{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:L7BHBDM7G6HL5YCHRHYHT6ZKVL","short_pith_number":"pith:L7BHBDM7","schema_version":"1.0","canonical_sha256":"5fc2708d9f378ebee04789f079fb2aaad5f1db6074818f226337dd31f9eb65d7","source":{"kind":"arxiv","id":"1509.01946","version":2},"attestation_state":"computed","paper":{"title":"Implicit Lagrange-Routh Equations and Dirac Reduction","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.DG","authors_text":"Eduardo Garc\\'ia-Tora\\~no Andr\\'es, Hiroaki Yoshimura, Tom Mestdag","submitted_at":"2015-09-07T08:31:09Z","abstract_excerpt":"In this paper, we make a generalization of Routh's reduction method for Lagrangian systems with symmetry to the case where not any regularity condition is imposed on the Lagrangian. First, we show how implicit Lagrange-Routh equations can be obtained from the Hamilton-Pontryagin principle, by making use of an anholonomic frame, and how these equations can be reduced. To do this, we keep the momentum constraint implicit throughout and we make use of a Routhian function defined on a certain submanifold of the Pontryagin bundle. Then, we show how the reduced implicit Lagrange-Routh equations can "},"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":"1509.01946","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-09-07T08:31:09Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"4034d486b164fbc9d03b2346c9d11b48013974b5e856b8a2bf06ba4a0e23f390","abstract_canon_sha256":"ee073c6db63818c629f6160776c20b224f02470d0abc508b7ee9495f13f869bc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:18:18.303656Z","signature_b64":"BjstAy7OQGrQKioGA9MORdrH8YjJStkl3Y7egPXTUmuK8QdRH7PaceMWrIaMr88/hU5L4ry4XXO2wewHwkwQDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5fc2708d9f378ebee04789f079fb2aaad5f1db6074818f226337dd31f9eb65d7","last_reissued_at":"2026-05-18T01:18:18.303135Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:18:18.303135Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Implicit Lagrange-Routh Equations and Dirac Reduction","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.DG","authors_text":"Eduardo Garc\\'ia-Tora\\~no Andr\\'es, Hiroaki Yoshimura, Tom Mestdag","submitted_at":"2015-09-07T08:31:09Z","abstract_excerpt":"In this paper, we make a generalization of Routh's reduction method for Lagrangian systems with symmetry to the case where not any regularity condition is imposed on the Lagrangian. First, we show how implicit Lagrange-Routh equations can be obtained from the Hamilton-Pontryagin principle, by making use of an anholonomic frame, and how these equations can be reduced. To do this, we keep the momentum constraint implicit throughout and we make use of a Routhian function defined on a certain submanifold of the Pontryagin bundle. Then, we show how the reduced implicit Lagrange-Routh equations can "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.01946","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1509.01946","created_at":"2026-05-18T01:18:18.303220+00:00"},{"alias_kind":"arxiv_version","alias_value":"1509.01946v2","created_at":"2026-05-18T01:18:18.303220+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.01946","created_at":"2026-05-18T01:18:18.303220+00:00"},{"alias_kind":"pith_short_12","alias_value":"L7BHBDM7G6HL","created_at":"2026-05-18T12:29:29.992203+00:00"},{"alias_kind":"pith_short_16","alias_value":"L7BHBDM7G6HL5YCH","created_at":"2026-05-18T12:29:29.992203+00:00"},{"alias_kind":"pith_short_8","alias_value":"L7BHBDM7","created_at":"2026-05-18T12:29:29.992203+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/L7BHBDM7G6HL5YCHRHYHT6ZKVL","json":"https://pith.science/pith/L7BHBDM7G6HL5YCHRHYHT6ZKVL.json","graph_json":"https://pith.science/api/pith-number/L7BHBDM7G6HL5YCHRHYHT6ZKVL/graph.json","events_json":"https://pith.science/api/pith-number/L7BHBDM7G6HL5YCHRHYHT6ZKVL/events.json","paper":"https://pith.science/paper/L7BHBDM7"},"agent_actions":{"view_html":"https://pith.science/pith/L7BHBDM7G6HL5YCHRHYHT6ZKVL","download_json":"https://pith.science/pith/L7BHBDM7G6HL5YCHRHYHT6ZKVL.json","view_paper":"https://pith.science/paper/L7BHBDM7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1509.01946&json=true","fetch_graph":"https://pith.science/api/pith-number/L7BHBDM7G6HL5YCHRHYHT6ZKVL/graph.json","fetch_events":"https://pith.science/api/pith-number/L7BHBDM7G6HL5YCHRHYHT6ZKVL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/L7BHBDM7G6HL5YCHRHYHT6ZKVL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/L7BHBDM7G6HL5YCHRHYHT6ZKVL/action/storage_attestation","attest_author":"https://pith.science/pith/L7BHBDM7G6HL5YCHRHYHT6ZKVL/action/author_attestation","sign_citation":"https://pith.science/pith/L7BHBDM7G6HL5YCHRHYHT6ZKVL/action/citation_signature","submit_replication":"https://pith.science/pith/L7BHBDM7G6HL5YCHRHYHT6ZKVL/action/replication_record"}},"created_at":"2026-05-18T01:18:18.303220+00:00","updated_at":"2026-05-18T01:18:18.303220+00:00"}