{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:7U23DPYXNIV3NQGSJO43IZEABH","short_pith_number":"pith:7U23DPYX","canonical_record":{"source":{"id":"1105.5766","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2011-05-29T07:23:12Z","cross_cats_sorted":["cs.SY"],"title_canon_sha256":"94674c941c5d33970d8d1fee19c73e1d440a0bdcebc66856ac87728dc5c81a1a","abstract_canon_sha256":"be91e147a73e4d144521a0f93fb2634ab5379f7d2795e85d6b5ca2735ff37246"},"schema_version":"1.0"},"canonical_sha256":"fd35b1bf176a2bb6c0d24bb9b4648009ec8aa5094042895c177691ff1ba055d9","source":{"kind":"arxiv","id":"1105.5766","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.5766","created_at":"2026-05-18T04:09:34Z"},{"alias_kind":"arxiv_version","alias_value":"1105.5766v2","created_at":"2026-05-18T04:09:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.5766","created_at":"2026-05-18T04:09:34Z"},{"alias_kind":"pith_short_12","alias_value":"7U23DPYXNIV3","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"7U23DPYXNIV3NQGS","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"7U23DPYX","created_at":"2026-05-18T12:26:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:7U23DPYXNIV3NQGSJO43IZEABH","target":"record","payload":{"canonical_record":{"source":{"id":"1105.5766","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2011-05-29T07:23:12Z","cross_cats_sorted":["cs.SY"],"title_canon_sha256":"94674c941c5d33970d8d1fee19c73e1d440a0bdcebc66856ac87728dc5c81a1a","abstract_canon_sha256":"be91e147a73e4d144521a0f93fb2634ab5379f7d2795e85d6b5ca2735ff37246"},"schema_version":"1.0"},"canonical_sha256":"fd35b1bf176a2bb6c0d24bb9b4648009ec8aa5094042895c177691ff1ba055d9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:09:34.766994Z","signature_b64":"VjZy7XGrFT+XGjvsgQh95tNqM1NzzhpSTLYgdqLHwfzsne3mZJfPCGViA9+NcFDIz0IRf6fAN+PAVShbnmHFCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fd35b1bf176a2bb6c0d24bb9b4648009ec8aa5094042895c177691ff1ba055d9","last_reissued_at":"2026-05-18T04:09:34.766242Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:09:34.766242Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1105.5766","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":"2026-05-18T04:09:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"q7tI02SZneM+sUsvTB6ksMAjroQM5REelsCLQEv0QL6/IowwxPZ3cBy7YqNr09PqE3pJcQVNftcWoXM2SazqDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T12:53:24.892058Z"},"content_sha256":"668440a62c006a022d000961d39b7f44b80a147a9ea9c5407db45ec49a694db9","schema_version":"1.0","event_id":"sha256:668440a62c006a022d000961d39b7f44b80a147a9ea9c5407db45ec49a694db9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:7U23DPYXNIV3NQGSJO43IZEABH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On 2-step, corank 2 nilpotent sub-Riemannian metrics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SY"],"primary_cat":"math.OC","authors_text":"Davide Barilari (SISSA/ISAS), Jean-Paul Gauthier (LSIS), Ugo Boscain (CMAP)","submitted_at":"2011-05-29T07:23:12Z","abstract_excerpt":"In this paper we study the nilpotent 2-step, corank 2 sub-Riemannian metrics that are nilpotent approximations of general sub-Riemannian metrics. We exhibit optimal syntheses for these problems. It turns out that in general the cut time is not equal to the first conjugate time but has a simple explicit expression. As a byproduct of this study we get some smoothness properties of the spherical Hausdorff measure in the case of a generic 6 dimensional, 2-step corank 2 sub-Riemannian metric."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.5766","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":"2026-05-18T04:09:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Y4XDmDizhXkB7qVUhZfNzZEDlu1IdGQs6HedM3oQPgxUDL+Okk5zuR/Ffv0pc9uDVGVVP8zqsDEqdSzrSm4hBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T12:53:24.892435Z"},"content_sha256":"43a571d2b68de0b0ca3d5f45c3cb58f01f35e7c2e95f5aa7286707dd09312533","schema_version":"1.0","event_id":"sha256:43a571d2b68de0b0ca3d5f45c3cb58f01f35e7c2e95f5aa7286707dd09312533"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7U23DPYXNIV3NQGSJO43IZEABH/bundle.json","state_url":"https://pith.science