{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:7HFISH6YIR2L6XQ2AGCTPUIDRF","short_pith_number":"pith:7HFISH6Y","canonical_record":{"source":{"id":"2110.09938","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2021-10-19T12:53:55Z","cross_cats_sorted":["math.DG","math.MP","nlin.SI"],"title_canon_sha256":"4e010cdfa289dcce0fd331e7d33c1a89208deda4a47139f77114325d011b7848","abstract_canon_sha256":"b379e589772616b52def88d5a8e230f516e0de35c726f39cdf2feb7555ce886a"},"schema_version":"1.0"},"canonical_sha256":"f9ca891fd84474bf5e1a018537d1038943b990fe61fb40205fe52b8c08742a4b","source":{"kind":"arxiv","id":"2110.09938","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2110.09938","created_at":"2026-07-05T05:51:55Z"},{"alias_kind":"arxiv_version","alias_value":"2110.09938v2","created_at":"2026-07-05T05:51:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2110.09938","created_at":"2026-07-05T05:51:55Z"},{"alias_kind":"pith_short_12","alias_value":"7HFISH6YIR2L","created_at":"2026-07-05T05:51:55Z"},{"alias_kind":"pith_short_16","alias_value":"7HFISH6YIR2L6XQ2","created_at":"2026-07-05T05:51:55Z"},{"alias_kind":"pith_short_8","alias_value":"7HFISH6Y","created_at":"2026-07-05T05:51:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:7HFISH6YIR2L6XQ2AGCTPUIDRF","target":"record","payload":{"canonical_record":{"source":{"id":"2110.09938","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2021-10-19T12:53:55Z","cross_cats_sorted":["math.DG","math.MP","nlin.SI"],"title_canon_sha256":"4e010cdfa289dcce0fd331e7d33c1a89208deda4a47139f77114325d011b7848","abstract_canon_sha256":"b379e589772616b52def88d5a8e230f516e0de35c726f39cdf2feb7555ce886a"},"schema_version":"1.0"},"canonical_sha256":"f9ca891fd84474bf5e1a018537d1038943b990fe61fb40205fe52b8c08742a4b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:51:55.192012Z","signature_b64":"/GeJD2yWpHxvEC1egQwUYd+o61KYzN+cEpKpR7g7OjjnZN6aZn7gop06enWiHxrUSAQo82i3fECqzZ3eYZSpCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f9ca891fd84474bf5e1a018537d1038943b990fe61fb40205fe52b8c08742a4b","last_reissued_at":"2026-07-05T05:51:55.191596Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:51:55.191596Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2110.09938","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":"2026-07-05T05:51:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AxmVOD0+cdFQYAVYKzNQtfzq5dI/UNlz4KkGbskGo2fFAj+2OhuFOJLImymUUqiKdxtWzYRn69l+rBgqIb/OBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T08:54:49.640921Z"},"content_sha256":"1cc34d39b35ec4cc1a3178a192b435b054bb7f75aa7821214a6531ab8cba7274","schema_version":"1.0","event_id":"sha256:1cc34d39b35ec4cc1a3178a192b435b054bb7f75aa7821214a6531ab8cba7274"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:7HFISH6YIR2L6XQ2AGCTPUIDRF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Gyroscopic Chaplygin systems and integrable magnetic flows on spheres","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG","math.MP","nlin.SI"],"primary_cat":"math-ph","authors_text":"Borislav Gajic, Bozidar Jovanovic, Vladimir Dragovic","submitted_at":"2021-10-19T12:53:55Z","abstract_excerpt":"We introduce and study the Chaplygin systems with gyroscopic forces. This natural class of nonholonomic systems has not been treated before. We put a special emphasis on the important subclass of such systems with magnetic forces. The existence of an invariant measure and the problem of Hamiltonization are studied, both within the Lagrangian and the almost-Hamiltonian framework. In addition, we introduce problems of rolling of a ball with the gyroscope without slipping and twisting over a plane and over a sphere in $\\mathbb R^n$ as examples of gyroscopic $SO(n)$--Chaplygin systems. We describe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2110.09938","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2110.09938/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T05:51:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"e3fB2oTiHgeKuBRdC4ZrY9qC2c1b1xsjHkqkoyCY0KGUJcAUU88Va9J2t9GWAkI80pUaihpLFQRXQ3JdbVHTDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T08:54:49.642715Z"},"content_sha256":"b7210f6cff345138a856652e85b2462fe966661f0d44ae480eb98cbf0386f6b2","schema_version":"1.0","event_id":"sha256:b7210f6cff345138a856652e85b2462fe966661f0d44ae480eb98cbf0386f6b2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7HFISH6YIR2L6XQ2AGCTPUIDRF/bundle.json","state_url":"https://pith.science/pith/7HFISH6YIR2L6XQ2AGCTPUIDRF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7HFISH6YIR2L6XQ2AGCTPUIDRF/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":"2026-08-13T08:54:49Z","links":{"resolver":"https://pith.science/pith/7HFISH6YIR2L6XQ2AGCTPUIDRF","bundle":"https://pith.science/pith/7HFISH6YIR2L6XQ2AGCTPUIDRF/bundle.json","state":"https://pith.science/pith/7HFISH6YIR2L6XQ2AGCTPUIDRF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7HFISH6YIR2L6XQ2AGCTPUIDRF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:7HFISH6YIR2L6XQ2AGCTPUIDRF","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":"b379e589772616b52def88d5a8e230f516e0de35c726f39cdf2feb7555ce886a","cross_cats_sorted":["math.DG","math.MP","nlin.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2021-10-19T12:53:55Z","title_canon_sha256":"4e010cdfa289dcce0fd331e7d33c1a89208deda4a47139f77114325d011b7848"},"schema_version":"1.0","source":{"id":"2110.09938","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2110.09938","created_at":"2026-07-05T05:51:55Z"},{"alias_kind":"arxiv_version","alias_value":"2110.09938v2","created_at":"2026-07-05T05:51:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2110.09938","created_at":"2026-07-05T05:51:55Z"},{"alias_kind":"pith_short_12","alias_value":"7HFISH6YIR2L","created_at":"2026-07-05T05:51:55Z"},{"alias_kind":"pith_short_16","alias_value":"7HFISH6YIR2L6XQ2","created_at":"2026-07-05T05:51:55Z"},{"alias_kind":"pith_short_8","alias_value":"7HFISH6Y","created_at":"2026-07-05T05:51:55Z"}],"graph_snapshots":[{"event_id":"sha256:b7210f6cff345138a856652e85b2462fe966661f0d44ae480eb98cbf0386f6b2","target":"graph","created_at":"2026-07-05T05:51:55Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2110.09938/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We introduce and study the Chaplygin systems with gyroscopic forces. This natural class of nonholonomic systems has not been treated before. We put a special emphasis on the important subclass of such systems with magnetic forces. The existence of an invariant measure and the problem of Hamiltonization are studied, both within the Lagrangian and the almost-Hamiltonian framework. In addition, we introduce problems of rolling of a ball with the gyroscope without slipping and twisting over a plane and over a sphere in $\\mathbb R^n$ as examples of gyroscopic $SO(n)$--Chaplygin systems. We describe","authors_text":"Borislav Gajic, Bozidar Jovanovic, Vladimir Dragovic","cross_cats":["math.DG","math.MP","nlin.SI"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2021-10-19T12:53:55Z","title":"Gyroscopic Chaplygin systems and integrable magnetic flows on spheres"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2110.09938","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":"sha256:1cc34d39b35ec4cc1a3178a192b435b054bb7f75aa7821214a6531ab8cba7274","target":"record","created_at":"2026-07-05T05:51:55Z","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":"b379e589772616b52def88d5a8e230f516e0de35c726f39cdf2feb7555ce886a","cross_cats_sorted":["math.DG","math.MP","nlin.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2021-10-19T12:53:55Z","title_canon_sha256":"4e010cdfa289dcce0fd331e7d33c1a89208deda4a47139f77114325d011b7848"},"schema_version":"1.0","source":{"id":"2110.09938","kind":"arxiv","version":2}},"canonical_sha256":"f9ca891fd84474bf5e1a018537d1038943b990fe61fb40205fe52b8c08742a4b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f9ca891fd84474bf5e1a018537d1038943b990fe61fb40205fe52b8c08742a4b","first_computed_at":"2026-07-05T05:51:55.191596Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:51:55.191596Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/GeJD2yWpHxvEC1egQwUYd+o61KYzN+cEpKpR7g7OjjnZN6aZn7gop06enWiHxrUSAQo82i3fECqzZ3eYZSpCg==","signature_status":"signed_v1","signed_at":"2026-07-05T05:51:55.192012Z","signed_message":"canonical_sha256_bytes"},"source_id":"2110.09938","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1cc34d39b35ec4cc1a3178a192b435b054bb7f75aa7821214a6531ab8cba7274","sha256:b7210f6cff345138a856652e85b2462fe966661f0d44ae480eb98cbf0386f6b2"],"state_sha256":"dfbfa72dc12eabfe9df74303c5f47ac45ccb4b2297bb8a643a0c7e78776955c2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oD84ehRhkubfSt/4EF78/b0QUqMnsAEdDkWkA6gEzUIomFEKQeCwkdNSW+jW/ePjobBLXx0i+U4C1NQuORkGCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T08:54:49.652389Z","bundle_sha256":"b7abc8961dac64ea1219e02a3ac6f3c85a94dc6b53c688fa20fa651d3e980e79"}}