{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:FLHFRAYHY57K6SF7FVD46PC6SC","short_pith_number":"pith:FLHFRAYH","canonical_record":{"source":{"id":"1212.3916","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-12-17T08:10:09Z","cross_cats_sorted":[],"title_canon_sha256":"77915d59c349fb8991107ee3652d5c6d7c87bf6aeadf19f5117c95eb0714e83f","abstract_canon_sha256":"36ec98020a72c631548674a1b4828b0e63bd22443f2872816629b00d921600d1"},"schema_version":"1.0"},"canonical_sha256":"2ace588307c77eaf48bf2d47cf3c5e90ac3339272b20bb06c28f411aba9d8ad2","source":{"kind":"arxiv","id":"1212.3916","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.3916","created_at":"2026-05-18T03:38:22Z"},{"alias_kind":"arxiv_version","alias_value":"1212.3916v1","created_at":"2026-05-18T03:38:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.3916","created_at":"2026-05-18T03:38:22Z"},{"alias_kind":"pith_short_12","alias_value":"FLHFRAYHY57K","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_16","alias_value":"FLHFRAYHY57K6SF7","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_8","alias_value":"FLHFRAYH","created_at":"2026-05-18T12:27:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:FLHFRAYHY57K6SF7FVD46PC6SC","target":"record","payload":{"canonical_record":{"source":{"id":"1212.3916","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-12-17T08:10:09Z","cross_cats_sorted":[],"title_canon_sha256":"77915d59c349fb8991107ee3652d5c6d7c87bf6aeadf19f5117c95eb0714e83f","abstract_canon_sha256":"36ec98020a72c631548674a1b4828b0e63bd22443f2872816629b00d921600d1"},"schema_version":"1.0"},"canonical_sha256":"2ace588307c77eaf48bf2d47cf3c5e90ac3339272b20bb06c28f411aba9d8ad2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:38:22.072747Z","signature_b64":"iYfvZDLFcWCUnN1JJUCq7o0ERTWKGpfuxOaRONv6I48vycSauRveNYwm8+ac7KguSUgaigR/l8tPoNymvfYXBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2ace588307c77eaf48bf2d47cf3c5e90ac3339272b20bb06c28f411aba9d8ad2","last_reissued_at":"2026-05-18T03:38:22.072090Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:38:22.072090Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1212.3916","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:38:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sGV++j2NSml+fjTQRlkRWvtXAZOevTnN6BKzsDFO4l4TwVf893+qxzGbtl3pS5xmgEExBpkmXpLsURPGwOoBAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T21:33:02.552487Z"},"content_sha256":"0c728e00cc91b962f48c3d6a607ba9060be9335ea5fcb6fc5ea840f7f745c87d","schema_version":"1.0","event_id":"sha256:0c728e00cc91b962f48c3d6a607ba9060be9335ea5fcb6fc5ea840f7f745c87d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:FLHFRAYHY57K6SF7FVD46PC6SC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Global solutions to 2-d inhomogeneous navier-stokes system with general velocity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jingchi Huang (AMSS), Marius Paicu, Ping Zhang (AMSS)","submitted_at":"2012-12-17T08:10:09Z","abstract_excerpt":"In this paper, we are concerned with the global wellposedness of 2-D density-dependent incompressible Navier-Stokes equations with variable viscosity, in a critical functional frame- work which is invariant by the scaling of the equations and under a non-linear smallness condition on fluctuation of the initial density which has to be doubly exponential small compared with the size of the initial velocity. In the second part of the paper, we apply our methods combined with the techniques of R. Danchin and P. B. Mucha to prove the global existence of solutions to inhomogeneous Navier-Stokes syst"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.3916","kind":"arxiv","version":1},"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":"2026-05-18T03:38:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6MTZ8EzRo3BFCl24R37YZCXCrnD6XkeCcS7gtrastsCGwuydmkHO5y16S7aAu0W9xTKsseBRftDn9p3tdgVVCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T21:33:02.553127Z"},"content_sha256":"8b5122dd64cb37a5de63a9b909f0e01d06897afa4047b417cecbda74613a4275","schema_version":"1.0","event_id":"sha256:8b5122dd64cb37a5de63a9b909f0e01d06897afa4047b417cecbda74613a4275"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FLHFRAYHY57K6SF7FVD46PC6SC/bundle.json","state_url":"https://