{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:UCZFGWTV2VOGCMOYK4QGZOLN67","short_pith_number":"pith:UCZFGWTV","schema_version":"1.0","canonical_sha256":"a0b2535a75d55c6131d857206cb96df7f0c1285c809c29a189a82ff1980d77cf","source":{"kind":"arxiv","id":"2603.07262","version":2},"attestation_state":"computed","paper":{"title":"Existence of the longest arcs for left-invariant three-dimensional contact sub-Lorentzian structures","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.MG","math.OC"],"primary_cat":"math.DG","authors_text":"A.V. Podobryaev","submitted_at":"2026-03-07T15:39:36Z","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)."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2603.07262","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2026-03-07T15:39:36Z","cross_cats_sorted":["math.MG","math.OC"],"title_canon_sha256":"bc80762cffab87db51a35cec5519bb54b57a83cd5eabaea5e09254feaa3f3dbf","abstract_canon_sha256":"6644f760e7d24a6e5e8b6281b7d1b2843acc3728edda0f7f07399db5f6d01a69"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-14T02:21:30.738855Z","signature_b64":"lNrFEE49mHdF7UepIEUiGtY9L/6UiQfOws0zZe2y/lWPWlvsYEKQ/eBNy2Umw1rQVM8ZYHhpzKCdxGThq7TgDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a0b2535a75d55c6131d857206cb96df7f0c1285c809c29a189a82ff1980d77cf","last_reissued_at":"2026-07-14T02:21:30.737906Z","signature_status":"signed_v1","first_computed_at":"2026-07-14T02:21:30.737906Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Existence of the longest arcs for left-invariant three-dimensional contact sub-Lorentzian structures","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.MG","math.OC"],"primary_cat":"math.DG","authors_text":"A.V. Podobryaev","submitted_at":"2026-03-07T15:39:36Z","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)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2603.07262","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2603.07262/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2603.07262","created_at":"2026-07-14T02:21:30.738339+00:00"},{"alias_kind":"arxiv_version","alias_value":"2603.07262v2","created_at":"2026-07-14T02:21:30.738339+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2603.07262","created_at":"2026-07-14T02:21:30.738339+00:00"},{"alias_kind":"pith_short_12","alias_value":"UCZFGWTV2VOG","created_at":"2026-07-14T02:21:30.738339+00:00"},{"alias_kind":"pith_short_16","alias_value":"UCZFGWTV2VOGCMOY","created_at":"2026-07-14T02:21:30.738339+00:00"},{"alias_kind":"pith_short_8","alias_value":"UCZFGWTV","created_at":"2026-07-14T02:21:30.738339+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/UCZFGWTV2VOGCMOYK4QGZOLN67","json":"https://pith.science/pith/UCZFGWTV2VOGCMOYK4QGZOLN67.json","graph_json":"https://pith.science/api/pith-number/UCZFGWTV2VOGCMOYK4QGZOLN67/graph.json","events_json":"https://pith.science/api/pith-number/UCZFGWTV2VOGCMOYK4QGZOLN67/events.json","paper":"https://pith.science/paper/UCZFGWTV"},"agent_actions":{"view_html":"https://pith.science/pith/UCZFGWTV2VOGCMOYK4QGZOLN67","download_json":"https://pith.science/pith/UCZFGWTV2VOGCMOYK4QGZOLN67.json","view_paper":"https://pith.science/paper/UCZFGWTV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2603.07262&json=true","fetch_graph":"https://pith.science/api/pith-number/UCZFGWTV2VOGCMOYK4QGZOLN67/graph.json","fetch_events":"https://pith.science/api/pith-number/UCZFGWTV2VOGCMOYK4QGZOLN67/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UCZFGWTV2VOGCMOYK4QGZOLN67/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UCZFGWTV2VOGCMOYK4QGZOLN67/action/storage_attestation","attest_author":"https://pith.science/pith/UCZFGWTV2VOGCMOYK4QGZOLN67/action/author_attestation","sign_citation":"https://pith.science/pith/UCZFGWTV2VOGCMOYK4QGZOLN67/action/citation_signature","submit_replication":"https://pith.science/pith/UCZFGWTV2VOGCMOYK4QGZOLN67/action/replication_record"}},"created_at":"2026-07-14T02:21:30.738339+00:00","updated_at":"2026-07-14T02:21:30.738339+00:00"}