{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:ZY7NUEMK2FDT2B4EAPOLJK76TY","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":"244602e87c36f6ec9e5ea75d318bd5cf76df81441e37624c3773abe0d36bdbaa","cross_cats_sorted":["math.DS","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2010-07-28T10:30:03Z","title_canon_sha256":"fe736207ad8bf06221324712c7ff9476079e2728c2b14e2de12f7b26bd29dd79"},"schema_version":"1.0","source":{"id":"1007.4920","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1007.4920","created_at":"2026-05-18T02:27:29Z"},{"alias_kind":"arxiv_version","alias_value":"1007.4920v3","created_at":"2026-05-18T02:27:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1007.4920","created_at":"2026-05-18T02:27:29Z"},{"alias_kind":"pith_short_12","alias_value":"ZY7NUEMK2FDT","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_16","alias_value":"ZY7NUEMK2FDT2B4E","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_8","alias_value":"ZY7NUEMK","created_at":"2026-05-18T12:26:18Z"}],"graph_snapshots":[{"event_id":"sha256:2abe3222273f8f767889572f3a0900c982bcd813380c1dfefcd7cb60f2537e9d","target":"graph","created_at":"2026-05-18T02:27:29Z","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 self propelled stokesian robots composed of assemblies of balls, in dimensions 2 and 3, and prove that they are able to control their position and orientation. This is a result of controllability, and its proof relies on applying Chow's theorem in an analytic framework, similarly to what has been done in [3] for an axisymmetric system swimming along the axis of symmetry. However, we simplify drastically the analyticity result given in [3] and apply it to a situation where more complex swimmers move either in a plane or in three-dimensional space, hence experiencing also rotations. We ","authors_text":"Aline Lefebvre, Antonio DeSimone, Beno\\^it Merlet, Fran\\c{c}ois Alouges, Luca Heltai","cross_cats":["math.DS","math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2010-07-28T10:30:03Z","title":"Optimally swimming Stokesian robots"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.4920","kind":"arxiv","version":3},"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":"sha256:0fea54397a8b0ed9eec94a533340dd261eaebf9d74b4d73c8b6c531ea5bf81ac","target":"record","created_at":"2026-05-18T02:27:29Z","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":"244602e87c36f6ec9e5ea75d318bd5cf76df81441e37624c3773abe0d36bdbaa","cross_cats_sorted":["math.DS","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2010-07-28T10:30:03Z","title_canon_sha256":"fe736207ad8bf06221324712c7ff9476079e2728c2b14e2de12f7b26bd29dd79"},"schema_version":"1.0","source":{"id":"1007.4920","kind":"arxiv","version":3}},"canonical_sha256":"ce3eda118ad1473d078403dcb4abfe9e217429bb6dd1a0d1c4d9d8492d9eb9d6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ce3eda118ad1473d078403dcb4abfe9e217429bb6dd1a0d1c4d9d8492d9eb9d6","first_computed_at":"2026-05-18T02:27:29.753569Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:27:29.753569Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cRo6J7dqQRDLuUoIuBh/cPoC0ij4syOl35yxe2hSZyhBu8sRbwMosM0CY2eCDywvzCkGz+XjHEJ/B9mujaREAA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:27:29.754344Z","signed_message":"canonical_sha256_bytes"},"source_id":"1007.4920","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0fea54397a8b0ed9eec94a533340dd261eaebf9d74b4d73c8b6c531ea5bf81ac","sha256:2abe3222273f8f767889572f3a0900c982bcd813380c1dfefcd7cb60f2537e9d"],"state_sha256":"c250b12ed342b395be8cf0564a1938805f5d366bc112979bcf08df7834cfecc2"}