{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:NGESP2QKFUGJ2VFI4BWMXCBRXJ","short_pith_number":"pith:NGESP2QK","canonical_record":{"source":{"id":"1609.03704","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-09-13T07:09:06Z","cross_cats_sorted":[],"title_canon_sha256":"05d5b6c8562552d3a33afaac5f80873b471f1e7463bed6524f8d7856221d42f7","abstract_canon_sha256":"394a37210a91bb8d708e2e4df703a9540e7fb02aca834a228ba050e6397aeba2"},"schema_version":"1.0"},"canonical_sha256":"698927ea0a2d0c9d54a8e06ccb8831ba74d5197c79c5e44815db30a9edbbb1ac","source":{"kind":"arxiv","id":"1609.03704","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.03704","created_at":"2026-05-18T00:47:10Z"},{"alias_kind":"arxiv_version","alias_value":"1609.03704v1","created_at":"2026-05-18T00:47:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.03704","created_at":"2026-05-18T00:47:10Z"},{"alias_kind":"pith_short_12","alias_value":"NGESP2QKFUGJ","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_16","alias_value":"NGESP2QKFUGJ2VFI","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_8","alias_value":"NGESP2QK","created_at":"2026-05-18T12:30:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:NGESP2QKFUGJ2VFI4BWMXCBRXJ","target":"record","payload":{"canonical_record":{"source":{"id":"1609.03704","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-09-13T07:09:06Z","cross_cats_sorted":[],"title_canon_sha256":"05d5b6c8562552d3a33afaac5f80873b471f1e7463bed6524f8d7856221d42f7","abstract_canon_sha256":"394a37210a91bb8d708e2e4df703a9540e7fb02aca834a228ba050e6397aeba2"},"schema_version":"1.0"},"canonical_sha256":"698927ea0a2d0c9d54a8e06ccb8831ba74d5197c79c5e44815db30a9edbbb1ac","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:47:10.732055Z","signature_b64":"tMKcGl30LntsE16Z2kL3D/6vn0Fr6hrJd8hrrcMMzU6h9MSMyIh1Vn71tfLpxFExI2J++Wv4cX33m6LvoNHiBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"698927ea0a2d0c9d54a8e06ccb8831ba74d5197c79c5e44815db30a9edbbb1ac","last_reissued_at":"2026-05-18T00:47:10.731399Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:47:10.731399Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1609.03704","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:47:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EEZ4MtWTJ0wTDXBszL5u7J1wrYG0IxvgS9lmABKLvcPEbhhlGHZjBdGCDYkuBWC2KZK95z6g4DX/1LnJ+3qxBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T00:55:15.598357Z"},"content_sha256":"91485d487023268ffb90b88200331592b8b7ce2ca5f62076dcab3e9956921711","schema_version":"1.0","event_id":"sha256:91485d487023268ffb90b88200331592b8b7ce2ca5f62076dcab3e9956921711"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:NGESP2QKFUGJ2VFI4BWMXCBRXJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Relation between Euler's Elasticae and Sub-Riemannian Geodesics on SE(2)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Alexey Mashtakov, Andrei Ardentov, Yuri Sachkov","submitted_at":"2016-09-13T07:09:06Z","abstract_excerpt":"In this note we describe a relation between Euler's elasticae and sub-Riemannian geodesics on SE(2). Analyzing the Hamiltonian system of Pontryagin maximum principle we show that these two curves coincide only in the case when they are segments of a straight line."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.03704","kind":"arxiv","version":1},"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":"2026-05-18T00:47:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fzhK4BwijfBbcxfI8YKov1G3kVWOGVE9qPoH2KXxPjy7/e1O4tBXMcCVZ5uz3gWdFvKO/zMKj/xMHO7+qTrkBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T00:55:15.598776Z"},"content_sha256":"33d027f1c61ae1877accfcfdfba48dccb523b25145f247990d7197658b0ecf47","schema_version":"1.0","event_id":"sha256:33d027f1c61ae1877accfcfdfba48dccb523b25145f247990d7197658b0ecf47"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NGESP2QKFUGJ2VFI4BWMXCBRXJ/bundle.json","state_url":"https