{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:COVTHMD4RSZ3JAMR74PEKR4E2B","short_pith_number":"pith:COVTHMD4","canonical_record":{"source":{"id":"1101.1537","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.OC","submitted_at":"2011-01-07T21:39:05Z","cross_cats_sorted":[],"title_canon_sha256":"46fc5dfea5e7d49c25face334dd76e5b12b3697961d41debad1e3461b09846d9","abstract_canon_sha256":"da67bcb784595829e1d8ceaf2e89017a6340bf2561278f141d77c81ed9e3b676"},"schema_version":"1.0"},"canonical_sha256":"13ab33b07c8cb3b48191ff1e454784d04fe166fda1ef84930bb777f58d380cc0","source":{"kind":"arxiv","id":"1101.1537","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1101.1537","created_at":"2026-05-18T04:31:52Z"},{"alias_kind":"arxiv_version","alias_value":"1101.1537v1","created_at":"2026-05-18T04:31:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.1537","created_at":"2026-05-18T04:31:52Z"},{"alias_kind":"pith_short_12","alias_value":"COVTHMD4RSZ3","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"COVTHMD4RSZ3JAMR","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"COVTHMD4","created_at":"2026-05-18T12:26:26Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:COVTHMD4RSZ3JAMR74PEKR4E2B","target":"record","payload":{"canonical_record":{"source":{"id":"1101.1537","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.OC","submitted_at":"2011-01-07T21:39:05Z","cross_cats_sorted":[],"title_canon_sha256":"46fc5dfea5e7d49c25face334dd76e5b12b3697961d41debad1e3461b09846d9","abstract_canon_sha256":"da67bcb784595829e1d8ceaf2e89017a6340bf2561278f141d77c81ed9e3b676"},"schema_version":"1.0"},"canonical_sha256":"13ab33b07c8cb3b48191ff1e454784d04fe166fda1ef84930bb777f58d380cc0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:31:52.046870Z","signature_b64":"tEOPRbgNdtA3gcO9bnV/RDM2vzr7PaP6yc6hw6N7XIgHiwbjrYK9lg61e/dDwjEbWsnIvqL2z1xjazc3Nl0CDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"13ab33b07c8cb3b48191ff1e454784d04fe166fda1ef84930bb777f58d380cc0","last_reissued_at":"2026-05-18T04:31:52.046500Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:31:52.046500Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1101.1537","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:31:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IdZNCWmv37glNrpB3K2SP1TiT3Fiuty3HssJXE9qdoCZWdkQG2ythQ0sxagiXTJRn2uA9+6hovBMOaBPeKAEDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T07:47:00.461905Z"},"content_sha256":"e33fc16a261d094ff3fac1988a4d24795ff5f6ecb8037fb828fb416a822af007","schema_version":"1.0","event_id":"sha256:e33fc16a261d094ff3fac1988a4d24795ff5f6ecb8037fb828fb416a822af007"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:COVTHMD4RSZ3JAMR74PEKR4E2B","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Time-Optimal solutions of Parallel Navigation and Finsler geodesics","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"M. Rafie-Rad","submitted_at":"2011-01-07T21:39:05Z","abstract_excerpt":"A geometric approach to kinematics in control theory is illustrated. A non-linear control system is derived for the problem and the Pontryagin maximum principle is used to find the time-optimal trajectories of the Parallel navigation. The time-optimal trajectories of the Parallel navigation are characterized through a geometric formulation. It is notable that the approach has the advantages using feedback."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.1537","kind":"arxiv","version":1},"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":"2026-05-18T04:31:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9+2TTWHGdb4N4hD/mDVFign2lNbcTMm5ynMp5JssmHpRPrPkA8y1wUS7tQ/qfBJ7DpNgFPQTGWC30rON2fpLBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T07:47:00.462242Z"},"content_sha256":"94901aca6d2af395a4eada2301a3a61ea9f65270772e29da4357cd5cd3ff132c","schema_version":"1.0","event_id":"sha256:94901aca6d2af395a4eada2301a3a61ea9f65270772e29da4357cd5cd3ff132c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/COVTHMD4RSZ3JAMR74PEKR4E2B/bundle.json","state_url":"https://pith.science/pith/COVTHMD4RSZ3JAMR74PEKR4E2B/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/COVTHMD4RSZ3JAMR74PEKR4E2B/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":"2026-06-03T07:47:00Z","links":{"resolver":"https://pith.science/pith/COVTHMD4RSZ3JAMR74PEKR4E2B","bundle":"https://pith.science/pith/COVTHMD4RSZ3JAMR74PEKR4E2B/bundle.json","state":"https://pith.science/pith/COVTHMD4RSZ3JAMR74PEKR4E2B/state.json","well_known_bundle":"https://pith.science/.well-known/pith/COVTHMD4RSZ3JAMR74PEKR4E2B/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:COVTHMD4RSZ3JAMR74PEKR4E2B","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":"da67bcb784595829e1d8ceaf2e89017a6340bf2561278f141d77c81ed9e3b676","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.OC","submitted_at":"2011-01-07T21:39:05Z","title_canon_sha256":"46fc5dfea5e7d49c25face334dd76e5b12b3697961d41debad1e3461b09846d9"},"schema_version":"1.0","source":{"id":"1101.1537","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1101.1537","created_at":"2026-05-18T04:31:52Z"},{"alias_kind":"arxiv_version","alias_value":"1101.1537v1","created_at":"2026-05-18T04:31:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.1537","created_at":"2026-05-18T04:31:52Z"},{"alias_kind":"pith_short_12","alias_value":"COVTHMD4RSZ3","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"COVTHMD4RSZ3JAMR","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"COVTHMD4","created_at":"2026-05-18T12:26:26Z"}],"graph_snapshots":[{"event_id":"sha256:94901aca6d2af395a4eada2301a3a61ea9f65270772e29da4357cd5cd3ff132c","target":"graph","created_at":"2026-05-18T04:31:52Z","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":"A geometric approach to kinematics in control theory is illustrated. A non-linear control system is derived for the problem and the Pontryagin maximum principle is used to find the time-optimal trajectories of the Parallel navigation. The time-optimal trajectories of the Parallel navigation are characterized through a geometric formulation. It is notable that the approach has the advantages using feedback.","authors_text":"M. Rafie-Rad","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.OC","submitted_at":"2011-01-07T21:39:05Z","title":"Time-Optimal solutions of Parallel Navigation and Finsler geodesics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.1537","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:e33fc16a261d094ff3fac1988a4d24795ff5f6ecb8037fb828fb416a822af007","target":"record","created_at":"2026-05-18T04:31:52Z","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":"da67bcb784595829e1d8ceaf2e89017a6340bf2561278f141d77c81ed9e3b676","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.OC","submitted_at":"2011-01-07T21:39:05Z","title_canon_sha256":"46fc5dfea5e7d49c25face334dd76e5b12b3697961d41debad1e3461b09846d9"},"schema_version":"1.0","source":{"id":"1101.1537","kind":"arxiv","version":1}},"canonical_sha256":"13ab33b07c8cb3b48191ff1e454784d04fe166fda1ef84930bb777f58d380cc0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"13ab33b07c8cb3b48191ff1e454784d04fe166fda1ef84930bb777f58d380cc0","first_computed_at":"2026-05-18T04:31:52.046500Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:31:52.046500Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tEOPRbgNdtA3gcO9bnV/RDM2vzr7PaP6yc6hw6N7XIgHiwbjrYK9lg61e/dDwjEbWsnIvqL2z1xjazc3Nl0CDA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:31:52.046870Z","signed_message":"canonical_sha256_bytes"},"source_id":"1101.1537","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e33fc16a261d094ff3fac1988a4d24795ff5f6ecb8037fb828fb416a822af007","sha256:94901aca6d2af395a4eada2301a3a61ea9f65270772e29da4357cd5cd3ff132c"],"state_sha256":"114e123fe44ba67dfe433a8be409850d8074878c4daaa2d9e8b37a266d02e507"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mNkuX/0iuYI8tHK3YuouLUrocSlPbT5mETDdTof7RBIC5mg6VfW1kOaa32ZLYA0r9ZyLVV+HAS7IMYy9mra5Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T07:47:00.464130Z","bundle_sha256":"47fa9afbecaec971e435e0a56ed3772601566e4ebf5e102381313954c3698fee"}}