{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:3FVHYMP3U6BVQ4FKJBNXVG3N32","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":"094c178bf2c847818ba893793c24d4dc6dbedb2f4ae695c34b076fc2dc676ca4","cross_cats_sorted":["math-ph","math.MP","math.SG"],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.DS","submitted_at":"2015-10-28T14:10:11Z","title_canon_sha256":"6f91a53735905f73d7d8e8548392587d6be79ef4e76b4dd5a657c471ee2ba7ea"},"schema_version":"1.0","source":{"id":"1510.08314","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.08314","created_at":"2026-05-18T01:20:16Z"},{"alias_kind":"arxiv_version","alias_value":"1510.08314v2","created_at":"2026-05-18T01:20:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.08314","created_at":"2026-05-18T01:20:16Z"},{"alias_kind":"pith_short_12","alias_value":"3FVHYMP3U6BV","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"3FVHYMP3U6BVQ4FK","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"3FVHYMP3","created_at":"2026-05-18T12:29:02Z"}],"graph_snapshots":[{"event_id":"sha256:b1fb81ae2bae315631ddeb2658f1ed153d0befc4185b7066e80c55933ca12864","target":"graph","created_at":"2026-05-18T01:20:16Z","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 existence of first integrals in nonholonomic systems with symmetry. First we define the concept of $\\mathcal{M}$-cotangent lift of a vector field on a manifold $Q$ in order to unify the works [Balseiro P., Arch. Ration. Mech. Anal. 214 (2014), 453-501, arXiv:1301.1091], [Fass\\`o F., Ramos A., Sansonetto N., Regul. Chaotic Dyn. 12 (2007), 579-588], and [Fass\\`o F., Giacobbe A., Sansonetto N., Rep. Math. Phys. 62 (2008), 345-367]. Second, we study gauge symmetries and gauge momenta, in the cases in which there are the symmetries that satisfy the so-called vertical symmetry condition","authors_text":"Nicola Sansonetto, Paula Balseiro","cross_cats":["math-ph","math.MP","math.SG"],"headline":"","license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.DS","submitted_at":"2015-10-28T14:10:11Z","title":"A Geometric Characterization of Certain First Integrals for Nonholonomic Systems with Symmetries"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.08314","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:fe62358a60533e71448cf95fd9b5386a4622ff10559aa65b80571e3a074338eb","target":"record","created_at":"2026-05-18T01:20:16Z","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":"094c178bf2c847818ba893793c24d4dc6dbedb2f4ae695c34b076fc2dc676ca4","cross_cats_sorted":["math-ph","math.MP","math.SG"],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.DS","submitted_at":"2015-10-28T14:10:11Z","title_canon_sha256":"6f91a53735905f73d7d8e8548392587d6be79ef4e76b4dd5a657c471ee2ba7ea"},"schema_version":"1.0","source":{"id":"1510.08314","kind":"arxiv","version":2}},"canonical_sha256":"d96a7c31fba7835870aa485b7a9b6dde8cc8a98f803b929cf434e247b0600479","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d96a7c31fba7835870aa485b7a9b6dde8cc8a98f803b929cf434e247b0600479","first_computed_at":"2026-05-18T01:20:16.646877Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:20:16.646877Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/jkMJ9rebWRdSx5bzra5M8pYY3kXBf0ODSMiF6FdvMtTkSJ/FTzwduBdiW/M1FPimkp4qH1Ko7JenoPKjQIdBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:20:16.647448Z","signed_message":"canonical_sha256_bytes"},"source_id":"1510.08314","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fe62358a60533e71448cf95fd9b5386a4622ff10559aa65b80571e3a074338eb","sha256:b1fb81ae2bae315631ddeb2658f1ed153d0befc4185b7066e80c55933ca12864"],"state_sha256":"ea58751da90b6da2c8051c5459d35cfeafa7e3dba4d4d2aab692d07725b6adb9"}