://pith.science/pith/NGESP2QKFUGJ2VFI4BWMXCBRXJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NGESP2QKFUGJ2VFI4BWMXCBRXJ/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":"2026-05-31T00:55:15Z","links":{"resolver":"https://pith.science/pith/NGESP2QKFUGJ2VFI4BWMXCBRXJ","bundle":"https://pith.science/pith/NGESP2QKFUGJ2VFI4BWMXCBRXJ/bundle.json","state":"https://pith.science/pith/NGESP2QKFUGJ2VFI4BWMXCBRXJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NGESP2QKFUGJ2VFI4BWMXCBRXJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:NGESP2QKFUGJ2VFI4BWMXCBRXJ","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":"394a37210a91bb8d708e2e4df703a9540e7fb02aca834a228ba050e6397aeba2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-09-13T07:09:06Z","title_canon_sha256":"05d5b6c8562552d3a33afaac5f80873b471f1e7463bed6524f8d7856221d42f7"},"schema_version":"1.0","source":{"id":"1609.03704","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.03704","created_at":"2026-05-18T00:47:10Z"},{"alias_kind":"arxiv_version","alias_value":"1609.03704v1","created_at":"2026-05-18T00:47:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.03704","created_at":"2026-05-18T00:47:10Z"},{"alias_kind":"pith_short_12","alias_value":"NGESP2QKFUGJ","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_16","alias_value":"NGESP2QKFUGJ2VFI","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_8","alias_value":"NGESP2QK","created_at":"2026-05-18T12:30:32Z"}],"graph_snapshots":[{"event_id":"sha256:33d027f1c61ae1877accfcfdfba48dccb523b25145f247990d7197658b0ecf47","target":"graph","created_at":"2026-05-18T00:47:10Z","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 note we describe a relation between Euler's elasticae and sub-Riemannian geodesics on SE(2). Analyzing the Hamiltonian system of Pontryagin maximum principle we show that these two curves coincide only in the case when they are segments of a straight line.","authors_text":"Alexey Mashtakov, Andrei Ardentov, Yuri Sachkov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-09-13T07:09:06Z","title":"Relation between Euler's Elasticae and Sub-Riemannian Geodesics on SE(2)"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.03704","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":"sha256:91485d487023268ffb90b88200331592b8b7ce2ca5f62076dcab3e9956921711","target":"record","created_at":"2026-05-18T00:47:10Z","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":"394a37210a91bb8d708e2e4df703a9540e7fb02aca834a228ba050e6397aeba2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-09-13T07:09:06Z","title_canon_sha256":"05d5b6c8562552d3a33afaac5f80873b471f1e7463bed6524f8d7856221d42f7"},"schema_version":"1.0","source":{"id":"1609.03704","kind":"arxiv","version":1}},"canonical_sha256":"698927ea0a2d0c9d54a8e06ccb8831ba74d5197c79c5e44815db30a9edbbb1ac","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"698927ea0a2d0c9d54a8e06ccb8831ba74d5197c79c5e44815db30a9edbbb1ac","first_computed_at":"2026-05-18T00:47:10.731399Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:47:10.731399Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tMKcGl30LntsE16Z2kL3D/6vn0Fr6hrJd8hrrcMMzU6h9MSMyIh1Vn71tfLpxFExI2J++Wv4cX33m6LvoNHiBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:47:10.732055Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.03704","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:91485d487023268ffb90b88200331592b8b7ce2ca5f62076dcab3e9956921711","sha256:33d027f1c61ae1877accfcfdfba48dccb523b25145f247990d7197658b0ecf47"],"state_sha256":"65b4cee4ad4ead63b6460cb7862cda4fb17c996cc118fdc4b9853e6f8bcf3ca9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kh0taZfutw+yoHwnxXZy9YxR+5d6qSNgPDhmfNaI7jAudnpjyvcH9Yeb9mLiKi8TGjKaDDzgwMcWeQ4x4oJsBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T00:55:15.601723Z","bundle_sha256":"ce6b956453f5ec90253b4a2bbf382514f3ae622a3ed857f4838e31daff31419e"}}