{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:6TGPBXJB7PCWQMPT4ZATIK5BO7","short_pith_number":"pith:6TGPBXJB","canonical_record":{"source":{"id":"2411.16640","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2024-11-25T18:16:27Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"a07cf42d9f6496bf2b1f31049c08697ba9a2d706fea63a493ca4a0c5939da186","abstract_canon_sha256":"2547f08fa2db8badc34d925531f45f26f71ca328432058261b697a4df176a304"},"schema_version":"1.0"},"canonical_sha256":"f4ccf0dd21fbc56831f3e641342ba177ee1c78e97f332a0a27a2a32fd350b2f7","source":{"kind":"arxiv","id":"2411.16640","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.16640","created_at":"2026-07-05T09:40:12Z"},{"alias_kind":"arxiv_version","alias_value":"2411.16640v1","created_at":"2026-07-05T09:40:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.16640","created_at":"2026-07-05T09:40:12Z"},{"alias_kind":"pith_short_12","alias_value":"6TGPBXJB7PCW","created_at":"2026-07-05T09:40:12Z"},{"alias_kind":"pith_short_16","alias_value":"6TGPBXJB7PCWQMPT","created_at":"2026-07-05T09:40:12Z"},{"alias_kind":"pith_short_8","alias_value":"6TGPBXJB","created_at":"2026-07-05T09:40:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:6TGPBXJB7PCWQMPT4ZATIK5BO7","target":"record","payload":{"canonical_record":{"source":{"id":"2411.16640","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2024-11-25T18:16:27Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"a07cf42d9f6496bf2b1f31049c08697ba9a2d706fea63a493ca4a0c5939da186","abstract_canon_sha256":"2547f08fa2db8badc34d925531f45f26f71ca328432058261b697a4df176a304"},"schema_version":"1.0"},"canonical_sha256":"f4ccf0dd21fbc56831f3e641342ba177ee1c78e97f332a0a27a2a32fd350b2f7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:40:12.216008Z","signature_b64":"KXziafeYip9odc0W3d1AShpdP0xXZndT1M0HhPDGpHLJjZK/Tz4efcUM4k22/9GYVWYsV+ISgVvqo1Z+Ak4nCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f4ccf0dd21fbc56831f3e641342ba177ee1c78e97f332a0a27a2a32fd350b2f7","last_reissued_at":"2026-07-05T09:40:12.215628Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:40:12.215628Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2411.16640","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":"2026-07-05T09:40:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iqVGQx3eNJ2Jzm9veMfK+9oRuL+qv439FXSdQswcJAq5qazcn0vRNyuikqyucRgclbK1jLcW8bf0iMaLsRElAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T00:10:55.107399Z"},"content_sha256":"e4af31a0c336aba0711bc15d09cecf3e8ac0aeaa070ccd59fa4eafebe454c9f6","schema_version":"1.0","event_id":"sha256:e4af31a0c336aba0711bc15d09cecf3e8ac0aeaa070ccd59fa4eafebe454c9f6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:6TGPBXJB7PCWQMPT4ZATIK5BO7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Optimal control problems on the co-adjoint Lie groupoids","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.OC","authors_text":"Ghorbanali Haghighatdoost","submitted_at":"2024-11-25T18:16:27Z","abstract_excerpt":"In this work we study the invariant optimal control problem on Lie groupoids. We show that any invariant optimal control problem on a Lie groupoid reduces to its co-adjoint Lie algebroid. In the final section of the paper, we present an illustrative example."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.16640","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2411.16640/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":"2026-07-05T09:40:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+dC/hb1P/3Y5jDFIGU+YV2rh+cfDcZHc+yljGokJbpprOShSuMupKb1fLUWHh1uw9L84rQQJdcWKybhUkjwtDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T00:10:55.108375Z"},"content_sha256":"e290a6c116ecb275675baf59af1c5d84f9f280a8d346f73e3c2457509aa340cf","schema_version":"1.0","event_id":"sha256:e290a6c116ecb275675baf59af1c5d84f9f280a8d346f73e3c2457509aa340cf"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6TGPBXJB7PCWQMPT4ZATIK5BO7/bundle.json","state_url":"https://pith.science/pith/6TGPBXJB7