{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:MRB34XEA5Q26C76FD4SGJSUOUD","short_pith_number":"pith:MRB34XEA","canonical_record":{"source":{"id":"1608.05361","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2016-08-18T18:23:51Z","cross_cats_sorted":[],"title_canon_sha256":"2108af1e6b16cae3188f711738c2b7df5e26698b78743d6a2e0f07eab331753e","abstract_canon_sha256":"287852b21315c9c3e84d4cbeaebbe2e543cd463379fd97e42b429aec51f73ec8"},"schema_version":"1.0"},"canonical_sha256":"6443be5c80ec35e17fc51f2464ca8ea0fbbb5ffcaf9e435224f916bd7aa7cfed","source":{"kind":"arxiv","id":"1608.05361","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.05361","created_at":"2026-05-18T00:54:19Z"},{"alias_kind":"arxiv_version","alias_value":"1608.05361v2","created_at":"2026-05-18T00:54:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.05361","created_at":"2026-05-18T00:54:19Z"},{"alias_kind":"pith_short_12","alias_value":"MRB34XEA5Q26","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_16","alias_value":"MRB34XEA5Q26C76F","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_8","alias_value":"MRB34XEA","created_at":"2026-05-18T12:30:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:MRB34XEA5Q26C76FD4SGJSUOUD","target":"record","payload":{"canonical_record":{"source":{"id":"1608.05361","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2016-08-18T18:23:51Z","cross_cats_sorted":[],"title_canon_sha256":"2108af1e6b16cae3188f711738c2b7df5e26698b78743d6a2e0f07eab331753e","abstract_canon_sha256":"287852b21315c9c3e84d4cbeaebbe2e543cd463379fd97e42b429aec51f73ec8"},"schema_version":"1.0"},"canonical_sha256":"6443be5c80ec35e17fc51f2464ca8ea0fbbb5ffcaf9e435224f916bd7aa7cfed","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:54:19.806604Z","signature_b64":"Iaml0gzSdfvU96F+U/ZZI0xiMa8iZHvjbnpEQUdr/Whz/UPWDItJI7nJG8YEE8reSylZsEWs8VMRNvEJE0wfCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6443be5c80ec35e17fc51f2464ca8ea0fbbb5ffcaf9e435224f916bd7aa7cfed","last_reissued_at":"2026-05-18T00:54:19.806196Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:54:19.806196Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1608.05361","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":"2026-05-18T00:54:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wOv57oFRr2kNgUfOTV7ZfVcsaY8YTtCpQNCrBhqk5O//MXiprioYjZvoc24vfxUB3R25QI/84xrzEhT3ia4tCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T11:21:59.987566Z"},"content_sha256":"28e232203cd5d9c668d8c9cfe47243e90e0526af31f4fb713c35f9229e213ac4","schema_version":"1.0","event_id":"sha256:28e232203cd5d9c668d8c9cfe47243e90e0526af31f4fb713c35f9229e213ac4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:MRB34XEA5Q26C76FD4SGJSUOUD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A regularity criterion for solutions of the three-dimensional Cahn-Hilliard-Navier-Stokes equations and associated computations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"physics.flu-dyn","authors_text":"Anupam Gupta, John D. Gibbon, Nairita Pal, Rahul Pandit","submitted_at":"2016-08-18T18:23:51Z","abstract_excerpt":"We consider the 3D Cahn-Hilliard equations coupled to, and driven by, the forced, incompressible 3D Navier-Stokes equations. The combination, known as the Cahn-Hilliard-Navier-Stokes (CHNS) equations, is used in statistical mechanics to model the motion of a binary fluid. The potential development of singularities (blow-up) in the contours of the order parameter $\\phi$ is an open problem. To address this we have proved a theorem that closely mimics the Beale-Kato-Majda theorem for the $3D$ incompressible Euler equations [Beale et al. Commun. Math. Phys., Commun. Math. Phys., ${\\rm 94}$, $ 