{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:2Z5OCC3SDDWEC76OQVTPHPWQXK","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":"71d849fe1e95f382105fcf42af4a97d084085e8bd5eaad645b5a98d4fb638df0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2023-03-19T16:24:17Z","title_canon_sha256":"3c94f70658fa965d48cd825eaed7eb9510d87b46aa1ffed5c47168f759c97515"},"schema_version":"1.0","source":{"id":"2303.10705","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2303.10705","created_at":"2026-07-05T08:41:25Z"},{"alias_kind":"arxiv_version","alias_value":"2303.10705v2","created_at":"2026-07-05T08:41:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2303.10705","created_at":"2026-07-05T08:41:25Z"},{"alias_kind":"pith_short_12","alias_value":"2Z5OCC3SDDWE","created_at":"2026-07-05T08:41:25Z"},{"alias_kind":"pith_short_16","alias_value":"2Z5OCC3SDDWEC76O","created_at":"2026-07-05T08:41:25Z"},{"alias_kind":"pith_short_8","alias_value":"2Z5OCC3S","created_at":"2026-07-05T08:41:25Z"}],"graph_snapshots":[{"event_id":"sha256:ff1ed304c2cfca3285c56c8a3fa94ef430d3b066f4b7fdcf2f4ca92d44fbbd58","target":"graph","created_at":"2026-07-05T08:41:25Z","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/2303.10705/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We introduce a new numerical method to approximate the solutions of a class of stationary Hamilton-Jacobi (HJ) partial differential equations arising from minimum time optimal control problems. We rely on nested grid approximations, and look for the optimal trajectories by using the coarse grid approximations to reduce the search space in fine grids. This provides an infinitesimal version of the ``highway hierarchy'' method which has been developed to solve shortest path problems (with discrete time and discrete state). We obtain, for each level, an approximate value function on a sub-domain o","authors_text":"Marianne Akian, Shanqing Liu, St\\'ephane Gaubert","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2023-03-19T16:24:17Z","title":"A Multi-Level Fast-Marching Method For The Minimum Time Problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2303.10705","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":"sha256:171638464f1e9783d7da7cf71ba481ad34f0e4a65d526d173b18535b4fbe9e96","target":"record","created_at":"2026-07-05T08:41:25Z","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":"71d849fe1e95f382105fcf42af4a97d084085e8bd5eaad645b5a98d4fb638df0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2023-03-19T16:24:17Z","title_canon_sha256":"3c94f70658fa965d48cd825eaed7eb9510d87b46aa1ffed5c47168f759c97515"},"schema_version":"1.0","source":{"id":"2303.10705","kind":"arxiv","version":2}},"canonical_sha256":"d67ae10b7218ec417fce8566f3bed0babe322ab5a84f45500dc200adfa2dcc82","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d67ae10b7218ec417fce8566f3bed0babe322ab5a84f45500dc200adfa2dcc82","first_computed_at":"2026-07-05T08:41:25.280049Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:41:25.280049Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AygCOcEug+MKwuy3IaunBfgq75i36kJ5oKoKdIQwcq6ZbRjzA3s3q0AsREIdWsvZR65vFW26U5OzPO95+GagBA==","signature_status":"signed_v1","signed_at":"2026-07-05T08:41:25.280477Z","signed_message":"canonical_sha256_bytes"},"source_id":"2303.10705","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:171638464f1e9783d7da7cf71ba481ad34f0e4a65d526d173b18535b4fbe9e96","sha256:ff1ed304c2cfca3285c56c8a3fa94ef430d3b066f4b7fdcf2f4ca92d44fbbd58"],"state_sha256":"5eea9bcdac72e5c16b2c4027372ea136456c4473f077ffee0aedb77d3b6a070f"}