{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:2AS4BQYPDV6VKZ3CDH53JTW6NJ","short_pith_number":"pith:2AS4BQYP","canonical_record":{"source":{"id":"1803.11337","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-03-30T04:29:22Z","cross_cats_sorted":[],"title_canon_sha256":"f561802eeea4adcd6cf089b456f36527fc18be60bfc226a2c2eb9a38d5b2096a","abstract_canon_sha256":"be4918aed02163b16301f56c6c09d1cb0a61ad56235f18037cdf3ee79cfc2fb9"},"schema_version":"1.0"},"canonical_sha256":"d025c0c30f1d7d55676219fbb4cede6a6caa515250a90661cd204311f563abbd","source":{"kind":"arxiv","id":"1803.11337","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.11337","created_at":"2026-05-17T23:50:59Z"},{"alias_kind":"arxiv_version","alias_value":"1803.11337v2","created_at":"2026-05-17T23:50:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.11337","created_at":"2026-05-17T23:50:59Z"},{"alias_kind":"pith_short_12","alias_value":"2AS4BQYPDV6V","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_16","alias_value":"2AS4BQYPDV6VKZ3C","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_8","alias_value":"2AS4BQYP","created_at":"2026-05-18T12:31:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:2AS4BQYPDV6VKZ3CDH53JTW6NJ","target":"record","payload":{"canonical_record":{"source":{"id":"1803.11337","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-03-30T04:29:22Z","cross_cats_sorted":[],"title_canon_sha256":"f561802eeea4adcd6cf089b456f36527fc18be60bfc226a2c2eb9a38d5b2096a","abstract_canon_sha256":"be4918aed02163b16301f56c6c09d1cb0a61ad56235f18037cdf3ee79cfc2fb9"},"schema_version":"1.0"},"canonical_sha256":"d025c0c30f1d7d55676219fbb4cede6a6caa515250a90661cd204311f563abbd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:50:59.797867Z","signature_b64":"tkJB+sue0c/M/9zflgnScCMG5qQzah11Gk7VUY37ZhOYz2jnal9jETyAPcLKCbDWzuemfgmf1vNF1XbnCV1RAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d025c0c30f1d7d55676219fbb4cede6a6caa515250a90661cd204311f563abbd","last_reissued_at":"2026-05-17T23:50:59.797369Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:50:59.797369Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1803.11337","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":"2026-05-17T23:50:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Aiz0b0a+Am+y1BnJgs1AtSDve9/46FrV1aZsFqtBsP323gkYdCYwr0AK9wmDLJkVt0Ze2WupT6oTLl2fJjUYCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T19:01:28.977266Z"},"content_sha256":"df4f1f8a53969b9e5bcbc54df6e1adcab3b17580aa7f415071574b2c2ba5f69f","schema_version":"1.0","event_id":"sha256:df4f1f8a53969b9e5bcbc54df6e1adcab3b17580aa7f415071574b2c2ba5f69f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:2AS4BQYPDV6VKZ3CDH53JTW6NJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Maximum Principle and Data Assimilation Problem for the Optimal Control Problems Governed by 2D Nonlocal Cahn-Hillard-Navier-Stokes Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Manil T Mohan, Sheetal Dharmatti, Tania Biswas","submitted_at":"2018-03-30T04:29:22Z","abstract_excerpt":"We study some optimal control problems associated to the evolution of two isothermal, incompressible, immisible fluids in a two-dimensional bounded domain. The Cahn- Hilliard-Navier-Stokes model consists of a Navier-Stokes equation governing the fluid velocity field coupled with a convective Cahn-Hilliard equation for the relative concentration of one of the fluids. A distributed optimal control problem is formulated as the minimization of a cost functional subject to the controlled nonlocal Cahn-Hilliard- Navier-Stokes equations. We establish the first-order necessary conditions of optimality"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.11337","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":"2026-05-17T23:50:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3JCe8YZGtKMBiUvNwkRPCKhxQFAgtVGDOIk2ugczvIqHyqer4kGt4W6AgiwXMoJ09oBMEdW5d6RpqT7s6vzKCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T19:01:28.977940Z"},"content_sha256":"2cea28315e159c10a743ad7a0772fa721245cc862d49a17dd934f4ae711c82b6","schema_version":"1.0","event_id":"sha256:2cea28315e159c10a743ad7a0772fa721245cc862d49a17dd934f4ae711c82b6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2AS4BQYPDV6VKZ3CDH53JTW6NJ/bundle.json","state_url":"https://pith.science/pith/2AS4BQYPDV6VKZ3CDH53JTW6NJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2AS4BQYPDV6VKZ3CDH53JTW6NJ/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":"2026-06-06T19:01:28Z","links":{"resolver":"https://pith.science/pith/2AS4BQYPDV6VKZ3CDH53JTW6NJ","bundle":"https://pith.science/pith/2AS4BQYPDV6VKZ3CDH53JTW6NJ/bundle.json","state":"https://pith.science/pith/2AS4BQYPDV6VKZ3CDH53JTW6NJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2AS4BQYPDV6VKZ3CDH53JTW6NJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:2AS4BQYPDV6VKZ3CDH53JTW6NJ","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":"be4918aed02163b16301f56c6c09d1cb0a61ad56235f18037cdf3ee79cfc2fb9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-03-30T04:29:22Z","title_canon_sha256":"f561802eeea4adcd6cf089b456f36527fc18be60bfc226a2c2eb9a38d5b2096a"},"schema_version":"1.0","source":{"id":"1803.11337","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.11337","created_at":"2026-05-17T23:50:59Z"},{"alias_kind":"arxiv_version","alias_value":"1803.11337v2","created_at":"2026-05-17T23:50:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.11337","created_at":"2026-05-17T23:50:59Z"},{"alias_kind":"pith_short_12","alias_value":"2AS4BQYPDV6V","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_16","alias_value":"2AS4BQYPDV6VKZ3C","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_8","alias_value":"2AS4BQYP","created_at":"2026-05-18T12:31:59Z"}],"graph_snapshots":[{"event_id":"sha256:2cea28315e159c10a743ad7a0772fa721245cc862d49a17dd934f4ae711c82b6","target":"graph","created_at":"2026-05-17T23:50:59Z","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 study some optimal control problems associated to the evolution of two isothermal, incompressible, immisible fluids in a two-dimensional bounded domain. The Cahn- Hilliard-Navier-Stokes model consists of a Navier-Stokes equation governing the fluid velocity field coupled with a convective Cahn-Hilliard equation for the relative concentration of one of the fluids. A distributed optimal control problem is formulated as the minimization of a cost functional subject to the controlled nonlocal Cahn-Hilliard- Navier-Stokes equations. We establish the first-order necessary conditions of optimality","authors_text":"Manil T Mohan, Sheetal Dharmatti, Tania Biswas","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-03-30T04:29:22Z","title":"Maximum Principle and Data Assimilation Problem for the Optimal Control Problems Governed by 2D Nonlocal Cahn-Hillard-Navier-Stokes Equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.11337","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:df4f1f8a53969b9e5bcbc54df6e1adcab3b17580aa7f415071574b2c2ba5f69f","target":"record","created_at":"2026-05-17T23:50:59Z","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":"be4918aed02163b16301f56c6c09d1cb0a61ad56235f18037cdf3ee79cfc2fb9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-03-30T04:29:22Z","title_canon_sha256":"f561802eeea4adcd6cf089b456f36527fc18be60bfc226a2c2eb9a38d5b2096a"},"schema_version":"1.0","source":{"id":"1803.11337","kind":"arxiv","version":2}},"canonical_sha256":"d025c0c30f1d7d55676219fbb4cede6a6caa515250a90661cd204311f563abbd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d025c0c30f1d7d55676219fbb4cede6a6caa515250a90661cd204311f563abbd","first_computed_at":"2026-05-17T23:50:59.797369Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:50:59.797369Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tkJB+sue0c/M/9zflgnScCMG5qQzah11Gk7VUY37ZhOYz2jnal9jETyAPcLKCbDWzuemfgmf1vNF1XbnCV1RAA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:50:59.797867Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.11337","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:df4f1f8a53969b9e5bcbc54df6e1adcab3b17580aa7f415071574b2c2ba5f69f","sha256:2cea28315e159c10a743ad7a0772fa721245cc862d49a17dd934f4ae711c82b6"],"state_sha256":"7795d6ee0a8624454191b8d7e51f5b13ac3fe779b4782e8c5819c36c571238fa"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FOIv0OFwqGsQKGXjXYaQuRV2bbTtniBZJGNHaZ2MVRDmkL8tVv9oS+97NoHE7v9ONWIDggXJdsmcCFRmy72HAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T19:01:28.981897Z","bundle_sha256":"de3c11ddbc1ff1f3cf890632d4fd04b8ac88b006287aa7f5504b4945adaded83"}}