{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:JG4FW7HJ2HPHOGWGR25EB5BGIX","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":"d07bc6312218342252882a4295d2699f6653941a1c130f8b58ed96e8b7ea700b","cross_cats_sorted":["physics.class-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-12-17T08:11:45Z","title_canon_sha256":"473bcb016a77634b9984dc9437675b78d730034d26dcbdbc3b880e91d9a6ac6a"},"schema_version":"1.0","source":{"id":"1212.3918","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.3918","created_at":"2026-05-18T03:36:03Z"},{"alias_kind":"arxiv_version","alias_value":"1212.3918v3","created_at":"2026-05-18T03:36:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.3918","created_at":"2026-05-18T03:36:03Z"},{"alias_kind":"pith_short_12","alias_value":"JG4FW7HJ2HPH","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_16","alias_value":"JG4FW7HJ2HPHOGWG","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_8","alias_value":"JG4FW7HJ","created_at":"2026-05-18T12:27:11Z"}],"graph_snapshots":[{"event_id":"sha256:5cf0b484b717e9c249e95d62484b0e2113e2ede764307d2852aa95bcb9b6f77c","target":"graph","created_at":"2026-05-18T03:36:03Z","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 investigate the time decay behavior to Lions weak solution of 2D incompressible density-dependent Navier-Stokes equations with variable viscosity.","authors_text":"Jingchi Huang (AMSS), Marius Paicu","cross_cats":["physics.class-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-12-17T08:11:45Z","title":"Decay estimates of global solutions to 2D incompressible inhomogeneous Navier-Stokes equations with variable viscosity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.3918","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":"sha256:188afaf337dc9478fd6662fe182e91ae481ecbc997281ef79da97f95067a4b15","target":"record","created_at":"2026-05-18T03:36:03Z","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":"d07bc6312218342252882a4295d2699f6653941a1c130f8b58ed96e8b7ea700b","cross_cats_sorted":["physics.class-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-12-17T08:11:45Z","title_canon_sha256":"473bcb016a77634b9984dc9437675b78d730034d26dcbdbc3b880e91d9a6ac6a"},"schema_version":"1.0","source":{"id":"1212.3918","kind":"arxiv","version":3}},"canonical_sha256":"49b85b7ce9d1de771ac68eba40f42645fd61e96d15eacfc60f78d3f70fdb04f1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"49b85b7ce9d1de771ac68eba40f42645fd61e96d15eacfc60f78d3f70fdb04f1","first_computed_at":"2026-05-18T03:36:03.943580Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:36:03.943580Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"q7uSBib6khxHb+uR4L8zSREpOVj8OjvRT1Jh456yJxMT87WHIJ4+ZHCkiJGw5A9vAnjV/ILgC/G/kki4FL8SCw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:36:03.944442Z","signed_message":"canonical_sha256_bytes"},"source_id":"1212.3918","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:188afaf337dc9478fd6662fe182e91ae481ecbc997281ef79da97f95067a4b15","sha256:5cf0b484b717e9c249e95d62484b0e2113e2ede764307d2852aa95bcb9b6f77c"],"state_sha256":"db03f7351e8eb1504ce568033bf8ba9c8a56d94828368ec6fc2b56f1ae02093d"}