{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:MZHXQIV5JLEM3XLVKRCSXWTZKH","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":"8b9a8791de9c33e0ade166bd13416554e42672937119351d4045b3cb611168e8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-09-05T10:17:19Z","title_canon_sha256":"147ed9abb4cd16d782e8e1629500f66dc462ee7d9463170e9c7c2074aa7caf37"},"schema_version":"1.0","source":{"id":"1709.01319","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.01319","created_at":"2026-05-18T00:31:44Z"},{"alias_kind":"arxiv_version","alias_value":"1709.01319v2","created_at":"2026-05-18T00:31:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.01319","created_at":"2026-05-18T00:31:44Z"},{"alias_kind":"pith_short_12","alias_value":"MZHXQIV5JLEM","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_16","alias_value":"MZHXQIV5JLEM3XLV","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_8","alias_value":"MZHXQIV5","created_at":"2026-05-18T12:31:31Z"}],"graph_snapshots":[{"event_id":"sha256:bbdad66228866598406d780c7719d39a5a13e13b90b9eb9bdd7dfb3b4e5646f1","target":"graph","created_at":"2026-05-18T00:31:44Z","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, let $\\mathcal{S}$ denote the possible interior singular set of suitable weak solutions of the 3D Navier-Stokes equations. We improve the known upper box-counting dimension of this set from $360/277(\\approx1.300)$ in [24] to $975/758(\\approx1.286)$. It is also shown that $\\Lambda(\\mathcal{S},r(\\log(e/r))^{\\sigma})=0(0\\leq\\sigma<27/113)$, which extends the previous corresponding results concerning the improvement of the classical Caffarelli-Kohn-Nirenberg theorem by a logarithmic factor in Choe and Lewis [3, J. Funct. Anal., 175: 348-369, 2000] and in Choe and Yang et al. [4, Comm","authors_text":"Gang Wu, Wei Ren, Yanqing Wang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-09-05T10:17:19Z","title":"Remarks on the singular set of suitable weak solutions to the 3D Navier-Stokes equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.01319","kind":"arxiv","version":2},"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":"sha256:6559cfd6f0866f09a2f904366b1031964c447de17e6030f3fc8c760298b0d63f","target":"record","created_at":"2026-05-18T00:31:44Z","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":"8b9a8791de9c33e0ade166bd13416554e42672937119351d4045b3cb611168e8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-09-05T10:17:19Z","title_canon_sha256":"147ed9abb4cd16d782e8e1629500f66dc462ee7d9463170e9c7c2074aa7caf37"},"schema_version":"1.0","source":{"id":"1709.01319","kind":"arxiv","version":2}},"canonical_sha256":"664f7822bd4ac8cddd7554452bda7951e7afb8ee58bca15ac7cc62ba26699a85","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"664f7822bd4ac8cddd7554452bda7951e7afb8ee58bca15ac7cc62ba26699a85","first_computed_at":"2026-05-18T00:31:44.857074Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:31:44.857074Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dO9QWjAdxiF3e81bBmePbfrfxIOFTYzVMF+PvbxllimQzWQ+ET17dpOlXKGy78FRLc6wcWz6FlkApkmOD/r/AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:31:44.857571Z","signed_message":"canonical_sha256_bytes"},"source_id":"1709.01319","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6559cfd6f0866f09a2f904366b1031964c447de17e6030f3fc8c760298b0d63f","sha256:bbdad66228866598406d780c7719d39a5a13e13b90b9eb9bdd7dfb3b4e5646f1"],"state_sha256":"fea130cb4e7a82f0e64e9e1467e2457791c0b58f7f9b159c40ab19ce3363d8a4"}