oi2CAUwriPLv/3y+/bhdzM+I8eyJCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:28:22.820706Z","signed_message":"canonical_sha256_bytes"},"source_id":"1408.3019","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b5b58a9393ea193238e9f24c92785985d88a72201cdfe66c0e007d765cac8ed1","sha256:077de29ab65855011f8bd6202d33a28a86d0ef94f178cd45d0e38a3d6137db39"],"state_sha256":"ee47597a6cf685e4b86bef09b73b6e01b07bc8c84ca25ce30f0eafa92338006e"}