pith.science/pith/FLHFRAYHY57K6SF7FVD46PC6SC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FLHFRAYHY57K6SF7FVD46PC6SC/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":"2026-05-26T21:33:02Z","links":{"resolver":"https://pith.science/pith/FLHFRAYHY57K6SF7FVD46PC6SC","bundle":"https://pith.science/pith/FLHFRAYHY57K6SF7FVD46PC6SC/bundle.json","state":"https://pith.science/pith/FLHFRAYHY57K6SF7FVD46PC6SC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FLHFRAYHY57K6SF7FVD46PC6SC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:FLHFRAYHY57K6SF7FVD46PC6SC","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":"36ec98020a72c631548674a1b4828b0e63bd22443f2872816629b00d921600d1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-12-17T08:10:09Z","title_canon_sha256":"77915d59c349fb8991107ee3652d5c6d7c87bf6aeadf19f5117c95eb0714e83f"},"schema_version":"1.0","source":{"id":"1212.3916","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.3916","created_at":"2026-05-18T03:38:22Z"},{"alias_kind":"arxiv_version","alias_value":"1212.3916v1","created_at":"2026-05-18T03:38:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.3916","created_at":"2026-05-18T03:38:22Z"},{"alias_kind":"pith_short_12","alias_value":"FLHFRAYHY57K","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_16","alias_value":"FLHFRAYHY57K6SF7","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_8","alias_value":"FLHFRAYH","created_at":"2026-05-18T12:27:06Z"}],"graph_snapshots":[{"event_id":"sha256:8b5122dd64cb37a5de63a9b909f0e01d06897afa4047b417cecbda74613a4275","target":"graph","created_at":"2026-05-18T03:38:22Z","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 paper, we are concerned with the global wellposedness of 2-D density-dependent incompressible Navier-Stokes equations with variable viscosity, in a critical functional frame- work which is invariant by the scaling of the equations and under a non-linear smallness condition on fluctuation of the initial density which has to be doubly exponential small compared with the size of the initial velocity. In the second part of the paper, we apply our methods combined with the techniques of R. Danchin and P. B. Mucha to prove the global existence of solutions to inhomogeneous Navier-Stokes syst","authors_text":"Jingchi Huang (AMSS), Marius Paicu, Ping Zhang (AMSS)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-12-17T08:10:09Z","title":"Global solutions to 2-d inhomogeneous navier-stokes system with general velocity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.3916","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":"sha256:0c728e00cc91b962f48c3d6a607ba9060be9335ea5fcb6fc5ea840f7f745c87d","target":"record","created_at":"2026-05-18T03:38:22Z","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":"36ec98020a72c631548674a1b4828b0e63bd22443f2872816629b00d921600d1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-12-17T08:10:09Z","title_canon_sha256":"77915d59c349fb8991107ee3652d5c6d7c87bf6aeadf19f5117c95eb0714e83f"},"schema_version":"1.0","source":{"id":"1212.3916","kind":"arxiv","version":1}},"canonical_sha256":"2ace588307c77eaf48bf2d47cf3c5e90ac3339272b20bb06c28f411aba9d8ad2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2ace588307c77eaf48bf2d47cf3c5e90ac3339272b20bb06c28f411aba9d8ad2","first_computed_at":"2026-05-18T03:38:22.072090Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:38:22.072090Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iYfvZDLFcWCUnN1JJUCq7o0ERTWKGpfuxOaRONv6I48vycSauRveNYwm8+ac7KguSUgaigR/l8tPoNymvfYXBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:38:22.072747Z","signed_message":"canonical_sha256_bytes"},"source_id":"1212.3916","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0c728e00cc91b962f48c3d6a607ba9060be9335ea5fcb6fc5ea840f7f745c87d","sha256:8b5122dd64cb37a5de63a9b909f0e01d06897afa4047b417cecbda74613a4275"],"state_sha256":"2a986e00bd5d411fefdce7f7186a32549b26b1dddc2d75d50921450e941ffb00"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YHJiedUd8eVwkPVRcGQoyTjwotEuOImFoQQy0z6Qw20FXsy/H4EZAio9KmFPNtTk1RZKOHbOKPZWG9eN1xH1CA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T21:33:02.556343Z","bundle_sha256":"c50eb0a2ed0ca03a2c528c497dfda0c84b3e7511fe8b84f175377d32f050cea6"}}