{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:LXR4MHSSTEJJS2WXW23SCADNQT","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":"1d93e36f02d09848c268d81fc38daef75fac7a2e3eab81a12eb056cf1605c933","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-12-01T14:53:19Z","title_canon_sha256":"4394b5e221421340799045547c4afbadde9010af5e3d41ade494ea8d2cee19ef"},"schema_version":"1.0","source":{"id":"1612.00282","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.00282","created_at":"2026-05-18T00:56:05Z"},{"alias_kind":"arxiv_version","alias_value":"1612.00282v1","created_at":"2026-05-18T00:56:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.00282","created_at":"2026-05-18T00:56:05Z"},{"alias_kind":"pith_short_12","alias_value":"LXR4MHSSTEJJ","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"LXR4MHSSTEJJS2WX","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"LXR4MHSS","created_at":"2026-05-18T12:30:29Z"}],"graph_snapshots":[{"event_id":"sha256:814db3087d1fa4a63d91d3c57a1bd138273cd4d3ab07971d5110121bc4e0e7eb","target":"graph","created_at":"2026-05-18T00:56:05Z","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  our recent work dedicated to   the Boussinesq equations [Danchin and Zhang 2016], we established the persistence of solutions with piecewise constant temperature along interfaces with H\\\"older regularity. We here address the same problem for   the inhomogeneous Navier-Stokes equations satisfied by a viscous incompressibleand inhomogeneous fluid. We establish that, indeed, in the slightly inhomogeneous case, patches of densities with $\\mathcal{C}^{1, \\varepsilon}$ regularity propagate for all time. As in   [Danchin and Zhang 2016],   our result follows from the conservation of H\\\"older regu","authors_text":"Rapha\\\"el Danchin, Xin Zhang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-12-01T14:53:19Z","title":"On the persistence of H\\\"older regular patches of density for the inhomogeneous Navier-Stokes equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.00282","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:ff8f101bbf39f0710b32a27a6678199541ca2993986e33b3be8266f0594e43a6","target":"record","created_at":"2026-05-18T00:56:05Z","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":"1d93e36f02d09848c268d81fc38daef75fac7a2e3eab81a12eb056cf1605c933","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-12-01T14:53:19Z","title_canon_sha256":"4394b5e221421340799045547c4afbadde9010af5e3d41ade494ea8d2cee19ef"},"schema_version":"1.0","source":{"id":"1612.00282","kind":"arxiv","version":1}},"canonical_sha256":"5de3c61e529912996ad7b6b721006d84d1919da3f9724d6c8da1a86e44a13150","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5de3c61e529912996ad7b6b721006d84d1919da3f9724d6c8da1a86e44a13150","first_computed_at":"2026-05-18T00:56:05.563570Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:56:05.563570Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wSgHmSZVEROw96u0Gzp8JPNh243zQExP1T/rZveZkMqyGrptfoBf50qiZuA/euDebKiHyfnzYstWTfnHBox9Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:56:05.564044Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.00282","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ff8f101bbf39f0710b32a27a6678199541ca2993986e33b3be8266f0594e43a6","sha256:814db3087d1fa4a63d91d3c57a1bd138273cd4d3ab07971d5110121bc4e0e7eb"],"state_sha256":"161054234661a224d1c0c763328f1c7534addb93098af838f1fdf4b98edff8c7"}