PCWQMPT4ZATIK5BO7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6TGPBXJB7PCWQMPT4ZATIK5BO7/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":"2026-08-14T00:10:55Z","links":{"resolver":"https://pith.science/pith/6TGPBXJB7PCWQMPT4ZATIK5BO7","bundle":"https://pith.science/pith/6TGPBXJB7PCWQMPT4ZATIK5BO7/bundle.json","state":"https://pith.science/pith/6TGPBXJB7PCWQMPT4ZATIK5BO7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6TGPBXJB7PCWQMPT4ZATIK5BO7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:6TGPBXJB7PCWQMPT4ZATIK5BO7","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":"2547f08fa2db8badc34d925531f45f26f71ca328432058261b697a4df176a304","cross_cats_sorted":["math-ph","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2024-11-25T18:16:27Z","title_canon_sha256":"a07cf42d9f6496bf2b1f31049c08697ba9a2d706fea63a493ca4a0c5939da186"},"schema_version":"1.0","source":{"id":"2411.16640","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.16640","created_at":"2026-07-05T09:40:12Z"},{"alias_kind":"arxiv_version","alias_value":"2411.16640v1","created_at":"2026-07-05T09:40:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.16640","created_at":"2026-07-05T09:40:12Z"},{"alias_kind":"pith_short_12","alias_value":"6TGPBXJB7PCW","created_at":"2026-07-05T09:40:12Z"},{"alias_kind":"pith_short_16","alias_value":"6TGPBXJB7PCWQMPT","created_at":"2026-07-05T09:40:12Z"},{"alias_kind":"pith_short_8","alias_value":"6TGPBXJB","created_at":"2026-07-05T09:40:12Z"}],"graph_snapshots":[{"event_id":"sha256:e290a6c116ecb275675baf59af1c5d84f9f280a8d346f73e3c2457509aa340cf","target":"graph","created_at":"2026-07-05T09:40:12Z","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/2411.16640/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this work we study the invariant optimal control problem on Lie groupoids. We show that any invariant optimal control problem on a Lie groupoid reduces to its co-adjoint Lie algebroid. In the final section of the paper, we present an illustrative example.","authors_text":"Ghorbanali Haghighatdoost","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2024-11-25T18:16:27Z","title":"Optimal control problems on the co-adjoint Lie groupoids"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.16640","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:e4af31a0c336aba0711bc15d09cecf3e8ac0aeaa070ccd59fa4eafebe454c9f6","target":"record","created_at":"2026-07-05T09:40:12Z","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":"2547f08fa2db8badc34d925531f45f26f71ca328432058261b697a4df176a304","cross_cats_sorted":["math-ph","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2024-11-25T18:16:27Z","title_canon_sha256":"a07cf42d9f6496bf2b1f31049c08697ba9a2d706fea63a493ca4a0c5939da186"},"schema_version":"1.0","source":{"id":"2411.16640","kind":"arxiv","version":1}},"canonical_sha256":"f4ccf0dd21fbc56831f3e641342ba177ee1c78e97f332a0a27a2a32fd350b2f7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f4ccf0dd21fbc56831f3e641342ba177ee1c78e97f332a0a27a2a32fd350b2f7","first_computed_at":"2026-07-05T09:40:12.215628Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:40:12.215628Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KXziafeYip9odc0W3d1AShpdP0xXZndT1M0HhPDGpHLJjZK/Tz4efcUM4k22/9GYVWYsV+ISgVvqo1Z+Ak4nCg==","signature_status":"signed_v1","signed_at":"2026-07-05T09:40:12.216008Z","signed_message":"canonical_sha256_bytes"},"source_id":"2411.16640","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e4af31a0c336aba0711bc15d09cecf3e8ac0aeaa070ccd59fa4eafebe454c9f6","sha256:e290a6c116ecb275675baf59af1c5d84f9f280a8d346f73e3c2457509aa340cf"],"state_sha256":"5d59dbd4246f66cd1bd6e6f1e38019492544ab94b8aa25d5cd1182a775592ef9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"S6lYoSnEJkYuoJrt1ybRg4i+fHnXhw5+pdz57Z8mq8nx1M+961oMmYHx8BNNL/rzfxNQktGh9BfwSCTu3rH9Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-14T00:10:55.142420Z","bundle_sha256":"9f616ee7369e335cd5114c66a62c056bbde9aa1c7fac644612acd0788ef0598d"}}