{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:OMEDHOXOZHFDFOU5Y5WTNKXENA","short_pith_number":"pith:OMEDHOXO","canonical_record":{"source":{"id":"1301.7155","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-01-30T07:58:51Z","cross_cats_sorted":[],"title_canon_sha256":"c1d6d85d57501c4e238c2e00502b885e3d5c41322b97a390f8eafc42ff76943d","abstract_canon_sha256":"dd9b6e5f281879f014da4cf3000dc297126801e58b22f501bfad60d7e6ce2db6"},"schema_version":"1.0"},"canonical_sha256":"730833baeec9ca32ba9dc76d36aae46814f379f0eb4e20d5f7a499868b063de4","source":{"kind":"arxiv","id":"1301.7155","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.7155","created_at":"2026-05-18T03:27:32Z"},{"alias_kind":"arxiv_version","alias_value":"1301.7155v1","created_at":"2026-05-18T03:27:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.7155","created_at":"2026-05-18T03:27:32Z"},{"alias_kind":"pith_short_12","alias_value":"OMEDHOXOZHFD","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"OMEDHOXOZHFDFOU5","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"OMEDHOXO","created_at":"2026-05-18T12:27:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:OMEDHOXOZHFDFOU5Y5WTNKXENA","target":"record","payload":{"canonical_record":{"source":{"id":"1301.7155","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-01-30T07:58:51Z","cross_cats_sorted":[],"title_canon_sha256":"c1d6d85d57501c4e238c2e00502b885e3d5c41322b97a390f8eafc42ff76943d","abstract_canon_sha256":"dd9b6e5f281879f014da4cf3000dc297126801e58b22f501bfad60d7e6ce2db6"},"schema_version":"1.0"},"canonical_sha256":"730833baeec9ca32ba9dc76d36aae46814f379f0eb4e20d5f7a499868b063de4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:27:32.070904Z","signature_b64":"oHbQUfISc5KgHJMKVCkjiN7SkEL9fKTtNVzCcwjMjgdQQQBf7V9xAJRcZLUxZ4Mo8W4V5QvPMiW0y0FiJtX7Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"730833baeec9ca32ba9dc76d36aae46814f379f0eb4e20d5f7a499868b063de4","last_reissued_at":"2026-05-18T03:27:32.070264Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:27:32.070264Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1301.7155","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":"2026-05-18T03:27:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fRujJUVBxJ0Iply7YkX5aYn2D6iCAuQQJtrpQoxqOyZ2y+GP9hRJv6xDHnBi57PW30QhMZxeYwj+n3UmqAcjDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T05:55:53.792960Z"},"content_sha256":"b4b8e4af8e14a529c82a0dfc615d4d20883c1056f5c00ce30e58191c77c8c4d0","schema_version":"1.0","event_id":"sha256:b4b8e4af8e14a529c82a0dfc615d4d20883c1056f5c00ce30e58191c77c8c4d0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:OMEDHOXOZHFDFOU5Y5WTNKXENA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Global Wellposeness for the 3D inhomogeneous incompressible Navier-Stokes equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Walter Craig, Xiangdi Huang, Yun Wang","submitted_at":"2013-01-30T07:58:51Z","abstract_excerpt":"This paper addresses the three-dimensional Navier-Stokes equations for an incompressible fluid whose density is permitted to be inhomogeneous. We establish a theorem of global existence and uniqueness of strong solutions for initial data with small $\\dot{H}^{\\frac12}$-norm, which also satisfies a natural compatibility condition. A key point of the theorem is that the initial density need not be strictly positive."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.7155","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":"2026-05-18T03:27:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kKcFUA9ZOGZgyVa2KDnA6bz8WKwNXzpgCwT6qEm89WoX3y+nDHWWfIF7TDOsuznTypwfNUUPvT7GLpOZfN7SDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T05:55:53.793286Z"},"content_sha256":"993975a5437f7c9066193f2a21e0af9eacb3b3dd378f636f8fb6cab4e0439d01","schema_version":"1.0","event_id":"sha256:993975a5437f7c9066193f2a21e0af9eacb3b3dd378f636f8fb6cab4e0439d01"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OMEDHOXOZHFDFOU5Y5WTNKXENA/bundle.json","state_url":"https://pith.science/pith/OMEDHOXOZHFDFOU5Y5WTNKXENA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OMEDHOXOZHFDFOU5Y5WTNKXENA/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":"2026-06-24T05:55:53Z","links":{"resolver":"https://pith.science/pith/OMEDHOXOZHFDFOU5Y5WTNKXENA","bundle":"https://pith.science/pith/OMEDHOXOZHFDFOU5Y5WTNKXENA/bundle.json","state":"https://pith.science/pith/OMEDHOXOZHFDFOU5Y5WTNKXENA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OMEDHOXOZHFDFOU5Y5WTNKXENA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:OMEDHOXOZHFDFOU5Y5WTNKXENA","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":"dd9b6e5f281879f014da4cf3000dc297126801e58b22f501bfad60d7e6ce2db6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-01-30T07:58:51Z","title_canon_sha256":"c1d6d85d57501c4e238c2e00502b885e3d5c41322b97a390f8eafc42ff76943d"},"schema_version":"1.0","source":{"id":"1301.7155","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.7155","created_at":"2026-05-18T03:27:32Z"},{"alias_kind":"arxiv_version","alias_value":"1301.7155v1","created_at":"2026-05-18T03:27:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.7155","created_at":"2026-05-18T03:27:32Z"},{"alias_kind":"pith_short_12","alias_value":"OMEDHOXOZHFD","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"OMEDHOXOZHFDFOU5","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"OMEDHOXO","created_at":"2026-05-18T12:27:54Z"}],"graph_snapshots":[{"event_id":"sha256:993975a5437f7c9066193f2a21e0af9eacb3b3dd378f636f8fb6cab4e0439d01","target":"graph","created_at":"2026-05-18T03:27:32Z","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":"This paper addresses the three-dimensional Navier-Stokes equations for an incompressible fluid whose density is permitted to be inhomogeneous. We establish a theorem of global existence and uniqueness of strong solutions for initial data with small $\\dot{H}^{\\frac12}$-norm, which also satisfies a natural compatibility condition. A key point of the theorem is that the initial density need not be strictly positive.","authors_text":"Walter Craig, Xiangdi Huang, Yun Wang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-01-30T07:58:51Z","title":"Global Wellposeness for the 3D inhomogeneous incompressible Navier-Stokes equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.7155","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:b4b8e4af8e14a529c82a0dfc615d4d20883c1056f5c00ce30e58191c77c8c4d0","target":"record","created_at":"2026-05-18T03:27:32Z","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":"dd9b6e5f281879f014da4cf3000dc297126801e58b22f501bfad60d7e6ce2db6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-01-30T07:58:51Z","title_canon_sha256":"c1d6d85d57501c4e238c2e00502b885e3d5c41322b97a390f8eafc42ff76943d"},"schema_version":"1.0","source":{"id":"1301.7155","kind":"arxiv","version":1}},"canonical_sha256":"730833baeec9ca32ba9dc76d36aae46814f379f0eb4e20d5f7a499868b063de4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"730833baeec9ca32ba9dc76d36aae46814f379f0eb4e20d5f7a499868b063de4","first_computed_at":"2026-05-18T03:27:32.070264Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:27:32.070264Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oHbQUfISc5KgHJMKVCkjiN7SkEL9fKTtNVzCcwjMjgdQQQBf7V9xAJRcZLUxZ4Mo8W4V5QvPMiW0y0FiJtX7Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T03:27:32.070904Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.7155","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b4b8e4af8e14a529c82a0dfc615d4d20883c1056f5c00ce30e58191c77c8c4d0","sha256:993975a5437f7c9066193f2a21e0af9eacb3b3dd378f636f8fb6cab4e0439d01"],"state_sha256":"b5ab44b7e648c26d72817ef17de4baa37ac6089e42ba8f8e4e155f0d5c0b2588"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+gfei+kFFQtwLJI9ObzCfsbBJB4gLAx7Xl7JW9z2ZX3660ngCgj9mgf6eswbQ/9GcMWm4HAnyQoRm6y3u1LhBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T05:55:53.795078Z","bundle_sha256":"6d13e99fa3e3be49ba926eb1590971d8e6d53533a67801ed39a7d92f014683b5"}}