{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:V4PSF4NGRRGKC2ZXV6S2NT4UPX","short_pith_number":"pith:V4PSF4NG","canonical_record":{"source":{"id":"1106.2950","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math-ph","submitted_at":"2011-06-15T12:07:42Z","cross_cats_sorted":["math.DS","math.MP"],"title_canon_sha256":"68c4bdfdd497fdc0cf5b3e0e79ab84952b5df44a643a28547134efb69fd0d777","abstract_canon_sha256":"f7ea6a5ca6287a233cf442a5fabfa9ef403d748dcd251f2df5c4ec630c41c055"},"schema_version":"1.0"},"canonical_sha256":"af1f22f1a68c4ca16b37afa5a6cf947de707417be23a28e76bb5d2282d6d8291","source":{"kind":"arxiv","id":"1106.2950","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.2950","created_at":"2026-05-18T04:07:29Z"},{"alias_kind":"arxiv_version","alias_value":"1106.2950v2","created_at":"2026-05-18T04:07:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.2950","created_at":"2026-05-18T04:07:29Z"},{"alias_kind":"pith_short_12","alias_value":"V4PSF4NGRRGK","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"V4PSF4NGRRGKC2ZX","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"V4PSF4NG","created_at":"2026-05-18T12:26:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:V4PSF4NGRRGKC2ZXV6S2NT4UPX","target":"record","payload":{"canonical_record":{"source":{"id":"1106.2950","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math-ph","submitted_at":"2011-06-15T12:07:42Z","cross_cats_sorted":["math.DS","math.MP"],"title_canon_sha256":"68c4bdfdd497fdc0cf5b3e0e79ab84952b5df44a643a28547134efb69fd0d777","abstract_canon_sha256":"f7ea6a5ca6287a233cf442a5fabfa9ef403d748dcd251f2df5c4ec630c41c055"},"schema_version":"1.0"},"canonical_sha256":"af1f22f1a68c4ca16b37afa5a6cf947de707417be23a28e76bb5d2282d6d8291","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:07:29.170205Z","signature_b64":"qms90F11UFWOAisRHZeiqSzSD+rZe00vcUNb9pO+RWGl3h3p5BgULqL3obMxeS8jP5Eow1g0qIXQvfNP03JaCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"af1f22f1a68c4ca16b37afa5a6cf947de707417be23a28e76bb5d2282d6d8291","last_reissued_at":"2026-05-18T04:07:29.169720Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:07:29.169720Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1106.2950","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:07:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2CAqwYLa3/1tHdRdTHuvWdpoICKWRYmr4nJdKHebiFMQBMORc5CItTLMHhl7MnEKmqMOnCqfq96/E/b5/ijNAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T08:27:07.202388Z"},"content_sha256":"311e148d30d3b4cccd518e7c070d0f0c65cb3381392143a871dc49659b16a059","schema_version":"1.0","event_id":"sha256:311e148d30d3b4cccd518e7c070d0f0c65cb3381392143a871dc49659b16a059"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:V4PSF4NGRRGKC2ZXV6S2NT4UPX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Routh Reduction by Stages","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":["math.DS","math.MP"],"primary_cat":"math-ph","authors_text":"Bavo Langerock, Joris Vankerschaver, Tom Mestdag","submitted_at":"2011-06-15T12:07:42Z","abstract_excerpt":"This paper deals with the Lagrangian analogue of symplectic or point reduction by stages. We develop Routh reduction as a reduction technique that preserves the Lagrangian nature of the dynamics. To do so we heavily rely on the relation between Routh reduction and cotangent symplectic reduction. The main results in this paper are: (i) we develop a class of so called magnetic Lagrangian systems and this class has the property that it is closed under Routh reduction; (ii) we construct a transformation relating the magnetic Lagrangian system obtained after two subsequent Routh reductions and the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.2950","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":""},"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":"2026-05-18T04:07:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qhb73oDaxZbX07jvrxTo28f3KJRH1EEH02hlEMdeGbPVdVyOkG+YK9VDRGYZTrIaKzkYUnrs9JdYrN7gC2OSDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T08:27:07.203183Z"},"content_sha256":"6d0dfa411c3b32cdd831a3c4bab1442a4d53a3397696085f9145313158510d47","schema_version":"1.0","event_id":"sha256:6d0dfa411c3b32cdd831a3c4bab1442a4d53a3397696085f9145313158510d47"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/V4PSF4NGRRGKC2ZXV6S2NT4UPX/bundle.json","state_url":"https://pith.science