{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:2OMOFLHPXBO3XKGDNBOT45ZQTJ","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":"91964a8def4422fcd90cf27a5859b6324b73d14be134ea6fd471d5bbd95cffd7","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-05-26T19:43:06Z","title_canon_sha256":"3bc5bf099d7cb15aa620f34d0e61bc068b35bfbb8671507906562545d82d7d78"},"schema_version":"1.0","source":{"id":"1305.6061","kind":"arxiv","version":9}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.6061","created_at":"2026-05-18T01:17:31Z"},{"alias_kind":"arxiv_version","alias_value":"1305.6061v9","created_at":"2026-05-18T01:17:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.6061","created_at":"2026-05-18T01:17:31Z"},{"alias_kind":"pith_short_12","alias_value":"2OMOFLHPXBO3","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"2OMOFLHPXBO3XKGD","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"2OMOFLHP","created_at":"2026-05-18T12:27:32Z"}],"graph_snapshots":[{"event_id":"sha256:3763c3a25a6959e0158da2497292c164e3e3434dbb8f16b7483858200c0bfdda","target":"graph","created_at":"2026-05-18T01:17:31Z","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 consider the problem $\\mathbf{P_{curve}}$ of minimizing $\\int \\limits_0^L \\sqrt{\\xi^2 + \\kappa^2(s)} \\, {\\rm d}s$ for a curve $\\mathbf{x}$ on $\\mathbb R$ with fixed boundary points and directions. Here the total length $L\\geq 0$ is free, $s$ denotes the arclength parameter, $\\kappa$ denotes the absolute curvature of $\\mathbf{x}$, and $\\xi>0$ is constant. We lift problem $\\mathbf{P_{curve}}$ on $\\mathbb R^3$ to a sub-Riemannian problem $\\mathbf{P_{mec}}$ on $\\operatorname{SE(3)}\\nolimits/(\\{\\mathbf{0}\\}\\times \\operatorname{SO(2)}\\nolimits)$. Here, for admissible boundary conditions, the spat","authors_text":"Alexey Mashtakov, Arpan Ghosh, Remco Duits, Tom Dela Haije","cross_cats":["math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-05-26T19:43:06Z","title":"On sub-Riemannian geodesics in $SE(3)$ whose spatial projections do not have cusps"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.6061","kind":"arxiv","version":9},"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":"sha256:836d04d89c9c761a2eef8f06b2ed6d4330ac9c1f42d4c4a906e67df6fcb90abe","target":"record","created_at":"2026-05-18T01:17:31Z","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":"91964a8def4422fcd90cf27a5859b6324b73d14be134ea6fd471d5bbd95cffd7","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-05-26T19:43:06Z","title_canon_sha256":"3bc5bf099d7cb15aa620f34d0e61bc068b35bfbb8671507906562545d82d7d78"},"schema_version":"1.0","source":{"id":"1305.6061","kind":"arxiv","version":9}},"canonical_sha256":"d398e2acefb85dbba8c3685d3e77309a41c7715059e3da209f065d0902e486b9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d398e2acefb85dbba8c3685d3e77309a41c7715059e3da209f065d0902e486b9","first_computed_at":"2026-05-18T01:17:31.042634Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:17:31.042634Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DOSqzW6a/ngv2nebetixnMsK08fanFFU/BhB2ZYck3i3seg31cmjOM95AenU8xHfBBpyJdRbt6UZwqvUwr8YAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:17:31.043277Z","signed_message":"canonical_sha256_bytes"},"source_id":"1305.6061","source_kind":"arxiv","source_version":9}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:836d04d89c9c761a2eef8f06b2ed6d4330ac9c1f42d4c4a906e67df6fcb90abe","sha256:3763c3a25a6959e0158da2497292c164e3e3434dbb8f16b7483858200c0bfdda"],"state_sha256":"d6e3a62705782154d428e0908c4421a7fbadce0bd9f51078523cdd508448c44f"}