61-6"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.05361","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":"2026-05-18T00:54:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"H4TfNKqmt3zFaCDlzsw70HCdpHnuw3C5swF6jTvpxQ9JEA5/etO/Q8bB7WpJypZvzkTmpGY9F0+oU8LaWNglDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T11:21:59.988229Z"},"content_sha256":"fb197aba61940a5653e3418ab0ee55e89413ccd914f1ce98735589a55a884ad9","schema_version":"1.0","event_id":"sha256:fb197aba61940a5653e3418ab0ee55e89413ccd914f1ce98735589a55a884ad9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MRB34XEA5Q26C76FD4SGJSUOUD/bundle.json","state_url":"https://pith.science/pith/MRB34XEA5Q26C76FD4SGJSUOUD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MRB34XEA5Q26C76FD4SGJSUOUD/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":"2026-05-27T11:21:59Z","links":{"resolver":"https://pith.science/pith/MRB34XEA5Q26C76FD4SGJSUOUD","bundle":"https://pith.science/pith/MRB34XEA5Q26C76FD4SGJSUOUD/bundle.json","state":"https://pith.science/pith/MRB34XEA5Q26C76FD4SGJSUOUD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MRB34XEA5Q26C76FD4SGJSUOUD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:MRB34XEA5Q26C76FD4SGJSUOUD","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":"287852b21315c9c3e84d4cbeaebbe2e543cd463379fd97e42b429aec51f73ec8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2016-08-18T18:23:51Z","title_canon_sha256":"2108af1e6b16cae3188f711738c2b7df5e26698b78743d6a2e0f07eab331753e"},"schema_version":"1.0","source":{"id":"1608.05361","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.05361","created_at":"2026-05-18T00:54:19Z"},{"alias_kind":"arxiv_version","alias_value":"1608.05361v2","created_at":"2026-05-18T00:54:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.05361","created_at":"2026-05-18T00:54:19Z"},{"alias_kind":"pith_short_12","alias_value":"MRB34XEA5Q26","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_16","alias_value":"MRB34XEA5Q26C76F","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_8","alias_value":"MRB34XEA","created_at":"2026-05-18T12:30:32Z"}],"graph_snapshots":[{"event_id":"sha256:fb197aba61940a5653e3418ab0ee55e89413ccd914f1ce98735589a55a884ad9","target":"graph","created_at":"2026-05-18T00:54:19Z","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 consider the 3D Cahn-Hilliard equations coupled to, and driven by, the forced, incompressible 3D Navier-Stokes equations. The combination, known as the Cahn-Hilliard-Navier-Stokes (CHNS) equations, is used in statistical mechanics to model the motion of a binary fluid. The potential development of singularities (blow-up) in the contours of the order parameter $\\phi$ is an open problem. To address this we have proved a theorem that closely mimics the Beale-Kato-Majda theorem for the $3D$ incompressible Euler equations [Beale et al. Commun. Math. Phys., Commun. Math. Phys., ${\\rm 94}$, $ 61-6","authors_text":"Anupam Gupta, John D. Gibbon, Nairita Pal, Rahul Pandit","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2016-08-18T18:23:51Z","title":"A regularity criterion for solutions of the three-dimensional Cahn-Hilliard-Navier-Stokes equations and associated computations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.05361","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":"sha256:28e232203cd5d9c668d8c9cfe47243e90e0526af31f4fb713c35f9229e213ac4","target":"record","created_at":"2026-05-18T00:54:19Z","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":"287852b21315c9c3e84d4cbeaebbe2e543cd463379fd97e42b429aec51f73ec8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2016-08-18T18:23:51Z","title_canon_sha256":"2108af1e6b16cae3188f711738c2b7df5e26698b78743d6a2e0f07eab331753e"},"schema_version":"1.0","source":{"id":"1608.05361","kind":"arxiv","version":2}},"canonical_sha256":"6443be5c80ec35e17fc51f2464ca8ea0fbbb5ffcaf9e435224f916bd7aa7cfed","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6443be5c80ec35e17fc51f2464ca8ea0fbbb5ffcaf9e435224f916bd7aa7cfed","first_computed_at":"2026-05-18T00:54:19.806196Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:54:19.806196Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Iaml0gzSdfvU96F+U/ZZI0xiMa8iZHvjbnpEQUdr/Whz/UPWDItJI7nJG8YEE8reSylZsEWs8VMRNvEJE0wfCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:54:19.806604Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.05361","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:28e232203cd5d9c668d8c9cfe47243e90e0526af31f4fb713c35f9229e213ac4","sha256:fb197aba61940a5653e3418ab0ee55e89413ccd914f1ce98735589a55a884ad9"],"state_sha256":"183a6ffb6cf5b09fc5360e42c3a7eb6747a9d78228cfda3f359e520e129d87e8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"K4/6ck6ws+jhF1FvSdRORw9LknE1QOHj4m/GpFA1VYjHtnqEERrn58CTbzFiKY7TjkZslAyotiNh7NA6RnKPCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T11:21:59.991980Z","bundle_sha256":"2c119dab4341f61846f5f4b0c6fc74f6f6b32e234874fa8054573c9e8d8508ea"}}