/pith/V4PSF4NGRRGKC2ZXV6S2NT4UPX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/V4PSF4NGRRGKC2ZXV6S2NT4UPX/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":"2026-06-11T08:27:07Z","links":{"resolver":"https://pith.science/pith/V4PSF4NGRRGKC2ZXV6S2NT4UPX","bundle":"https://pith.science/pith/V4PSF4NGRRGKC2ZXV6S2NT4UPX/bundle.json","state":"https://pith.science/pith/V4PSF4NGRRGKC2ZXV6S2NT4UPX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/V4PSF4NGRRGKC2ZXV6S2NT4UPX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:V4PSF4NGRRGKC2ZXV6S2NT4UPX","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":"f7ea6a5ca6287a233cf442a5fabfa9ef403d748dcd251f2df5c4ec630c41c055","cross_cats_sorted":["math.DS","math.MP"],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math-ph","submitted_at":"2011-06-15T12:07:42Z","title_canon_sha256":"68c4bdfdd497fdc0cf5b3e0e79ab84952b5df44a643a28547134efb69fd0d777"},"schema_version":"1.0","source":{"id":"1106.2950","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.2950","created_at":"2026-05-18T04:07:29Z"},{"alias_kind":"arxiv_version","alias_value":"1106.2950v2","created_at":"2026-05-18T04:07:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.2950","created_at":"2026-05-18T04:07:29Z"},{"alias_kind":"pith_short_12","alias_value":"V4PSF4NGRRGK","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"V4PSF4NGRRGKC2ZX","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"V4PSF4NG","created_at":"2026-05-18T12:26:42Z"}],"graph_snapshots":[{"event_id":"sha256:6d0dfa411c3b32cdd831a3c4bab1442a4d53a3397696085f9145313158510d47","target":"graph","created_at":"2026-05-18T04:07:29Z","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":"This paper deals with the Lagrangian analogue of symplectic or point reduction by stages. We develop Routh reduction as a reduction technique that preserves the Lagrangian nature of the dynamics. To do so we heavily rely on the relation between Routh reduction and cotangent symplectic reduction. The main results in this paper are: (i) we develop a class of so called magnetic Lagrangian systems and this class has the property that it is closed under Routh reduction; (ii) we construct a transformation relating the magnetic Lagrangian system obtained after two subsequent Routh reductions and the ","authors_text":"Bavo Langerock, Joris Vankerschaver, Tom Mestdag","cross_cats":["math.DS","math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math-ph","submitted_at":"2011-06-15T12:07:42Z","title":"Routh Reduction by Stages"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.2950","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":"sha256:311e148d30d3b4cccd518e7c070d0f0c65cb3381392143a871dc49659b16a059","target":"record","created_at":"2026-05-18T04:07:29Z","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":"f7ea6a5ca6287a233cf442a5fabfa9ef403d748dcd251f2df5c4ec630c41c055","cross_cats_sorted":["math.DS","math.MP"],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math-ph","submitted_at":"2011-06-15T12:07:42Z","title_canon_sha256":"68c4bdfdd497fdc0cf5b3e0e79ab84952b5df44a643a28547134efb69fd0d777"},"schema_version":"1.0","source":{"id":"1106.2950","kind":"arxiv","version":2}},"canonical_sha256":"af1f22f1a68c4ca16b37afa5a6cf947de707417be23a28e76bb5d2282d6d8291","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"af1f22f1a68c4ca16b37afa5a6cf947de707417be23a28e76bb5d2282d6d8291","first_computed_at":"2026-05-18T04:07:29.169720Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:07:29.169720Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qms90F11UFWOAisRHZeiqSzSD+rZe00vcUNb9pO+RWGl3h3p5BgULqL3obMxeS8jP5Eow1g0qIXQvfNP03JaCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:07:29.170205Z","signed_message":"canonical_sha256_bytes"},"source_id":"1106.2950","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:311e148d30d3b4cccd518e7c070d0f0c65cb3381392143a871dc49659b16a059","sha256:6d0dfa411c3b32cdd831a3c4bab1442a4d53a3397696085f9145313158510d47"],"state_sha256":"bd358923268654ff4e467d85d5116a0424cf7789f58ba56f11b8bf1e873c4c47"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hIXdGDB5S8gNUPTQa0CW6L/pDl56k7x8tgj9KIKH0hq3ZUVX1I19634deLQ+xC67UHBzUBVv56umou65zQQ9Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T08:27:07.207749Z","bundle_sha256":"30f9cee5878d390ed4905bb1753211ae8e178904f52984653417206f2cb1f1b5"}}