{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:LYDXGXFTYCVKVZWPBDPJJ2PKQH","short_pith_number":"pith:LYDXGXFT","canonical_record":{"source":{"id":"1608.08432","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-08-30T12:59:31Z","cross_cats_sorted":[],"title_canon_sha256":"d8cc21be443da7d95faa4f7f9fb6aeb269a0abe709ae130fd93ca161d228271d","abstract_canon_sha256":"20249be62416cfde3a451c228bbde390019c0553e91b770f9999c9cd79a06ed3"},"schema_version":"1.0"},"canonical_sha256":"5e07735cb3c0aaaae6cf08de94e9ea81f17e5e1e02b7417a025cabc1c7e58a70","source":{"kind":"arxiv","id":"1608.08432","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.08432","created_at":"2026-05-18T01:02:51Z"},{"alias_kind":"arxiv_version","alias_value":"1608.08432v3","created_at":"2026-05-18T01:02:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.08432","created_at":"2026-05-18T01:02:51Z"},{"alias_kind":"pith_short_12","alias_value":"LYDXGXFTYCVK","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"LYDXGXFTYCVKVZWP","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"LYDXGXFT","created_at":"2026-05-18T12:30:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:LYDXGXFTYCVKVZWPBDPJJ2PKQH","target":"record","payload":{"canonical_record":{"source":{"id":"1608.08432","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-08-30T12:59:31Z","cross_cats_sorted":[],"title_canon_sha256":"d8cc21be443da7d95faa4f7f9fb6aeb269a0abe709ae130fd93ca161d228271d","abstract_canon_sha256":"20249be62416cfde3a451c228bbde390019c0553e91b770f9999c9cd79a06ed3"},"schema_version":"1.0"},"canonical_sha256":"5e07735cb3c0aaaae6cf08de94e9ea81f17e5e1e02b7417a025cabc1c7e58a70","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:02:51.806234Z","signature_b64":"Syf5zHqMrS2nBv97yi5kd/foDw/i+LrH528Qg+bd22Wip1orqTaMgsKctI2jO7KGeg2qs6IYZIacZCAJiHnGCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5e07735cb3c0aaaae6cf08de94e9ea81f17e5e1e02b7417a025cabc1c7e58a70","last_reissued_at":"2026-05-18T01:02:51.805848Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:02:51.805848Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1608.08432","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:02:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VQmp/R72ChpNKVqg8cV6DwQ5tpAgGZdIzCYL8x0QGNDjOGaqaVJEvOQKS6d9Sp1Y2MFGxFi6lg1mUITWIvnDBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T20:46:45.513815Z"},"content_sha256":"bdb8d77e8ef934307fbdf6d62d2683bfe33c3d31c671684c82a37dc30bc02c30","schema_version":"1.0","event_id":"sha256:bdb8d77e8ef934307fbdf6d62d2683bfe33c3d31c671684c82a37dc30bc02c30"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:LYDXGXFTYCVKVZWPBDPJJ2PKQH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Global regularity of two dimensional inhomogeneous incompressible Navier-Stokes Equations with large data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ning Jiang, Yilong Luo","submitted_at":"2016-08-30T12:59:31Z","abstract_excerpt":"For two dimensional inhomogeneous Navier-Stokes of incompressible flows, with the assumption that the viscosity depends on the density but with a positive lower bound, using a partial regularity approach, in particular some enhanced decay estimates, we establish the global in time regularity for large data away from vacuum."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.08432","kind":"arxiv","version":3},"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":"2026-05-18T01:02:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fsfWv2xpWHSlP8gY4/XgKvhA6D/KvQgvniA5XbV90nYaOpjt2VxS8gz86fNAdUkqJUmWC2ZuWSZ8yMJJO0afBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T20:46:45.514543Z"},"content_sha256":"28fb6293631741808cb18a99580aabd4720705b147d0162210ad257d22a26da5","schema_version":"1.0","event_id":"sha256:28fb6293631741808cb18a99580aabd4720705b147d0162210ad257d22a26da5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LYDXGXFTYCVKVZWPBDPJJ2PKQH/bundle.json","state_url":"https://pith.science