{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:6NNRNRSCUPW4R4QWVYIHV2U6H4","short_pith_number":"pith:6NNRNRSC","canonical_record":{"source":{"id":"1802.08480","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-02-23T11:02:58Z","cross_cats_sorted":[],"title_canon_sha256":"5364147af4017fb0e30f2fb78be6877b45ba45e825149488775a207ac9925e3b","abstract_canon_sha256":"1e41fa6493e86c1b60b552beb0bfa122c51e22355917ec0241c10c20351a862a"},"schema_version":"1.0"},"canonical_sha256":"f35b16c642a3edc8f216ae107aea9e3f25d50b46b36d183ac6606ffcfe85ae17","source":{"kind":"arxiv","id":"1802.08480","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.08480","created_at":"2026-05-17T23:50:49Z"},{"alias_kind":"arxiv_version","alias_value":"1802.08480v3","created_at":"2026-05-17T23:50:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.08480","created_at":"2026-05-17T23:50:49Z"},{"alias_kind":"pith_short_12","alias_value":"6NNRNRSCUPW4","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_16","alias_value":"6NNRNRSCUPW4R4QW","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_8","alias_value":"6NNRNRSC","created_at":"2026-05-18T12:32:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:6NNRNRSCUPW4R4QWVYIHV2U6H4","target":"record","payload":{"canonical_record":{"source":{"id":"1802.08480","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-02-23T11:02:58Z","cross_cats_sorted":[],"title_canon_sha256":"5364147af4017fb0e30f2fb78be6877b45ba45e825149488775a207ac9925e3b","abstract_canon_sha256":"1e41fa6493e86c1b60b552beb0bfa122c51e22355917ec0241c10c20351a862a"},"schema_version":"1.0"},"canonical_sha256":"f35b16c642a3edc8f216ae107aea9e3f25d50b46b36d183ac6606ffcfe85ae17","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:50:49.312528Z","signature_b64":"SBdfBHCA3REQMT49YVmEhq+kbkKrGM+/e/ELAJ/5ri7tAi8D2YHWCzBTmTkO4ouDbD38i5Z+Hku7ot02MqWoAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f35b16c642a3edc8f216ae107aea9e3f25d50b46b36d183ac6606ffcfe85ae17","last_reissued_at":"2026-05-17T23:50:49.311777Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:50:49.311777Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1802.08480","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:50:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tNa1uhunSefgk64zT7IKJjWTrkgxTiix0CuLGzNFZLqCgwR5x8hfapx4udkGVwM8Tslaclk0WrCzJIh5tW52Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T10:35:47.080073Z"},"content_sha256":"61549b0759d7f0883b65ee1c1db5256b04987c3a07842c8aaf85e7d61e3e73b2","schema_version":"1.0","event_id":"sha256:61549b0759d7f0883b65ee1c1db5256b04987c3a07842c8aaf85e7d61e3e73b2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:6NNRNRSCUPW4R4QWVYIHV2U6H4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Local geometric control of a certain mechanism with the growth vector (4,7)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Jaroslav Hrdina, Lenka Zalabova","submitted_at":"2018-02-23T11:02:58Z","abstract_excerpt":"We study local control of the mechanism with the growth vector (4,7). We study controllability and extremal trajectories on the nilpotent approximation as an example of the control theory on Lie group. We give solutions of the system an show examples of local extremal trajectories."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.08480","kind":"arxiv","version":3},"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":"2026-05-17T23:50:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VuU54C+UP8aLK8bYe92VjcLmggb0wrqCTkrULFDrTkW7fO1df3j3zE2+ay3LgSFafG/t3IuaraXNECA6u7+1BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T10:35:47.080432Z"},"content_sha256":"1678f5fc3e4c0c5d7eb36ad4fd1e9c1a9398bb1fdb5c12c63329ae2c66848d76","schema_version":"1.0","event_id":"sha256:1678f5fc3e4c0c5d7eb36ad4fd1e9c1a9398bb1fdb5c12c63329ae2c66848d76"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6NNRNRSCUPW4R4QWVYIHV2U6H4/bundle.json","state_url":"https://pith.science/pith/6NNRNRSCUPW4R4QWVYIHV2U6H4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6NNRNRSCUPW4R4QWVYIHV2U6H4/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":"2026-06-22T10:35:47Z","links":{"resolver":"https://pith.science/pith/6NNRNRSCUPW4R4QWVYIHV2U6H4","bundle":"https://pith.science/pith/6NNRNRSCUPW4R4QWVYIHV2U6H4/bundle.json","state":"https://pith.science/pith/6NNRNRSCUPW4R4QWVYIHV2U6H4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6NNRNRSCUPW4R4QWVYIHV2U6H4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:6NNRNRSCUPW4R4QWVYIHV2U6H4","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":"1e41fa6493e86c1b60b552beb0bfa122c51e22355917ec0241c10c20351a862a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-02-23T11:02:58Z","title_canon_sha256":"5364147af4017fb0e30f2fb78be6877b45ba45e825149488775a207ac9925e3b"},"schema_version":"1.0","source":{"id":"1802.08480","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.08480","created_at":"2026-05-17T23:50:49Z"},{"alias_kind":"arxiv_version","alias_value":"1802.08480v3","created_at":"2026-05-17T23:50:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.08480","created_at":"2026-05-17T23:50:49Z"},{"alias_kind":"pith_short_12","alias_value":"6NNRNRSCUPW4","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_16","alias_value":"6NNRNRSCUPW4R4QW","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_8","alias_value":"6NNRNRSC","created_at":"2026-05-18T12:32:11Z"}],"graph_snapshots":[{"event_id":"sha256:1678f5fc3e4c0c5d7eb36ad4fd1e9c1a9398bb1fdb5c12c63329ae2c66848d76","target":"graph","created_at":"2026-05-17T23:50:49Z","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 local control of the mechanism with the growth vector (4,7). We study controllability and extremal trajectories on the nilpotent approximation as an example of the control theory on Lie group. We give solutions of the system an show examples of local extremal trajectories.","authors_text":"Jaroslav Hrdina, Lenka Zalabova","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-02-23T11:02:58Z","title":"Local geometric control of a certain mechanism with the growth vector (4,7)"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.08480","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":"sha256:61549b0759d7f0883b65ee1c1db5256b04987c3a07842c8aaf85e7d61e3e73b2","target":"record","created_at":"2026-05-17T23:50:49Z","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":"1e41fa6493e86c1b60b552beb0bfa122c51e22355917ec0241c10c20351a862a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-02-23T11:02:58Z","title_canon_sha256":"5364147af4017fb0e30f2fb78be6877b45ba45e825149488775a207ac9925e3b"},"schema_version":"1.0","source":{"id":"1802.08480","kind":"arxiv","version":3}},"canonical_sha256":"f35b16c642a3edc8f216ae107aea9e3f25d50b46b36d183ac6606ffcfe85ae17","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f35b16c642a3edc8f216ae107aea9e3f25d50b46b36d183ac6606ffcfe85ae17","first_computed_at":"2026-05-17T23:50:49.311777Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:50:49.311777Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SBdfBHCA3REQMT49YVmEhq+kbkKrGM+/e/ELAJ/5ri7tAi8D2YHWCzBTmTkO4ouDbD38i5Z+Hku7ot02MqWoAA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:50:49.312528Z","signed_message":"canonical_sha256_bytes"},"source_id":"1802.08480","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:61549b0759d7f0883b65ee1c1db5256b04987c3a07842c8aaf85e7d61e3e73b2","sha256:1678f5fc3e4c0c5d7eb36ad4fd1e9c1a9398bb1fdb5c12c63329ae2c66848d76"],"state_sha256":"db08658a2a18294dae0c8f6bcf0c5a6ab550868836dde60761830e8dfb8cd585"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"l4/JrCO/k4AS0pVZtFMn0XlMk0yxtOJnvRsG2z32GiZDql3p9LfCRFs7Go/BSy8dmxHZRCNhcJ2PdkxSwX9wDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T10:35:47.082404Z","bundle_sha256":"30c0b4f7183d3a9a7a08ff647d2000f2b49f6aa829db56e37afa1d44a9f404dd"}}