/pith/7U23DPYXNIV3NQGSJO43IZEABH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7U23DPYXNIV3NQGSJO43IZEABH/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":"2026-06-25T12:53:24Z","links":{"resolver":"https://pith.science/pith/7U23DPYXNIV3NQGSJO43IZEABH","bundle":"https://pith.science/pith/7U23DPYXNIV3NQGSJO43IZEABH/bundle.json","state":"https://pith.science/pith/7U23DPYXNIV3NQGSJO43IZEABH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7U23DPYXNIV3NQGSJO43IZEABH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:7U23DPYXNIV3NQGSJO43IZEABH","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":"be91e147a73e4d144521a0f93fb2634ab5379f7d2795e85d6b5ca2735ff37246","cross_cats_sorted":["cs.SY"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2011-05-29T07:23:12Z","title_canon_sha256":"94674c941c5d33970d8d1fee19c73e1d440a0bdcebc66856ac87728dc5c81a1a"},"schema_version":"1.0","source":{"id":"1105.5766","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.5766","created_at":"2026-05-18T04:09:34Z"},{"alias_kind":"arxiv_version","alias_value":"1105.5766v2","created_at":"2026-05-18T04:09:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.5766","created_at":"2026-05-18T04:09:34Z"},{"alias_kind":"pith_short_12","alias_value":"7U23DPYXNIV3","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"7U23DPYXNIV3NQGS","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"7U23DPYX","created_at":"2026-05-18T12:26:22Z"}],"graph_snapshots":[{"event_id":"sha256:43a571d2b68de0b0ca3d5f45c3cb58f01f35e7c2e95f5aa7286707dd09312533","target":"graph","created_at":"2026-05-18T04:09:34Z","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 nilpotent 2-step, corank 2 sub-Riemannian metrics that are nilpotent approximations of general sub-Riemannian metrics. We exhibit optimal syntheses for these problems. It turns out that in general the cut time is not equal to the first conjugate time but has a simple explicit expression. As a byproduct of this study we get some smoothness properties of the spherical Hausdorff measure in the case of a generic 6 dimensional, 2-step corank 2 sub-Riemannian metric.","authors_text":"Davide Barilari (SISSA/ISAS), Jean-Paul Gauthier (LSIS), Ugo Boscain (CMAP)","cross_cats":["cs.SY"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2011-05-29T07:23:12Z","title":"On 2-step, corank 2 nilpotent sub-Riemannian metrics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.5766","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":"sha256:668440a62c006a022d000961d39b7f44b80a147a9ea9c5407db45ec49a694db9","target":"record","created_at":"2026-05-18T04:09:34Z","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":"be91e147a73e4d144521a0f93fb2634ab5379f7d2795e85d6b5ca2735ff37246","cross_cats_sorted":["cs.SY"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2011-05-29T07:23:12Z","title_canon_sha256":"94674c941c5d33970d8d1fee19c73e1d440a0bdcebc66856ac87728dc5c81a1a"},"schema_version":"1.0","source":{"id":"1105.5766","kind":"arxiv","version":2}},"canonical_sha256":"fd35b1bf176a2bb6c0d24bb9b4648009ec8aa5094042895c177691ff1ba055d9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fd35b1bf176a2bb6c0d24bb9b4648009ec8aa5094042895c177691ff1ba055d9","first_computed_at":"2026-05-18T04:09:34.766242Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:09:34.766242Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VjZy7XGrFT+XGjvsgQh95tNqM1NzzhpSTLYgdqLHwfzsne3mZJfPCGViA9+NcFDIz0IRf6fAN+PAVShbnmHFCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:09:34.766994Z","signed_message":"canonical_sha256_bytes"},"source_id":"1105.5766","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:668440a62c006a022d000961d39b7f44b80a147a9ea9c5407db45ec49a694db9","sha256:43a571d2b68de0b0ca3d5f45c3cb58f01f35e7c2e95f5aa7286707dd09312533"],"state_sha256":"478d404f43c3554a39f74ee80d844086a6c8af17c17d51fb1483d4e4b4283af0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1CkAhv15GcjTiLBA7rNcNv3mUrBUPESwzW5HUlp7yVx92tJ2V5cpfGnbzv03EWFD0fwt80nXlUVLQC5QEWp0CA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T12:53:24.894533Z","bundle_sha256":"2947a2aa7cf427321f844cba21bc210e6f41f57d401f00240de8c60bb07288c0"}}