{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:C2MPF5A76WB3P3WFCKEGG7G4WH","short_pith_number":"pith:C2MPF5A7","canonical_record":{"source":{"id":"1812.10509","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-12-26T19:33:31Z","cross_cats_sorted":[],"title_canon_sha256":"df3ea1564b8f1824867e4b7b833fec6c39e5ae772b2d489c82ae22083af01a22","abstract_canon_sha256":"5eef1b1bb04301f7d2b52b8178090471b869d86fddcd89874ad334265299dc1e"},"schema_version":"1.0"},"canonical_sha256":"1698f2f41ff583b7eec51288637cdcb1cc2f47823917099c6e546565971c1c94","source":{"kind":"arxiv","id":"1812.10509","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.10509","created_at":"2026-05-17T23:57:20Z"},{"alias_kind":"arxiv_version","alias_value":"1812.10509v1","created_at":"2026-05-17T23:57:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.10509","created_at":"2026-05-17T23:57:20Z"},{"alias_kind":"pith_short_12","alias_value":"C2MPF5A76WB3","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_16","alias_value":"C2MPF5A76WB3P3WF","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_8","alias_value":"C2MPF5A7","created_at":"2026-05-18T12:32:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:C2MPF5A76WB3P3WFCKEGG7G4WH","target":"record","payload":{"canonical_record":{"source":{"id":"1812.10509","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-12-26T19:33:31Z","cross_cats_sorted":[],"title_canon_sha256":"df3ea1564b8f1824867e4b7b833fec6c39e5ae772b2d489c82ae22083af01a22","abstract_canon_sha256":"5eef1b1bb04301f7d2b52b8178090471b869d86fddcd89874ad334265299dc1e"},"schema_version":"1.0"},"canonical_sha256":"1698f2f41ff583b7eec51288637cdcb1cc2f47823917099c6e546565971c1c94","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:57:20.892271Z","signature_b64":"bNjZgZvdRdWTjl+KWySYJ7EVPcQwTzOSzNeYpgByySQWpt5OnhZmujZlsTc3As2QnysZdhWVm/GYL0rk86PlCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1698f2f41ff583b7eec51288637cdcb1cc2f47823917099c6e546565971c1c94","last_reissued_at":"2026-05-17T23:57:20.891572Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:57:20.891572Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1812.10509","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":"2026-05-17T23:57:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3Mnn6hdEYvyxPqz8FLtKwdbbq02u6lpjWwnxHFRfsMej/i/SPIaF838veIVM8/yNagWzMsvyhZh5S7+uXbU4AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T20:16:09.028965Z"},"content_sha256":"109eedd8b56af3761e239913008c4f2006c30b16570af63bea3cd4644914eb5c","schema_version":"1.0","event_id":"sha256:109eedd8b56af3761e239913008c4f2006c30b16570af63bea3cd4644914eb5c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:C2MPF5A76WB3P3WFCKEGG7G4WH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Short time regularity of Navier-Stokes flows with locally $L^3$ initial data and applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Hideyuki Miura, Kyungkeun Kang, Tai-Peng Tsai","submitted_at":"2018-12-26T19:33:31Z","abstract_excerpt":"We prove short time regularity of suitable weak solutions of 3D incompressible Navier-Stokes equations near a point where the initial data is locally in $L^3$. The result is applied to the regularity problems of solutions with uniformly small local $L^3$ norms, and of forward discretely self-similar solutions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.10509","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":"2026-05-17T23:57:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CSibXoyF9/1la89KmpP6iQz0JkmD6AIZFYOD9AfiEEpadmTwhUQFUiCc2psqmMryhgpPTunY0a9RQ0vFQ7LGAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T20:16:09.029331Z"},"content_sha256":"beafda39f024b201d2e3bfaf751045096a819cac4a8b9dfaededc9ec9e982782","schema_version":"1.0","event_id":"sha256:beafda39f024b201d2e3bfaf751045096a819cac4a8b9dfaededc9ec9e982782"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/C2MPF5A76WB3P3WFCKEGG7G4WH/bundle.json","state_url":"https://pith.science