{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:UCZFGWTV2VOGCMOYK4QGZOLN67","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":"6644f760e7d24a6e5e8b6281b7d1b2843acc3728edda0f7f07399db5f6d01a69","cross_cats_sorted":["math.MG","math.OC"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2026-03-07T15:39:36Z","title_canon_sha256":"bc80762cffab87db51a35cec5519bb54b57a83cd5eabaea5e09254feaa3f3dbf"},"schema_version":"1.0","source":{"id":"2603.07262","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2603.07262","created_at":"2026-07-14T02:21:30Z"},{"alias_kind":"arxiv_version","alias_value":"2603.07262v2","created_at":"2026-07-14T02:21:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2603.07262","created_at":"2026-07-14T02:21:30Z"},{"alias_kind":"pith_short_12","alias_value":"UCZFGWTV2VOG","created_at":"2026-07-14T02:21:30Z"},{"alias_kind":"pith_short_16","alias_value":"UCZFGWTV2VOGCMOY","created_at":"2026-07-14T02:21:30Z"},{"alias_kind":"pith_short_8","alias_value":"UCZFGWTV","created_at":"2026-07-14T02:21:30Z"}],"graph_snapshots":[{"event_id":"sha256:67f0c35eb5b6d212d048b198330c62b97a746010087177bb15c113355389257f","target":"graph","created_at":"2026-07-14T02:21:30Z","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/2603.07262/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The problem of finding optimal curves (the longest arcs) for sub-Lorentzian structures is an optimal control problem with an unbounded control set and a concave cost functional. The question of existence of an optimal solution is nontrivial for such problems. We solve here this question for some left-invariant three-dimensional contact sub-Lorentzian structures, whose classification is known. We propose sufficient conditions for the existence of the longest arcs for left-invariant (sub-)Lorentzian structures on solvable Lie groups and on the universal cover of the Lie group SL(2, R).","authors_text":"A.V. Podobryaev","cross_cats":["math.MG","math.OC"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2026-03-07T15:39:36Z","title":"Existence of the longest arcs for left-invariant three-dimensional contact sub-Lorentzian structures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2603.07262","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":"sha256:46a3449bd1041d62de01161bc5e54088d797952ed6237a57fdd6f81fc6e5e274","target":"record","created_at":"2026-07-14T02:21:30Z","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":"6644f760e7d24a6e5e8b6281b7d1b2843acc3728edda0f7f07399db5f6d01a69","cross_cats_sorted":["math.MG","math.OC"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2026-03-07T15:39:36Z","title_canon_sha256":"bc80762cffab87db51a35cec5519bb54b57a83cd5eabaea5e09254feaa3f3dbf"},"schema_version":"1.0","source":{"id":"2603.07262","kind":"arxiv","version":2}},"canonical_sha256":"a0b2535a75d55c6131d857206cb96df7f0c1285c809c29a189a82ff1980d77cf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a0b2535a75d55c6131d857206cb96df7f0c1285c809c29a189a82ff1980d77cf","first_computed_at":"2026-07-14T02:21:30.737906Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-14T02:21:30.737906Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lNrFEE49mHdF7UepIEUiGtY9L/6UiQfOws0zZe2y/lWPWlvsYEKQ/eBNy2Umw1rQVM8ZYHhpzKCdxGThq7TgDg==","signature_status":"signed_v1","signed_at":"2026-07-14T02:21:30.738855Z","signed_message":"canonical_sha256_bytes"},"source_id":"2603.07262","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:46a3449bd1041d62de01161bc5e54088d797952ed6237a57fdd6f81fc6e5e274","sha256:67f0c35eb5b6d212d048b198330c62b97a746010087177bb15c113355389257f"],"state_sha256":"e7effd8d528dec2edbb7cfa54f0c50ece885837ca45aa5fca81875603fe95c93"}