{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:KR6HQ2O44WCXMOVULE7LYKL25C","short_pith_number":"pith:KR6HQ2O4","canonical_record":{"source":{"id":"1802.08413","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-02-23T07:09:12Z","cross_cats_sorted":[],"title_canon_sha256":"813eedf3999bbada5f4fe427371e2fe63d271e07c5b7dfb483714fc3eeb15a57","abstract_canon_sha256":"2ca3960406c86c1376080be2ee219016813df530c8afbd477878382ebbb64480"},"schema_version":"1.0"},"canonical_sha256":"547c7869dce585763ab4593ebc297ae8863c194c2b872223d0c94045d1dd1b38","source":{"kind":"arxiv","id":"1802.08413","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.08413","created_at":"2026-05-17T23:53:51Z"},{"alias_kind":"arxiv_version","alias_value":"1802.08413v2","created_at":"2026-05-17T23:53:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.08413","created_at":"2026-05-17T23:53:51Z"},{"alias_kind":"pith_short_12","alias_value":"KR6HQ2O44WCX","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_16","alias_value":"KR6HQ2O44WCXMOVU","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_8","alias_value":"KR6HQ2O4","created_at":"2026-05-18T12:32:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:KR6HQ2O44WCXMOVULE7LYKL25C","target":"record","payload":{"canonical_record":{"source":{"id":"1802.08413","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-02-23T07:09:12Z","cross_cats_sorted":[],"title_canon_sha256":"813eedf3999bbada5f4fe427371e2fe63d271e07c5b7dfb483714fc3eeb15a57","abstract_canon_sha256":"2ca3960406c86c1376080be2ee219016813df530c8afbd477878382ebbb64480"},"schema_version":"1.0"},"canonical_sha256":"547c7869dce585763ab4593ebc297ae8863c194c2b872223d0c94045d1dd1b38","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:53:51.639747Z","signature_b64":"zBW1wKLwlv2yXI5Ra0f1emmL6SuEKgpsSnDrUP4L3uF6DZekHoZWc7LziXcyoGO7EpgnGjedPv/4bP6a9JE5Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"547c7869dce585763ab4593ebc297ae8863c194c2b872223d0c94045d1dd1b38","last_reissued_at":"2026-05-17T23:53:51.639077Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:53:51.639077Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1802.08413","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:53:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YdpRsQ/k3BnH7Bb8ItDijQ9TexTUS0+Ghh2VG+SKdDb27MmfDke+hUydfw69Lg82t4LF48XZ6MNsW0toACZKAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T13:35:37.948623Z"},"content_sha256":"1fc0d43a8e052d6cbf88e2756aa01f5240036eeeb885c57503cd812354667ae0","schema_version":"1.0","event_id":"sha256:1fc0d43a8e052d6cbf88e2756aa01f5240036eeeb885c57503cd812354667ae0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:KR6HQ2O44WCXMOVULE7LYKL25C","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Pontryagin's maximum principle and second order optimality condition for optimal control problems for the nonlocal Cahn-Hilliard-Navier-Stokes systems in two dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Manil T Mohan, Sheetal Dharmatti, Tania Biswas","submitted_at":"2018-02-23T07:09:12Z","abstract_excerpt":"In this work, we address some optimal control problems related to the evolution of two isothermal, incompressible, immisible fluids in a two dimensional bounded domain. A distributed optimal control problem is formulated as the minimization of a suitable cost functional subject to the controlled nonlocal Cahn-Hilliard-Navier-Stokes equations. We describe the first order necessary conditions of optimality via Pontryagin minimum principle and prove second order necessary and sufficient conditions of optimality for the problem."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.08413","kind":"arxiv","version":2},"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":"2026-05-17T23:53:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jwojOTFqs4v6ceW2qHTHOPxlkimzDN7bhbHfvj7sEQAD0vwfCxkKP0fZXpr6xICF6yKFJHI6sfkqDwuLfShvAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T13:35:37.948958Z"},"content_sha256":"82ed372508d8fee668c83fa6e9f6bc733336795a91c659a007bca96b300fc04c","schema_version":"1.0","event_id":"sha256:82ed372508d8fee668c83fa6e9f6bc733336795a91c659a007bca96b300fc04c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KR6HQ2O44WCXMOVULE7LYKL25C/bundle.json","state_url":"https://pith.science/