{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:2CJZSFFHEELPHS45AHJ64QZ4PJ","short_pith_number":"pith:2CJZSFFH","canonical_record":{"source":{"id":"1712.08226","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"eess.SY","submitted_at":"2017-12-21T21:48:01Z","cross_cats_sorted":["cs.SY","math.OC"],"title_canon_sha256":"817d4c93e1ad3d969134c3750421dd4883969547d1d4ce5af08aeb60382a1a34","abstract_canon_sha256":"006450a4b879ff62af3491976c8fb806fabd03b7788272f4c55ed8fc2783a295"},"schema_version":"1.0"},"canonical_sha256":"d0939914a72116f3cb9d01d3ee433c7a574870580b5927484d2a9fb97721b514","source":{"kind":"arxiv","id":"1712.08226","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.08226","created_at":"2026-06-04T19:11:22Z"},{"alias_kind":"arxiv_version","alias_value":"1712.08226v3","created_at":"2026-06-04T19:11:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.08226","created_at":"2026-06-04T19:11:22Z"},{"alias_kind":"pith_short_12","alias_value":"2CJZSFFHEELP","created_at":"2026-06-04T19:11:22Z"},{"alias_kind":"pith_short_16","alias_value":"2CJZSFFHEELPHS45","created_at":"2026-06-04T19:11:22Z"},{"alias_kind":"pith_short_8","alias_value":"2CJZSFFH","created_at":"2026-06-04T19:11:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:2CJZSFFHEELPHS45AHJ64QZ4PJ","target":"record","payload":{"canonical_record":{"source":{"id":"1712.08226","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"eess.SY","submitted_at":"2017-12-21T21:48:01Z","cross_cats_sorted":["cs.SY","math.OC"],"title_canon_sha256":"817d4c93e1ad3d969134c3750421dd4883969547d1d4ce5af08aeb60382a1a34","abstract_canon_sha256":"006450a4b879ff62af3491976c8fb806fabd03b7788272f4c55ed8fc2783a295"},"schema_version":"1.0"},"canonical_sha256":"d0939914a72116f3cb9d01d3ee433c7a574870580b5927484d2a9fb97721b514","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-04T19:11:22.012781Z","signature_b64":"xk0Ybr8ZJEpQR+3bn2kqfnCTT4JvsyPlq9xiNe023Ws8cnCu6CgD5ODwDMk+FrC7mIfh51dd938IJAcM6v9TDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d0939914a72116f3cb9d01d3ee433c7a574870580b5927484d2a9fb97721b514","last_reissued_at":"2026-06-04T19:11:22.012366Z","signature_status":"signed_v1","first_computed_at":"2026-06-04T19:11:22.012366Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1712.08226","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-04T19:11:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"W68WqcIEkyC9dX4jR1RnCwk/nQhyJA/JW38UhN7KsXVuUkw6wivzXAEO9X0mu+240xB/b3PRVMzkR8ySbAJYDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T10:04:01.795933Z"},"content_sha256":"e3f383a5aad760a47315f65ba6b3face48fb365fe77b5edc9831b04da6eed50f","schema_version":"1.0","event_id":"sha256:e3f383a5aad760a47315f65ba6b3face48fb365fe77b5edc9831b04da6eed50f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:2CJZSFFHEELPHS45AHJ64QZ4PJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Primal-Dual Method for Optimal Control and Trajectory Generation in High-Dimensional Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SY","math.OC"],"primary_cat":"eess.SY","authors_text":"Gary Hewer, Jerome Darbon, Matthew R. Kirchner, Stanley Osher","submitted_at":"2017-12-21T21:48:01Z","abstract_excerpt":"Presented is a method for efficient computation of the Hamilton-Jacobi (HJ) equation for time-optimal control problems using the generalized Hopf formula. Typically, numerical methods to solve the HJ equation rely on a discrete grid of the solution space and exhibit exponential scaling with dimension. The generalized Hopf formula avoids the use of grids and numerical gradients by formulating an unconstrained convex optimization problem. The solution at each point is completely independent, and allows a massively parallel implementation if solutions at multiple points are desired. This work pre"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.08226","kind":"arxiv","version":3},"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/1712.08226/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-04T19:11:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4waQZOhujcwkl1b8PlElOxkyq+HSYXU4CTQLvI9hVEib7ataDIN/JekWibLmXGFRIvc4SgWU3nxhsVIP124CDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T10:04:01.796303Z"},"content_sha256":"bebc61ff9bcb56add684e84646479acf7114a1bd298d714a36a96e5235f84068","schema_version":"1.0","event_id":"sha256:bebc61ff9bcb56add684e84646479acf7114a1bd298d714a36a96e5235f84068"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2CJZSFFHEELPHS45AHJ64QZ4PJ/bundle.json","state_url":"https://pith.science/pith/2CJZSFFHEELPHS45AHJ64QZ4PJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2CJZSFFHEELPHS45AHJ64QZ4PJ/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-07-06T10:04:01Z","links":{"resolver":"https://pith.science/pith/2CJZSFFHEELPHS45AHJ64QZ4PJ","bundle":"https://pith.science/pith/2CJZSFFHEELPHS45AHJ64QZ4PJ/bundle.json","state":"https://pith.science/pith/2CJZSFFHEELPHS45AHJ64QZ4PJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2CJZSFFHEELPHS45AHJ64QZ4PJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:2CJZSFFHEELPHS45AHJ64QZ4PJ","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":"006450a4b879ff62af3491976c8fb806fabd03b7788272f4c55ed8fc2783a295","cross_cats_sorted":["cs.SY","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"eess.SY","submitted_at":"2017-12-21T21:48:01Z","title_canon_sha256":"817d4c93e1ad3d969134c3750421dd4883969547d1d4ce5af08aeb60382a1a34"},"schema_version":"1.0","source":{"id":"1712.08226","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.08226","created_at":"2026-06-04T19:11:22Z"},{"alias_kind":"arxiv_version","alias_value":"1712.08226v3","created_at":"2026-06-04T19:11:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.08226","created_at":"2026-06-04T19:11:22Z"},{"alias_kind":"pith_short_12","alias_value":"2CJZSFFHEELP","created_at":"2026-06-04T19:11:22Z"},{"alias_kind":"pith_short_16","alias_value":"2CJZSFFHEELPHS45","created_at":"2026-06-04T19:11:22Z"},{"alias_kind":"pith_short_8","alias_value":"2CJZSFFH","created_at":"2026-06-04T19:11:22Z"}],"graph_snapshots":[{"event_id":"sha256:bebc61ff9bcb56add684e84646479acf7114a1bd298d714a36a96e5235f84068","target":"graph","created_at":"2026-06-04T19:11:22Z","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/1712.08226/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Presented is a method for efficient computation of the Hamilton-Jacobi (HJ) equation for time-optimal control problems using the generalized Hopf formula. Typically, numerical methods to solve the HJ equation rely on a discrete grid of the solution space and exhibit exponential scaling with dimension. The generalized Hopf formula avoids the use of grids and numerical gradients by formulating an unconstrained convex optimization problem. The solution at each point is completely independent, and allows a massively parallel implementation if solutions at multiple points are desired. This work pre","authors_text":"Gary Hewer, Jerome Darbon, Matthew R. Kirchner, Stanley Osher","cross_cats":["cs.SY","math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"eess.SY","submitted_at":"2017-12-21T21:48:01Z","title":"A Primal-Dual Method for Optimal Control and Trajectory Generation in High-Dimensional Systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.08226","kind":"arxiv","version":3},"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:e3f383a5aad760a47315f65ba6b3face48fb365fe77b5edc9831b04da6eed50f","target":"record","created_at":"2026-06-04T19:11:22Z","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":"006450a4b879ff62af3491976c8fb806fabd03b7788272f4c55ed8fc2783a295","cross_cats_sorted":["cs.SY","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"eess.SY","submitted_at":"2017-12-21T21:48:01Z","title_canon_sha256":"817d4c93e1ad3d969134c3750421dd4883969547d1d4ce5af08aeb60382a1a34"},"schema_version":"1.0","source":{"id":"1712.08226","kind":"arxiv","version":3}},"canonical_sha256":"d0939914a72116f3cb9d01d3ee433c7a574870580b5927484d2a9fb97721b514","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d0939914a72116f3cb9d01d3ee433c7a574870580b5927484d2a9fb97721b514","first_computed_at":"2026-06-04T19:11:22.012366Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-04T19:11:22.012366Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xk0Ybr8ZJEpQR+3bn2kqfnCTT4JvsyPlq9xiNe023Ws8cnCu6CgD5ODwDMk+FrC7mIfh51dd938IJAcM6v9TDQ==","signature_status":"signed_v1","signed_at":"2026-06-04T19:11:22.012781Z","signed_message":"canonical_sha256_bytes"},"source_id":"1712.08226","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e3f383a5aad760a47315f65ba6b3face48fb365fe77b5edc9831b04da6eed50f","sha256:bebc61ff9bcb56add684e84646479acf7114a1bd298d714a36a96e5235f84068"],"state_sha256":"efdbe2d2cab891130091909c1faab0f324d21d92eb26bb45516da3dd68f8c568"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"peIxaKj0ArMYOJVvDqaFj3MugdD1J0djJ/PpVThjyLXk1sE1cwx0dk3F5gLY2JT2hlmW+sJngar5o798SpXcAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-06T10:04:01.798241Z","bundle_sha256":"f685502bbc8abb77501e298715629ddeb70e878fe6e666974e883e4311308ba0"}}