{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:EHFUIEFRHY2VGYK4VTPYFTUHQH","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":"a3f1bb5c108b619e022ce061d88af7b458e905923cb2211120d92bfee14f3f51","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-01-11T19:25:44Z","title_canon_sha256":"eadf29952c6ae64a3ef5f2906e86f63606351e18eb947210e75daec0a7a1fa80"},"schema_version":"1.0","source":{"id":"1301.2579","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.2579","created_at":"2026-05-18T03:36:37Z"},{"alias_kind":"arxiv_version","alias_value":"1301.2579v1","created_at":"2026-05-18T03:36:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.2579","created_at":"2026-05-18T03:36:37Z"},{"alias_kind":"pith_short_12","alias_value":"EHFUIEFRHY2V","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"EHFUIEFRHY2VGYK4","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"EHFUIEFR","created_at":"2026-05-18T12:27:43Z"}],"graph_snapshots":[{"event_id":"sha256:0abe1484c40de82dcd2e8fd5991935bffa4fb0fa555b9a8b1e6163c10d22d606","target":"graph","created_at":"2026-05-18T03:36:37Z","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":"In the present paper, we study the infinitesimal symmetries of the model of two Riemannian manifolds $(M,g)$ and $(\\hat M,\\hat g)$ rolling without twisting or slipping. We show that, under certain genericity hypotheses, the natural bundle projection from the state space $Q$ of the rolling model onto $M$ is a principal bundle if and only if $\\hat M$ has constant sectional curvature. Additionally, we prove that when $M$ and $\\hat M$ have different constant sectional curvatures and dimension $n\\geq3$, the rolling distribution is never flat, contrary to the two dimensional situation of rolling two","authors_text":"Mauricio Godoy Molina, Petri Kokkonen, Yacine Chitour","cross_cats":["math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-01-11T19:25:44Z","title":"Symmetries of the Rolling Model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.2579","kind":"arxiv","version":1},"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":"sha256:1d76ff6ba70e788b7bfa61551f0e4cdd43ab801e3d03b2cd3e6a55de0b1b00e1","target":"record","created_at":"2026-05-18T03:36:37Z","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":"a3f1bb5c108b619e022ce061d88af7b458e905923cb2211120d92bfee14f3f51","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-01-11T19:25:44Z","title_canon_sha256":"eadf29952c6ae64a3ef5f2906e86f63606351e18eb947210e75daec0a7a1fa80"},"schema_version":"1.0","source":{"id":"1301.2579","kind":"arxiv","version":1}},"canonical_sha256":"21cb4410b13e3553615cacdf82ce8781c8fb2e55eafe6025c4ebaca60fd2a0c4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"21cb4410b13e3553615cacdf82ce8781c8fb2e55eafe6025c4ebaca60fd2a0c4","first_computed_at":"2026-05-18T03:36:37.534946Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:36:37.534946Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WKwvfSpq2fKkRGAbOkP97M2MgE+yYkwDelF1b1n6k+9RhXI5qEnwTin66LWEplliJdVv2OUxoX3oQv5ah66tCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:36:37.535452Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.2579","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1d76ff6ba70e788b7bfa61551f0e4cdd43ab801e3d03b2cd3e6a55de0b1b00e1","sha256:0abe1484c40de82dcd2e8fd5991935bffa4fb0fa555b9a8b1e6163c10d22d606"],"state_sha256":"e95d72a67d9804b683f8193803629fa1853e606cf5e0137065ec71b79bc9bd25"}