{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:DHQ23XILUHVYTNYWAZXKMY36OC","short_pith_number":"pith:DHQ23XIL","canonical_record":{"source":{"id":"1705.04561","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-05-12T13:29:38Z","cross_cats_sorted":[],"title_canon_sha256":"b4e3e6282575505a9fa398381e5075891aa0fecf50dbeec66768e57acce17300","abstract_canon_sha256":"53208b3bc8699b896d4d90c87a8348a893bd368ea44c6f424ee1cb8740f74108"},"schema_version":"1.0"},"canonical_sha256":"19e1addd0ba1eb89b716066ea6637e70a7f47125b0db48384e247ee2baa525d7","source":{"kind":"arxiv","id":"1705.04561","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.04561","created_at":"2026-05-18T00:44:37Z"},{"alias_kind":"arxiv_version","alias_value":"1705.04561v1","created_at":"2026-05-18T00:44:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.04561","created_at":"2026-05-18T00:44:37Z"},{"alias_kind":"pith_short_12","alias_value":"DHQ23XILUHVY","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_16","alias_value":"DHQ23XILUHVYTNYW","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_8","alias_value":"DHQ23XIL","created_at":"2026-05-18T12:31:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:DHQ23XILUHVYTNYWAZXKMY36OC","target":"record","payload":{"canonical_record":{"source":{"id":"1705.04561","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-05-12T13:29:38Z","cross_cats_sorted":[],"title_canon_sha256":"b4e3e6282575505a9fa398381e5075891aa0fecf50dbeec66768e57acce17300","abstract_canon_sha256":"53208b3bc8699b896d4d90c87a8348a893bd368ea44c6f424ee1cb8740f74108"},"schema_version":"1.0"},"canonical_sha256":"19e1addd0ba1eb89b716066ea6637e70a7f47125b0db48384e247ee2baa525d7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:44:37.795255Z","signature_b64":"fddI4gvwQBBCuIKUmMfl1m+kOCZwBK2yeuT1btnM2X0qOKH6uGQ1l7wxVsWUyLE7JeEFk9vhIu2mycl63OJ0DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"19e1addd0ba1eb89b716066ea6637e70a7f47125b0db48384e247ee2baa525d7","last_reissued_at":"2026-05-18T00:44:37.794862Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:44:37.794862Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1705.04561","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":"2026-05-18T00:44:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qU7aBc/KzeGMA1yYrxPO/ihzh5phVaWSoL+JkogpEOJKwm2g271yM0PHrGJbuW/H90MtqRrtMMPeVv7WCeT0AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T22:37:20.505086Z"},"content_sha256":"0f456c03dccd75ae2f0bd1fc31979baa70680269f32132537c249c0bb2f3f112","schema_version":"1.0","event_id":"sha256:0f456c03dccd75ae2f0bd1fc31979baa70680269f32132537c249c0bb2f3f112"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:DHQ23XILUHVYTNYWAZXKMY36OC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Local kinetic energy and singularities of the incompressible Navier--Stokes Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Hi Jun Choe, Minsuk Yang","submitted_at":"2017-05-12T13:29:38Z","abstract_excerpt":"We study the partial regularity problem of the incompressible Navier--Stokes equations. In this paper, we show that a reverse H\\\"older inequality of velocity gradient with increasing support holds under the condition that a scaled functional corresponding the local kinetic energy is uniformly bounded. As an application, we give a new bound for the Hausdorff dimension and the Minkowski dimension of singular set when weak solutions $v$ belong to $L^\\infty(0,T;L^{3,w}(\\mathbb{R}^3))$ where $L^{3,w}(\\mathbb{R}^3)$ denotes the standard weak Lebesgue space."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.04561","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":"2026-05-18T00:44:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Zid62khXi43dbgxucr3butLiOZfTwAOi/ALOtIcpzZYpNYKeBikooHBHnA70CcSw7/KtPAvux/OHw5NmelY6DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T22:37:20.505828Z"},"content_sha256":"fb0ad190377e04bcfb23e83a8e9f8026a3dba40f6e6376137f073ba82a45deb6","schema_version":"1.0","event_id":"sha256:fb0ad190377e04bcfb23e83a8e9f8026a3dba40f6e6376137f073ba82a45deb6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DHQ23XILUHVYTNYWAZXKMY36OC/bundle.json","state_url":"https://pith.science