/pith/LYDXGXFTYCVKVZWPBDPJJ2PKQH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LYDXGXFTYCVKVZWPBDPJJ2PKQH/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":"2026-05-25T20:46:45Z","links":{"resolver":"https://pith.science/pith/LYDXGXFTYCVKVZWPBDPJJ2PKQH","bundle":"https://pith.science/pith/LYDXGXFTYCVKVZWPBDPJJ2PKQH/bundle.json","state":"https://pith.science/pith/LYDXGXFTYCVKVZWPBDPJJ2PKQH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LYDXGXFTYCVKVZWPBDPJJ2PKQH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:LYDXGXFTYCVKVZWPBDPJJ2PKQH","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":"20249be62416cfde3a451c228bbde390019c0553e91b770f9999c9cd79a06ed3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-08-30T12:59:31Z","title_canon_sha256":"d8cc21be443da7d95faa4f7f9fb6aeb269a0abe709ae130fd93ca161d228271d"},"schema_version":"1.0","source":{"id":"1608.08432","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.08432","created_at":"2026-05-18T01:02:51Z"},{"alias_kind":"arxiv_version","alias_value":"1608.08432v3","created_at":"2026-05-18T01:02:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.08432","created_at":"2026-05-18T01:02:51Z"},{"alias_kind":"pith_short_12","alias_value":"LYDXGXFTYCVK","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"LYDXGXFTYCVKVZWP","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"LYDXGXFT","created_at":"2026-05-18T12:30:29Z"}],"graph_snapshots":[{"event_id":"sha256:28fb6293631741808cb18a99580aabd4720705b147d0162210ad257d22a26da5","target":"graph","created_at":"2026-05-18T01:02:51Z","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":"For two dimensional inhomogeneous Navier-Stokes of incompressible flows, with the assumption that the viscosity depends on the density but with a positive lower bound, using a partial regularity approach, in particular some enhanced decay estimates, we establish the global in time regularity for large data away from vacuum.","authors_text":"Ning Jiang, Yilong Luo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-08-30T12:59:31Z","title":"Global regularity of two dimensional inhomogeneous incompressible Navier-Stokes Equations with large data"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.08432","kind":"arxiv","version":3},"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:bdb8d77e8ef934307fbdf6d62d2683bfe33c3d31c671684c82a37dc30bc02c30","target":"record","created_at":"2026-05-18T01:02:51Z","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":"20249be62416cfde3a451c228bbde390019c0553e91b770f9999c9cd79a06ed3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-08-30T12:59:31Z","title_canon_sha256":"d8cc21be443da7d95faa4f7f9fb6aeb269a0abe709ae130fd93ca161d228271d"},"schema_version":"1.0","source":{"id":"1608.08432","kind":"arxiv","version":3}},"canonical_sha256":"5e07735cb3c0aaaae6cf08de94e9ea81f17e5e1e02b7417a025cabc1c7e58a70","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5e07735cb3c0aaaae6cf08de94e9ea81f17e5e1e02b7417a025cabc1c7e58a70","first_computed_at":"2026-05-18T01:02:51.805848Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:02:51.805848Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Syf5zHqMrS2nBv97yi5kd/foDw/i+LrH528Qg+bd22Wip1orqTaMgsKctI2jO7KGeg2qs6IYZIacZCAJiHnGCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:02:51.806234Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.08432","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bdb8d77e8ef934307fbdf6d62d2683bfe33c3d31c671684c82a37dc30bc02c30","sha256:28fb6293631741808cb18a99580aabd4720705b147d0162210ad257d22a26da5"],"state_sha256":"3bde0ebb0aba87c18d042ac48788628989ef4cc0c90f7a2e08ff5b78b8a5610d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Xkz6mg5ZxWoYDOgyK3Y5U7Mrz2Cx8Dsz6ZsgBZq2eRXoQX//ylv8pKoqbqFaEuMjdFGReimLaPBYjS262qAwCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T20:46:45.518456Z","bundle_sha256":"28a1932d1794db09249a6ec85df341ca1fef63dfecfb1c0175f62c8ba2557422"}}