{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:M7ICKSVOID4G3I4LKFBCD2YFYG","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":"7b0fcff1bb1c3c81e3444dcf334c0d7a5489b3319ad75f1bf07b66b63d572535","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2020-04-21T17:59:59Z","title_canon_sha256":"38d049e4b75f4032b9537dee61f2f316221fef661eeadfc6e3d6b462584c4b7b"},"schema_version":"1.0","source":{"id":"2004.10194","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2004.10194","created_at":"2026-07-05T02:30:57Z"},{"alias_kind":"arxiv_version","alias_value":"2004.10194v2","created_at":"2026-07-05T02:30:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2004.10194","created_at":"2026-07-05T02:30:57Z"},{"alias_kind":"pith_short_12","alias_value":"M7ICKSVOID4G","created_at":"2026-07-05T02:30:57Z"},{"alias_kind":"pith_short_16","alias_value":"M7ICKSVOID4G3I4L","created_at":"2026-07-05T02:30:57Z"},{"alias_kind":"pith_short_8","alias_value":"M7ICKSVO","created_at":"2026-07-05T02:30:57Z"}],"graph_snapshots":[{"event_id":"sha256:7efea991777d17af8180ce2af4070d88f06cb489e997db61f2a1abffa42bd01a","target":"graph","created_at":"2026-07-05T02:30:57Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2004.10194/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider a series of optimal control problems with 2-dimensional control lying in an arbitrary convex compact set $\\Omega$. The considered problems are well studied for the case when $\\Omega$ is a unit disc, but barely studied for arbitrary $\\Omega$. We derive extremals to these problems in general case by using machinery of convex trigonometry, which allows us to do this identically and independently on the shape of $\\Omega$. The paper describes geodesics in (i) the Finsler problem on the Lobachevsky hyperbolic plane; (ii) left-invariant sub-Finsler problems on all unimodular 3D Lie groups","authors_text":"A.A. Ardentov, L.V. Lokutsievskiy, Yu.L. Sachkov","cross_cats":["math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2020-04-21T17:59:59Z","title":"Extremals for a series of sub-Finsler problems with 2-dimensional control via convex trigonometry"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2004.10194","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:ae1c854369ed8592463529c106870c85e18f3af765633b4bc4f06105fa34ea2b","target":"record","created_at":"2026-07-05T02:30:57Z","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":"7b0fcff1bb1c3c81e3444dcf334c0d7a5489b3319ad75f1bf07b66b63d572535","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2020-04-21T17:59:59Z","title_canon_sha256":"38d049e4b75f4032b9537dee61f2f316221fef661eeadfc6e3d6b462584c4b7b"},"schema_version":"1.0","source":{"id":"2004.10194","kind":"arxiv","version":2}},"canonical_sha256":"67d0254aae40f86da38b514221eb05c1be1e71afe4daf07e25a7d191bdbe47db","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"67d0254aae40f86da38b514221eb05c1be1e71afe4daf07e25a7d191bdbe47db","first_computed_at":"2026-07-05T02:30:57.426930Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:30:57.426930Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zX18Stge+qaVcoBxrGOmk3+9y3OlVwV34AxWZKauk40yd5mC1HmrGOx7LYlaHFE/F3u0IomLeq1Oy5QZYWlKDg==","signature_status":"signed_v1","signed_at":"2026-07-05T02:30:57.427457Z","signed_message":"canonical_sha256_bytes"},"source_id":"2004.10194","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ae1c854369ed8592463529c106870c85e18f3af765633b4bc4f06105fa34ea2b","sha256:7efea991777d17af8180ce2af4070d88f06cb489e997db61f2a1abffa42bd01a"],"state_sha256":"4f05c9f161731847f1697b84cdb96d3676b5a329931b606be01a4d94913ef9cc"}