{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:6KJUOSUUGUSPZFFDVHVNTCMCE4","short_pith_number":"pith:6KJUOSUU","canonical_record":{"source":{"id":"1805.04973","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-05-13T23:24:31Z","cross_cats_sorted":[],"title_canon_sha256":"675bed3cd46744cf8b3927992098f15cf4389c7d1f7b06378a9bdf1b81d7d877","abstract_canon_sha256":"d94ad38c8e42057f6ce717bb76969c2938a179a866ce5b240d44d0a956a28877"},"schema_version":"1.0"},"canonical_sha256":"f293474a943524fc94a3a9ead98982273beac3193daa093f7c9ee56e5e832698","source":{"kind":"arxiv","id":"1805.04973","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.04973","created_at":"2026-05-18T00:12:37Z"},{"alias_kind":"arxiv_version","alias_value":"1805.04973v3","created_at":"2026-05-18T00:12:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.04973","created_at":"2026-05-18T00:12:37Z"},{"alias_kind":"pith_short_12","alias_value":"6KJUOSUUGUSP","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_16","alias_value":"6KJUOSUUGUSPZFFD","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_8","alias_value":"6KJUOSUU","created_at":"2026-05-18T12:32:08Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:6KJUOSUUGUSPZFFDVHVNTCMCE4","target":"record","payload":{"canonical_record":{"source":{"id":"1805.04973","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-05-13T23:24:31Z","cross_cats_sorted":[],"title_canon_sha256":"675bed3cd46744cf8b3927992098f15cf4389c7d1f7b06378a9bdf1b81d7d877","abstract_canon_sha256":"d94ad38c8e42057f6ce717bb76969c2938a179a866ce5b240d44d0a956a28877"},"schema_version":"1.0"},"canonical_sha256":"f293474a943524fc94a3a9ead98982273beac3193daa093f7c9ee56e5e832698","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:12:37.934001Z","signature_b64":"kbjNDmD0+Aw0jkRoGaNgSobVWtQPRRHgamcmQqRDxGRAIcjcGkLNv7O3MdSSr5bm9nPl5wS3jk84T3bGn5S9AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f293474a943524fc94a3a9ead98982273beac3193daa093f7c9ee56e5e832698","last_reissued_at":"2026-05-18T00:12:37.933326Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:12:37.933326Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1805.04973","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":"2026-05-18T00:12:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kPSAYxU/UK6eJBDlaBjUppGdMjmyHJ+uRk8HMaqNMTJtjOpqN7fLLXAuETlXwfXiq2V0RjgFZrm5/+sF1LzYCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T22:59:35.954591Z"},"content_sha256":"d4f0d46442b20d5a26e649deedbba90964f61bd47c58ae7158a92e4ba90adb0b","schema_version":"1.0","event_id":"sha256:d4f0d46442b20d5a26e649deedbba90964f61bd47c58ae7158a92e4ba90adb0b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:6KJUOSUUGUSPZFFDVHVNTCMCE4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Optimal Human Navigation in Steep Terrain: a Hamilton-Jacobi-Bellman Approach","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Andrea L. Bertozzi, Christian Parkinson, David Arnold, Stanley Osher, Yat Tin Chow","submitted_at":"2018-05-13T23:24:31Z","abstract_excerpt":"We present a method for determining optimal walking paths in steep terrain using the level set method and an optimal control formulation. By viewing the walking direction as a control variable, we can determine the optimal control by solving a Hamilton-Jacobi-Bellman equation. We then calculate the optimal walking path by solving an ordinary differential equation. We demonstrate the effectiveness of our method by computing optimal paths which travel throughout mountainous regions of Yosemite National Park. We include details regarding the numerical implementation of our model and address a spe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.04973","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":""},"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":"2026-05-18T00:12:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gdHfOMQE4QmW+JTh20+LKfb5N/fiZc5D9PJC6wwckorfxFNopahp1VbfD2faVVb3peTSvs68Ps5NBesPVooAAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T22:59:35.955306Z"},"content_sha256":"53fc5f05f71a125e3a872a0791fa255e80ba1bb64df218bb4a55baee5a5f60f2","schema_version":"1.0","event_id":"sha256:53fc5f05f71a125e3a872a0791fa255e80ba1bb64df218bb4a55baee5a5f60f2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6KJUOSUUGUSPZFFDVHVNTCMCE4/bundle