{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:I7YXKVAZEG63IIGN7EZYKAGKPI","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":"ea200d38b23b716bf536ef148fc917d992d8ac9b78c270c9a689ee6efd8f1a51","cross_cats_sorted":["cs.NI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-12-20T18:40:06Z","title_canon_sha256":"76894f0ec79788d7352417d63a411ebf3f416775d0912f06e7180a549ed82570"},"schema_version":"1.0","source":{"id":"1812.08759","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.08759","created_at":"2026-05-17T23:57:49Z"},{"alias_kind":"arxiv_version","alias_value":"1812.08759v1","created_at":"2026-05-17T23:57:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.08759","created_at":"2026-05-17T23:57:49Z"},{"alias_kind":"pith_short_12","alias_value":"I7YXKVAZEG63","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_16","alias_value":"I7YXKVAZEG63IIGN","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_8","alias_value":"I7YXKVAZ","created_at":"2026-05-18T12:32:28Z"}],"graph_snapshots":[{"event_id":"sha256:f0cb08fe28bb9f3bd1e8d3a60c94aa6ca376e5b8a10cda2ebcd81430afbd151a","target":"graph","created_at":"2026-05-17T23:57:49Z","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 paper, we consider the problem of optimizing the trajectory of an Unmanned Aerial Vehicle (UAV) Base Station (BS). We consider a map characterized by a traffic intensity of users to be served. The UAV BS must travel from a given initial location at an initial time to a final position within a given duration and serves the traffic on its way. The problem consists in finding the optimal trajectory that minimizes a certain cost depending on the velocity and on the amount of served traffic. We formulate the problem using the framework of Lagrangian mechanics. When the traffic intensity is ","authors_text":"Jean-Marc K\\'elif, J\\'er\\^ome Darbon, Marceau Coupechoux, Marc Sigelle","cross_cats":["cs.NI"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-12-20T18:40:06Z","title":"Optimal Trajectories of a UAV Base Station Using Lagrangian Mechanics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.08759","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:ab84c6f7f224f1346521b86da0bf1921f4013cd7bf57002beb6dcebe7821b97c","target":"record","created_at":"2026-05-17T23:57:49Z","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":"ea200d38b23b716bf536ef148fc917d992d8ac9b78c270c9a689ee6efd8f1a51","cross_cats_sorted":["cs.NI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-12-20T18:40:06Z","title_canon_sha256":"76894f0ec79788d7352417d63a411ebf3f416775d0912f06e7180a549ed82570"},"schema_version":"1.0","source":{"id":"1812.08759","kind":"arxiv","version":1}},"canonical_sha256":"47f175541921bdb420cdf9338500ca7a30c9aa475bd412e8d7949e48a14b1c72","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"47f175541921bdb420cdf9338500ca7a30c9aa475bd412e8d7949e48a14b1c72","first_computed_at":"2026-05-17T23:57:49.237917Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:57:49.237917Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"u/fd29lA5vZynTbcoJ7BztAt2yJZcyxChIbUu6cUiFKAlUCIY2FvXMY+1nx5tjXMyIyXm5M5dQRXIqtraXNuDg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:57:49.238460Z","signed_message":"canonical_sha256_bytes"},"source_id":"1812.08759","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ab84c6f7f224f1346521b86da0bf1921f4013cd7bf57002beb6dcebe7821b97c","sha256:f0cb08fe28bb9f3bd1e8d3a60c94aa6ca376e5b8a10cda2ebcd81430afbd151a"],"state_sha256":"f3b93e64001275cad2702b4cfc9745019a9cf53bf0e6bf86a14e92ad2ab77d5f"}