/pith/C2MPF5A76WB3P3WFCKEGG7G4WH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/C2MPF5A76WB3P3WFCKEGG7G4WH/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":"2026-05-26T20:16:09Z","links":{"resolver":"https://pith.science/pith/C2MPF5A76WB3P3WFCKEGG7G4WH","bundle":"https://pith.science/pith/C2MPF5A76WB3P3WFCKEGG7G4WH/bundle.json","state":"https://pith.science/pith/C2MPF5A76WB3P3WFCKEGG7G4WH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/C2MPF5A76WB3P3WFCKEGG7G4WH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:C2MPF5A76WB3P3WFCKEGG7G4WH","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":"5eef1b1bb04301f7d2b52b8178090471b869d86fddcd89874ad334265299dc1e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-12-26T19:33:31Z","title_canon_sha256":"df3ea1564b8f1824867e4b7b833fec6c39e5ae772b2d489c82ae22083af01a22"},"schema_version":"1.0","source":{"id":"1812.10509","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.10509","created_at":"2026-05-17T23:57:20Z"},{"alias_kind":"arxiv_version","alias_value":"1812.10509v1","created_at":"2026-05-17T23:57:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.10509","created_at":"2026-05-17T23:57:20Z"},{"alias_kind":"pith_short_12","alias_value":"C2MPF5A76WB3","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_16","alias_value":"C2MPF5A76WB3P3WF","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_8","alias_value":"C2MPF5A7","created_at":"2026-05-18T12:32:16Z"}],"graph_snapshots":[{"event_id":"sha256:beafda39f024b201d2e3bfaf751045096a819cac4a8b9dfaededc9ec9e982782","target":"graph","created_at":"2026-05-17T23:57:20Z","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 prove short time regularity of suitable weak solutions of 3D incompressible Navier-Stokes equations near a point where the initial data is locally in $L^3$. The result is applied to the regularity problems of solutions with uniformly small local $L^3$ norms, and of forward discretely self-similar solutions.","authors_text":"Hideyuki Miura, Kyungkeun Kang, Tai-Peng Tsai","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-12-26T19:33:31Z","title":"Short time regularity of Navier-Stokes flows with locally $L^3$ initial data and applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.10509","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":"sha256:109eedd8b56af3761e239913008c4f2006c30b16570af63bea3cd4644914eb5c","target":"record","created_at":"2026-05-17T23:57:20Z","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":"5eef1b1bb04301f7d2b52b8178090471b869d86fddcd89874ad334265299dc1e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-12-26T19:33:31Z","title_canon_sha256":"df3ea1564b8f1824867e4b7b833fec6c39e5ae772b2d489c82ae22083af01a22"},"schema_version":"1.0","source":{"id":"1812.10509","kind":"arxiv","version":1}},"canonical_sha256":"1698f2f41ff583b7eec51288637cdcb1cc2f47823917099c6e546565971c1c94","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1698f2f41ff583b7eec51288637cdcb1cc2f47823917099c6e546565971c1c94","first_computed_at":"2026-05-17T23:57:20.891572Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:57:20.891572Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bNjZgZvdRdWTjl+KWySYJ7EVPcQwTzOSzNeYpgByySQWpt5OnhZmujZlsTc3As2QnysZdhWVm/GYL0rk86PlCA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:57:20.892271Z","signed_message":"canonical_sha256_bytes"},"source_id":"1812.10509","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:109eedd8b56af3761e239913008c4f2006c30b16570af63bea3cd4644914eb5c","sha256:beafda39f024b201d2e3bfaf751045096a819cac4a8b9dfaededc9ec9e982782"],"state_sha256":"53f360430b5bee43235e4f0c0e4c14a8df507b90d0770424ecb20e80ef143e93"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9cawtOymkZUyhQZnzAhVBPJFtVyOAOLdrLAYNAEC5OX205FhwssI9LHOrIhuE17E0xXkgihkx0aGIAkBXI8wDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T20:16:09.032160Z","bundle_sha256":"245fe8c467ea31ba78256993a518871874ca2d6230fee1190129127f8096023c"}}