.json","state_url":"https://pith.science/pith/6KJUOSUUGUSPZFFDVHVNTCMCE4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6KJUOSUUGUSPZFFDVHVNTCMCE4/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":"2026-05-26T22:59:35Z","links":{"resolver":"https://pith.science/pith/6KJUOSUUGUSPZFFDVHVNTCMCE4","bundle":"https://pith.science/pith/6KJUOSUUGUSPZFFDVHVNTCMCE4/bundle.json","state":"https://pith.science/pith/6KJUOSUUGUSPZFFDVHVNTCMCE4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6KJUOSUUGUSPZFFDVHVNTCMCE4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:6KJUOSUUGUSPZFFDVHVNTCMCE4","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":"d94ad38c8e42057f6ce717bb76969c2938a179a866ce5b240d44d0a956a28877","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-05-13T23:24:31Z","title_canon_sha256":"675bed3cd46744cf8b3927992098f15cf4389c7d1f7b06378a9bdf1b81d7d877"},"schema_version":"1.0","source":{"id":"1805.04973","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.04973","created_at":"2026-05-18T00:12:37Z"},{"alias_kind":"arxiv_version","alias_value":"1805.04973v3","created_at":"2026-05-18T00:12:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.04973","created_at":"2026-05-18T00:12:37Z"},{"alias_kind":"pith_short_12","alias_value":"6KJUOSUUGUSP","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_16","alias_value":"6KJUOSUUGUSPZFFD","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_8","alias_value":"6KJUOSUU","created_at":"2026-05-18T12:32:08Z"}],"graph_snapshots":[{"event_id":"sha256:53fc5f05f71a125e3a872a0791fa255e80ba1bb64df218bb4a55baee5a5f60f2","target":"graph","created_at":"2026-05-18T00:12:37Z","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":"We present a method for determining optimal walking paths in steep terrain using the level set method and an optimal control formulation. By viewing the walking direction as a control variable, we can determine the optimal control by solving a Hamilton-Jacobi-Bellman equation. We then calculate the optimal walking path by solving an ordinary differential equation. We demonstrate the effectiveness of our method by computing optimal paths which travel throughout mountainous regions of Yosemite National Park. We include details regarding the numerical implementation of our model and address a spe","authors_text":"Andrea L. Bertozzi, Christian Parkinson, David Arnold, Stanley Osher, Yat Tin Chow","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-05-13T23:24:31Z","title":"Optimal Human Navigation in Steep Terrain: a Hamilton-Jacobi-Bellman Approach"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.04973","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:d4f0d46442b20d5a26e649deedbba90964f61bd47c58ae7158a92e4ba90adb0b","target":"record","created_at":"2026-05-18T00:12:37Z","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":"d94ad38c8e42057f6ce717bb76969c2938a179a866ce5b240d44d0a956a28877","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-05-13T23:24:31Z","title_canon_sha256":"675bed3cd46744cf8b3927992098f15cf4389c7d1f7b06378a9bdf1b81d7d877"},"schema_version":"1.0","source":{"id":"1805.04973","kind":"arxiv","version":3}},"canonical_sha256":"f293474a943524fc94a3a9ead98982273beac3193daa093f7c9ee56e5e832698","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f293474a943524fc94a3a9ead98982273beac3193daa093f7c9ee56e5e832698","first_computed_at":"2026-05-18T00:12:37.933326Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:12:37.933326Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kbjNDmD0+Aw0jkRoGaNgSobVWtQPRRHgamcmQqRDxGRAIcjcGkLNv7O3MdSSr5bm9nPl5wS3jk84T3bGn5S9AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:12:37.934001Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.04973","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d4f0d46442b20d5a26e649deedbba90964f61bd47c58ae7158a92e4ba90adb0b","sha256:53fc5f05f71a125e3a872a0791fa255e80ba1bb64df218bb4a55baee5a5f60f2"],"state_sha256":"533c007d5110b55e8449ef3c1d304be1ebd423571c2f88cbac5366b6b01797e2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aAX3ecYr1uhqT9JH1Qd6ZhGQiTZZCqwxLN3ckLPGFDo6wkhZnsKdP7IC9uH819yVrUef+APMf721p90rDUxeAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T22:59:35.958435Z","bundle_sha256":"b8478c759ae90e39c6888182571b6934b92210c65285131c0e505141fd109fd1"}}