{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:5P3SH3OCKL3W6GIE7MWANEAKR3","merge_version":"pith-open-graph-merge-v1","event_count":3,"valid_event_count":3,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"6bb71c0adb778b01edb413aa97b6859cc0563932622a3b00790f24305896ee77","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2026-07-03T15:12:35Z","title_canon_sha256":"b9c74c068c8761d4e4b205edbb985f068c148702e03839a8fb801439fd807087"},"schema_version":"1.0","source":{"id":"2607.03407","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.03407","created_at":"2026-07-07T02:17:41Z"},{"alias_kind":"arxiv_version","alias_value":"2607.03407v1","created_at":"2026-07-07T02:17:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.03407","created_at":"2026-07-07T02:17:41Z"},{"alias_kind":"pith_short_12","alias_value":"5P3SH3OCKL3W","created_at":"2026-07-07T02:17:41Z"},{"alias_kind":"pith_short_16","alias_value":"5P3SH3OCKL3W6GIE","created_at":"2026-07-07T02:17:41Z"},{"alias_kind":"pith_short_8","alias_value":"5P3SH3OC","created_at":"2026-07-07T02:17:41Z"}],"graph_snapshots":[{"event_id":"sha256:002dabf4d1d5505b544c5ddd91b75e50e2f4986b08e2d1450a03d9bbf859c137","target":"graph","created_at":"2026-07-07T02:17:41Z","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/2607.03407/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Unmanned underwater vehicles (UUV) integrate ocean forecasts with path planning algorithms in order to identify energy- or time-minimizing paths that enable mission completion. Typically, a well-defined deterministic ocean forecast is assumed to be available for path planning; however, in practice, different ocean forecasts can disagree. In this paper, we extend previous work on deterministic optimal path planning to identify optimal mean-time paths when presented with an ensemble of possible ocean forecasts. In particular, we formulate a system of time-independent Hamilton-Jacobi partial diff","authors_text":"Jeremy Brandman, Jonathan Valyou, Sanghyun Lee","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2026-07-03T15:12:35Z","title":"Optimal mean-time path planning for unmanned underwater vehicles: a Hamilton-Jacobi approach"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.03407","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":"sha256:82ebec9f8e9e361c872189fa290772b8d140d19422bd9a4762c0d508cd28d643","target":"record","created_at":"2026-07-07T02:17:41Z","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":"6bb71c0adb778b01edb413aa97b6859cc0563932622a3b00790f24305896ee77","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2026-07-03T15:12:35Z","title_canon_sha256":"b9c74c068c8761d4e4b205edbb985f068c148702e03839a8fb801439fd807087"},"schema_version":"1.0","source":{"id":"2607.03407","kind":"arxiv","version":1}},"canonical_sha256":"ebf723edc252f76f1904fb2c06900a8ee65ebb5988031ad44d42b4d763f5cf10","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ebf723edc252f76f1904fb2c06900a8ee65ebb5988031ad44d42b4d763f5cf10","first_computed_at":"2026-07-07T02:17:41.735561Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-07T02:17:41.735561Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"71rWNVxcXLAj0s24UShAJk7xPQ4U1OLloF7g3/8QP4xwT5h68gftsvgkmU5iUE/MkZPpiSPik0wp8RLJMfL8DA==","signature_status":"signed_v1","signed_at":"2026-07-07T02:17:41.736284Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.03407","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:82ebec9f8e9e361c872189fa290772b8d140d19422bd9a4762c0d508cd28d643","sha256:002dabf4d1d5505b544c5ddd91b75e50e2f4986b08e2d1450a03d9bbf859c137","sha256:b8895be9555f78161faf274aeaa928248f9aa936510a39c237d92ee6bc22e210"],"state_sha256":"629edc5aa1ff80bc655ba085117af4d1d1cf67ee2d99206adc5dc07f36fa7664"}