{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:LP6OZQG5GC5NSODPCSHJ2X5HAY","short_pith_number":"pith:LP6OZQG5","canonical_record":{"source":{"id":"1309.2571","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-09-10T16:38:03Z","cross_cats_sorted":[],"title_canon_sha256":"d224e57a127447939fa336d104f0951f4e6d566db04cf7417083f2f9115579eb","abstract_canon_sha256":"5f33649373e071ad4f6fb77c962e2799bffcd1f4a79af428699828329619e265"},"schema_version":"1.0"},"canonical_sha256":"5bfcecc0dd30bad9386f148e9d5fa706005aa9a7be61d7bcc28437eaccbc14f8","source":{"kind":"arxiv","id":"1309.2571","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.2571","created_at":"2026-05-18T02:19:36Z"},{"alias_kind":"arxiv_version","alias_value":"1309.2571v2","created_at":"2026-05-18T02:19:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.2571","created_at":"2026-05-18T02:19:36Z"},{"alias_kind":"pith_short_12","alias_value":"LP6OZQG5GC5N","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_16","alias_value":"LP6OZQG5GC5NSODP","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_8","alias_value":"LP6OZQG5","created_at":"2026-05-18T12:27:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:LP6OZQG5GC5NSODPCSHJ2X5HAY","target":"record","payload":{"canonical_record":{"source":{"id":"1309.2571","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-09-10T16:38:03Z","cross_cats_sorted":[],"title_canon_sha256":"d224e57a127447939fa336d104f0951f4e6d566db04cf7417083f2f9115579eb","abstract_canon_sha256":"5f33649373e071ad4f6fb77c962e2799bffcd1f4a79af428699828329619e265"},"schema_version":"1.0"},"canonical_sha256":"5bfcecc0dd30bad9386f148e9d5fa706005aa9a7be61d7bcc28437eaccbc14f8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:19:36.413904Z","signature_b64":"YD7Q1C8+j48McKcPCSZIbmwToREBKvJlmgZcO+bYsTlwYAGMA4T/yOpAIQvRAuRIgLtayqeaMvurArRV8gpmDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5bfcecc0dd30bad9386f148e9d5fa706005aa9a7be61d7bcc28437eaccbc14f8","last_reissued_at":"2026-05-18T02:19:36.413525Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:19:36.413525Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1309.2571","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":"2026-05-18T02:19:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vy2iOGoZSP21XdRsuvyOgUq5LMFnRLwFzOC5TssS+amJ3ZsKc3ggs1Izs5vXOZ05llIek/jRHCeLaV/DWIrqBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T04:15:28.620068Z"},"content_sha256":"f3de50efcbe2bd93921a6d4fa1afbc660678e3aa59a024de8780445f187abd07","schema_version":"1.0","event_id":"sha256:f3de50efcbe2bd93921a6d4fa1afbc660678e3aa59a024de8780445f187abd07"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:LP6OZQG5GC5NSODPCSHJ2X5HAY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Complexity of control-affine motion planning","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Dario Prandi, Fr\\'ed\\'eric Jean","submitted_at":"2013-09-10T16:38:03Z","abstract_excerpt":"In this paper we study the complexity of the motion planning problem for control-affine systems. Such complexities are already defined and rather well-understood in the particular case of nonholonomic (or sub-Riemannian) systems. Our aim is to generalize these notions and results to systems with a drift. Accordingly, we present various definitions of complexity, as functions of the curve that is approximated, and of the precision of the approximation. Due to the lack of time-rescaling invariance of these systems, we consider geometric and parametrized curves separately. Then, we give some asym"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.2571","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:19:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"n5Aw6L5W2Dk42b8VJg/cqgewEjXTsB5LFK+gTBV0hfmUCn3XWcxuxfHAUa7N9pprtJkFpxpoU9YsU+lifcEICQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T04:15:28.620726Z"},"content_sha256":"baf04284c71ad48f645208b7e2a1afdc252976741db7e612ca5110bb92a4d02c","schema_version":"1.0","event_id":"sha256:baf04284c71ad48f645208b7e2a1afdc252976741db7e612ca5110bb92a4d02c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LP6OZQG5GC5NSODPCSHJ2X5HAY/bundle.json","state_url":"https://pith.science