{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:HVFRN4ZL6ZDDU47E6P2HJT4IUZ","short_pith_number":"pith:HVFRN4ZL","schema_version":"1.0","canonical_sha256":"3d4b16f32bf6463a73e4f3f474cf88a65d9e0a9430aab250ac05c6a44d2e32e1","source":{"kind":"arxiv","id":"1011.2925","version":2},"attestation_state":"computed","paper":{"title":"Rolling Manifolds: Intrinsic Formulation and Controllability","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"math.DG","authors_text":"Petri Kokkonen, Yacine Chitour","submitted_at":"2010-11-12T14:45:28Z","abstract_excerpt":"In this paper, we consider two cases of rolling of one smooth connected complete Riemannian manifold $(M,g)$ onto another one $(\\hM,\\hg)$ of equal dimension $n\\geq 2$. The rolling problem $(NS)$ corresponds to the situation where there is no relative spin (or twist) of one manifold with respect to the other one. As for the rolling problem $(R)$, there is no relative spin and also no relative slip. Since the manifolds are not assumed to be embedded into an Euclidean space, we provide an intrinsic description of the two constraints \"without spinning\" and \"without slipping\" in terms of the Levi-C"},"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":"1011.2925","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-11-12T14:45:28Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"a67358432165976005a32fe07c74ab127ab3314d99502dcd755e44eb26af7d3d","abstract_canon_sha256":"11405c4c9d773d531fc374af80eb5ddfcea620c5fde89bccd24c773a7853f9c7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:22:10.244574Z","signature_b64":"QqiRFrkPdVjfqI+h3oXsbOR5wnuJXKxyj5HaiWFyaly/efmqPc8uHnSCFlzoH1e5xxYU+0MwUj273oSshwAzBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3d4b16f32bf6463a73e4f3f474cf88a65d9e0a9430aab250ac05c6a44d2e32e1","last_reissued_at":"2026-05-18T04:22:10.244113Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:22:10.244113Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Rolling Manifolds: Intrinsic Formulation and Controllability","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"math.DG","authors_text":"Petri Kokkonen, Yacine Chitour","submitted_at":"2010-11-12T14:45:28Z","abstract_excerpt":"In this paper, we consider two cases of rolling of one smooth connected complete Riemannian manifold $(M,g)$ onto another one $(\\hM,\\hg)$ of equal dimension $n\\geq 2$. The rolling problem $(NS)$ corresponds to the situation where there is no relative spin (or twist) of one manifold with respect to the other one. As for the rolling problem $(R)$, there is no relative spin and also no relative slip. Since the manifolds are not assumed to be embedded into an Euclidean space, we provide an intrinsic description of the two constraints \"without spinning\" and \"without slipping\" in terms of the Levi-C"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.2925","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":"1011.2925","created_at":"2026-05-18T04:22:10.244183+00:00"},{"alias_kind":"arxiv_version","alias_value":"1011.2925v2","created_at":"2026-05-18T04:22:10.244183+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.2925","created_at":"2026-05-18T04:22:10.244183+00:00"},{"alias_kind":"pith_short_12","alias_value":"HVFRN4ZL6ZDD","created_at":"2026-05-18T12:26:07.630475+00:00"},{"alias_kind":"pith_short_16","alias_value":"HVFRN4ZL6ZDDU47E","created_at":"2026-05-18T12:26:07.630475+00:00"},{"alias_kind":"pith_short_8","alias_value":"HVFRN4ZL","created_at":"2026-05-18T12:26:07.630475+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/HVFRN4ZL6ZDDU47E6P2HJT4IUZ","json":"https://pith.science/pith/HVFRN4ZL6ZDDU47E6P2HJT4IUZ.json","graph_json":"https://pith.science/api/pith-number/HVFRN4ZL6ZDDU47E6P2HJT4IUZ/graph.json","events_json":"https://pith.science/api/pith-number/HVFRN4ZL6ZDDU47E6P2HJT4IUZ/events.json","paper":"https://pith.science/paper/HVFRN4ZL"},"agent_actions":{"view_html":"https://pith.science/pith/HVFRN4ZL6ZDDU47E6P2HJT4IUZ","download_json":"https://pith.science/pith/HVFRN4ZL6ZDDU47E6P2HJT4IUZ.json","view_paper":"https://pith.science/paper/HVFRN4ZL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1011.2925&json=true","fetch_graph":"https://pith.science/api/pith-number/HVFRN4ZL6ZDDU47E6P2HJT4IUZ/graph.json","fetch_events":"https://pith.science/api/pith-number/HVFRN4ZL6ZDDU47E6P2HJT4IUZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HVFRN4ZL6ZDDU47E6P2HJT4IUZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HVFRN4ZL6ZDDU47E6P2HJT4IUZ/action/storage_attestation","attest_author":"https://pith.science/pith/HVFRN4ZL6ZDDU47E6P2HJT4IUZ/action/author_attestation","sign_citation":"https://pith.science/pith/HVFRN4ZL6ZDDU47E6P2HJT4IUZ/action/citation_signature","submit_replication":"https://pith.science/pith/HVFRN4ZL6ZDDU47E6P2HJT4IUZ/action/replication_record"}},"created_at":"2026-05-18T04:22:10.244183+00:00","updated_at":"2026-05-18T04:22:10.244183+00:00"}