/pith/DHQ23XILUHVYTNYWAZXKMY36OC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DHQ23XILUHVYTNYWAZXKMY36OC/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":"2026-05-30T22:37:20Z","links":{"resolver":"https://pith.science/pith/DHQ23XILUHVYTNYWAZXKMY36OC","bundle":"https://pith.science/pith/DHQ23XILUHVYTNYWAZXKMY36OC/bundle.json","state":"https://pith.science/pith/DHQ23XILUHVYTNYWAZXKMY36OC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DHQ23XILUHVYTNYWAZXKMY36OC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:DHQ23XILUHVYTNYWAZXKMY36OC","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":"53208b3bc8699b896d4d90c87a8348a893bd368ea44c6f424ee1cb8740f74108","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-05-12T13:29:38Z","title_canon_sha256":"b4e3e6282575505a9fa398381e5075891aa0fecf50dbeec66768e57acce17300"},"schema_version":"1.0","source":{"id":"1705.04561","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.04561","created_at":"2026-05-18T00:44:37Z"},{"alias_kind":"arxiv_version","alias_value":"1705.04561v1","created_at":"2026-05-18T00:44:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.04561","created_at":"2026-05-18T00:44:37Z"},{"alias_kind":"pith_short_12","alias_value":"DHQ23XILUHVY","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_16","alias_value":"DHQ23XILUHVYTNYW","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_8","alias_value":"DHQ23XIL","created_at":"2026-05-18T12:31:10Z"}],"graph_snapshots":[{"event_id":"sha256:fb0ad190377e04bcfb23e83a8e9f8026a3dba40f6e6376137f073ba82a45deb6","target":"graph","created_at":"2026-05-18T00:44:37Z","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":"We study the partial regularity problem of the incompressible Navier--Stokes equations. In this paper, we show that a reverse H\\\"older inequality of velocity gradient with increasing support holds under the condition that a scaled functional corresponding the local kinetic energy is uniformly bounded. As an application, we give a new bound for the Hausdorff dimension and the Minkowski dimension of singular set when weak solutions $v$ belong to $L^\\infty(0,T;L^{3,w}(\\mathbb{R}^3))$ where $L^{3,w}(\\mathbb{R}^3)$ denotes the standard weak Lebesgue space.","authors_text":"Hi Jun Choe, Minsuk Yang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-05-12T13:29:38Z","title":"Local kinetic energy and singularities of the incompressible Navier--Stokes Equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.04561","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":"sha256:0f456c03dccd75ae2f0bd1fc31979baa70680269f32132537c249c0bb2f3f112","target":"record","created_at":"2026-05-18T00:44:37Z","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":"53208b3bc8699b896d4d90c87a8348a893bd368ea44c6f424ee1cb8740f74108","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-05-12T13:29:38Z","title_canon_sha256":"b4e3e6282575505a9fa398381e5075891aa0fecf50dbeec66768e57acce17300"},"schema_version":"1.0","source":{"id":"1705.04561","kind":"arxiv","version":1}},"canonical_sha256":"19e1addd0ba1eb89b716066ea6637e70a7f47125b0db48384e247ee2baa525d7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"19e1addd0ba1eb89b716066ea6637e70a7f47125b0db48384e247ee2baa525d7","first_computed_at":"2026-05-18T00:44:37.794862Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:44:37.794862Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fddI4gvwQBBCuIKUmMfl1m+kOCZwBK2yeuT1btnM2X0qOKH6uGQ1l7wxVsWUyLE7JeEFk9vhIu2mycl63OJ0DA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:44:37.795255Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.04561","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0f456c03dccd75ae2f0bd1fc31979baa70680269f32132537c249c0bb2f3f112","sha256:fb0ad190377e04bcfb23e83a8e9f8026a3dba40f6e6376137f073ba82a45deb6"],"state_sha256":"d1b2e91b928ceb26e98fea1ef5bfc3b17b8e35d3966d882b1a8c614be8055688"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JdLcTJ9Ytz6AprD95JY1TPvnLOca14D4IiL+8SncnPXYvW86G0i06C3izgdIPhiMwnJAaEzanMo6tvcf7ON5Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T22:37:20.508958Z","bundle_sha256":"5c19afa8c46afcdafeaa5d08b0fc45780ab12914074195e7da2fe30a3df0ba63"}}