/pith/LP6OZQG5GC5NSODPCSHJ2X5HAY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LP6OZQG5GC5NSODPCSHJ2X5HAY/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":"2026-06-02T04:15:28Z","links":{"resolver":"https://pith.science/pith/LP6OZQG5GC5NSODPCSHJ2X5HAY","bundle":"https://pith.science/pith/LP6OZQG5GC5NSODPCSHJ2X5HAY/bundle.json","state":"https://pith.science/pith/LP6OZQG5GC5NSODPCSHJ2X5HAY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LP6OZQG5GC5NSODPCSHJ2X5HAY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:LP6OZQG5GC5NSODPCSHJ2X5HAY","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":"5f33649373e071ad4f6fb77c962e2799bffcd1f4a79af428699828329619e265","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-09-10T16:38:03Z","title_canon_sha256":"d224e57a127447939fa336d104f0951f4e6d566db04cf7417083f2f9115579eb"},"schema_version":"1.0","source":{"id":"1309.2571","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.2571","created_at":"2026-05-18T02:19:36Z"},{"alias_kind":"arxiv_version","alias_value":"1309.2571v2","created_at":"2026-05-18T02:19:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.2571","created_at":"2026-05-18T02:19:36Z"},{"alias_kind":"pith_short_12","alias_value":"LP6OZQG5GC5N","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_16","alias_value":"LP6OZQG5GC5NSODP","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_8","alias_value":"LP6OZQG5","created_at":"2026-05-18T12:27:51Z"}],"graph_snapshots":[{"event_id":"sha256:baf04284c71ad48f645208b7e2a1afdc252976741db7e612ca5110bb92a4d02c","target":"graph","created_at":"2026-05-18T02:19:36Z","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 this paper we study the complexity of the motion planning problem for control-affine systems. Such complexities are already defined and rather well-understood in the particular case of nonholonomic (or sub-Riemannian) systems. Our aim is to generalize these notions and results to systems with a drift. Accordingly, we present various definitions of complexity, as functions of the curve that is approximated, and of the precision of the approximation. Due to the lack of time-rescaling invariance of these systems, we consider geometric and parametrized curves separately. Then, we give some asym","authors_text":"Dario Prandi, Fr\\'ed\\'eric Jean","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-09-10T16:38:03Z","title":"Complexity of control-affine motion planning"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.2571","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:f3de50efcbe2bd93921a6d4fa1afbc660678e3aa59a024de8780445f187abd07","target":"record","created_at":"2026-05-18T02:19:36Z","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":"5f33649373e071ad4f6fb77c962e2799bffcd1f4a79af428699828329619e265","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-09-10T16:38:03Z","title_canon_sha256":"d224e57a127447939fa336d104f0951f4e6d566db04cf7417083f2f9115579eb"},"schema_version":"1.0","source":{"id":"1309.2571","kind":"arxiv","version":2}},"canonical_sha256":"5bfcecc0dd30bad9386f148e9d5fa706005aa9a7be61d7bcc28437eaccbc14f8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5bfcecc0dd30bad9386f148e9d5fa706005aa9a7be61d7bcc28437eaccbc14f8","first_computed_at":"2026-05-18T02:19:36.413525Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:19:36.413525Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YD7Q1C8+j48McKcPCSZIbmwToREBKvJlmgZcO+bYsTlwYAGMA4T/yOpAIQvRAuRIgLtayqeaMvurArRV8gpmDw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:19:36.413904Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.2571","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f3de50efcbe2bd93921a6d4fa1afbc660678e3aa59a024de8780445f187abd07","sha256:baf04284c71ad48f645208b7e2a1afdc252976741db7e612ca5110bb92a4d02c"],"state_sha256":"ba665f92764d87693587c901cd6df9cc3c0b9fed6f0a78961baa55b06bd52076"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RpUhYS7pgcSgpg+m44SSXM3EETH9Y2ID4OEQMaryhnb8pP7WjdwD1/z7mkccS3BeamKZYeZWEItadx9Rg+yjBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T04:15:28.624012Z","bundle_sha256":"140384352d6106160af2456617738d59b045ed3a6cd2ebf14cbe826e3629fe20"}}