pith/KR6HQ2O44WCXMOVULE7LYKL25C/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KR6HQ2O44WCXMOVULE7LYKL25C/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":"2026-06-22T13:35:37Z","links":{"resolver":"https://pith.science/pith/KR6HQ2O44WCXMOVULE7LYKL25C","bundle":"https://pith.science/pith/KR6HQ2O44WCXMOVULE7LYKL25C/bundle.json","state":"https://pith.science/pith/KR6HQ2O44WCXMOVULE7LYKL25C/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KR6HQ2O44WCXMOVULE7LYKL25C/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:KR6HQ2O44WCXMOVULE7LYKL25C","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":"2ca3960406c86c1376080be2ee219016813df530c8afbd477878382ebbb64480","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-02-23T07:09:12Z","title_canon_sha256":"813eedf3999bbada5f4fe427371e2fe63d271e07c5b7dfb483714fc3eeb15a57"},"schema_version":"1.0","source":{"id":"1802.08413","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.08413","created_at":"2026-05-17T23:53:51Z"},{"alias_kind":"arxiv_version","alias_value":"1802.08413v2","created_at":"2026-05-17T23:53:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.08413","created_at":"2026-05-17T23:53:51Z"},{"alias_kind":"pith_short_12","alias_value":"KR6HQ2O44WCX","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_16","alias_value":"KR6HQ2O44WCXMOVU","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_8","alias_value":"KR6HQ2O4","created_at":"2026-05-18T12:32:33Z"}],"graph_snapshots":[{"event_id":"sha256:82ed372508d8fee668c83fa6e9f6bc733336795a91c659a007bca96b300fc04c","target":"graph","created_at":"2026-05-17T23:53:51Z","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":"In this work, we address some optimal control problems related to the evolution of two isothermal, incompressible, immisible fluids in a two dimensional bounded domain. A distributed optimal control problem is formulated as the minimization of a suitable cost functional subject to the controlled nonlocal Cahn-Hilliard-Navier-Stokes equations. We describe the first order necessary conditions of optimality via Pontryagin minimum principle and prove second order necessary and sufficient conditions of optimality for the problem.","authors_text":"Manil T Mohan, Sheetal Dharmatti, Tania Biswas","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-02-23T07:09:12Z","title":"Pontryagin's maximum principle and second order optimality condition for optimal control problems for the nonlocal Cahn-Hilliard-Navier-Stokes systems in two dimensions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.08413","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":"sha256:1fc0d43a8e052d6cbf88e2756aa01f5240036eeeb885c57503cd812354667ae0","target":"record","created_at":"2026-05-17T23:53:51Z","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":"2ca3960406c86c1376080be2ee219016813df530c8afbd477878382ebbb64480","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-02-23T07:09:12Z","title_canon_sha256":"813eedf3999bbada5f4fe427371e2fe63d271e07c5b7dfb483714fc3eeb15a57"},"schema_version":"1.0","source":{"id":"1802.08413","kind":"arxiv","version":2}},"canonical_sha256":"547c7869dce585763ab4593ebc297ae8863c194c2b872223d0c94045d1dd1b38","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"547c7869dce585763ab4593ebc297ae8863c194c2b872223d0c94045d1dd1b38","first_computed_at":"2026-05-17T23:53:51.639077Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:53:51.639077Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zBW1wKLwlv2yXI5Ra0f1emmL6SuEKgpsSnDrUP4L3uF6DZekHoZWc7LziXcyoGO7EpgnGjedPv/4bP6a9JE5Cw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:53:51.639747Z","signed_message":"canonical_sha256_bytes"},"source_id":"1802.08413","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1fc0d43a8e052d6cbf88e2756aa01f5240036eeeb885c57503cd812354667ae0","sha256:82ed372508d8fee668c83fa6e9f6bc733336795a91c659a007bca96b300fc04c"],"state_sha256":"b01c4882839ad7d721a419c459f6e2f3648d014e952cd36a5b431235c552f148"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0bs0dGPzGrQnI1IgN3YJ77MYI4gP19GcHDsk0L5trU9ybQHZjb7nMtlSW49wy8zDq84H9JwbRZ+ysqwypVVZCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T13:35:37.950858Z","bundle_sha256":"77211f06f3f453ea16364397ab0964e4efec7e3f39f8eb3c3628449eb7fc6a98"}}