{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2003:XETKKFKEDCLDA737RNQCUK4DVA","short_pith_number":"pith:XETKKFKE","canonical_record":{"source":{"id":"math/0301207","kind":"arxiv","version":6},"metadata":{"license":"","primary_cat":"math.AP","submitted_at":"2003-01-20T05:44:25Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"8a532b3911ce74f93be6feef4806abd3140096f032379d9dd8e9f05724a673d4","abstract_canon_sha256":"9321b004bc7b209ea9b7a589c459c0bf8978311beb9aeaf7e8f07d99766ce480"},"schema_version":"1.0"},"canonical_sha256":"b926a515441896307f7f8b602a2b83a80cfc309498a29e91f3c18d60f0a395eb","source":{"kind":"arxiv","id":"math/0301207","version":6},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0301207","created_at":"2026-05-18T03:21:55Z"},{"alias_kind":"arxiv_version","alias_value":"math/0301207v6","created_at":"2026-05-18T03:21:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0301207","created_at":"2026-05-18T03:21:55Z"},{"alias_kind":"pith_short_12","alias_value":"XETKKFKEDCLD","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"XETKKFKEDCLDA737","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"XETKKFKE","created_at":"2026-05-18T12:25:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2003:XETKKFKEDCLDA737RNQCUK4DVA","target":"record","payload":{"canonical_record":{"source":{"id":"math/0301207","kind":"arxiv","version":6},"metadata":{"license":"","primary_cat":"math.AP","submitted_at":"2003-01-20T05:44:25Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"8a532b3911ce74f93be6feef4806abd3140096f032379d9dd8e9f05724a673d4","abstract_canon_sha256":"9321b004bc7b209ea9b7a589c459c0bf8978311beb9aeaf7e8f07d99766ce480"},"schema_version":"1.0"},"canonical_sha256":"b926a515441896307f7f8b602a2b83a80cfc309498a29e91f3c18d60f0a395eb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:21:55.070678Z","signature_b64":"oxKcppxcm3xDzDhSJBHkhnOXGdPjT3/fu8IxGGL/22DVLVPDzZsBzMly0dkZ9ArlR7B86NDrLGHRz+egBatCDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b926a515441896307f7f8b602a2b83a80cfc309498a29e91f3c18d60f0a395eb","last_reissued_at":"2026-05-18T03:21:55.070253Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:21:55.070253Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0301207","source_version":6,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:21:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1r4kIv0a+aIV41eRQmzN/2+LhKTXRteezReyJp4mo6b8cVlG/FVqX9NR11xToy3/yfEx23Vbu2S15hGpk9qZDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T20:23:34.981835Z"},"content_sha256":"b94e0aad1bea0fcf262d5e9385b0da1eb51fea0e57c154c64ec6affb74cd9506","schema_version":"1.0","event_id":"sha256:b94e0aad1bea0fcf262d5e9385b0da1eb51fea0e57c154c64ec6affb74cd9506"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2003:XETKKFKEDCLDA737RNQCUK4DVA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Conditions implying regularity of the three dimensional Navier-Stokes equation","license":"","headline":"","cross_cats":["math.PR"],"primary_cat":"math.AP","authors_text":"Stephen Montgomery-Smith","submitted_at":"2003-01-20T05:44:25Z","abstract_excerpt":"We obtain logarithmic improvements for conditions for regularity of the Navier-Stokes equation, similar to those of Prodi-Serrin or Beale-Kato-Majda. Some of the proofs make use of a stochastic approach involving Feynman-Kac like inequalities. As part of the our methods, we give a different approach to a priori estimates of Foias, Guillope and Temam."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0301207","kind":"arxiv","version":6},"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":"2026-05-18T03:21:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iumYX7t25Z8Wu6Gsbzyo29uT3vbxVGDpEiuCJtxC4r0clwR/0TMFgcUzcrbd82Qigc5Xiv+sf8Eju+g7PyMcBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T20:23:34.982536Z"},"content_sha256":"c974c5db17a89d7f6f36441d4d4ed5eadcdb63e2b79e544dc7119fcaf07a7cd0","schema_version":"1.0","event_id":"sha256:c974c5db17a89d7f6f36441d4d4ed5eadcdb63e2b79e544dc7119fcaf07a7cd0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XETKKFKEDCLDA737RNQCUK4DVA/bundle.json","state_url":"https://pith.science/pith/XETKKFKEDCLDA737RNQCUK4DVA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XETKKFKEDCLDA737RNQCUK4DVA/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":"2026-05-26T20:23:34Z","links":{"resolver":"https://pith.science/pith/XETKKFKEDCLDA737RNQCUK4DVA","bundle":"https://pith.science/pith/XETKKFKEDCLDA737RNQCUK4DVA/bundle.json","state":"https://pith.science/pith/XETKKFKEDCLDA737RNQCUK4DVA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XETKKFKEDCLDA737RNQCUK4DVA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2003:XETKKFKEDCLDA737RNQCUK4DVA","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":"9321b004bc7b209ea9b7a589c459c0bf8978311beb9aeaf7e8f07d99766ce480","cross_cats_sorted":["math.PR"],"license":"","primary_cat":"math.AP","submitted_at":"2003-01-20T05:44:25Z","title_canon_sha256":"8a532b3911ce74f93be6feef4806abd3140096f032379d9dd8e9f05724a673d4"},"schema_version":"1.0","source":{"id":"math/0301207","kind":"arxiv","version":6}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0301207","created_at":"2026-05-18T03:21:55Z"},{"alias_kind":"arxiv_version","alias_value":"math/0301207v6","created_at":"2026-05-18T03:21:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0301207","created_at":"2026-05-18T03:21:55Z"},{"alias_kind":"pith_short_12","alias_value":"XETKKFKEDCLD","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"XETKKFKEDCLDA737","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"XETKKFKE","created_at":"2026-05-18T12:25:52Z"}],"graph_snapshots":[{"event_id":"sha256:c974c5db17a89d7f6f36441d4d4ed5eadcdb63e2b79e544dc7119fcaf07a7cd0","target":"graph","created_at":"2026-05-18T03:21:55Z","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 obtain logarithmic improvements for conditions for regularity of the Navier-Stokes equation, similar to those of Prodi-Serrin or Beale-Kato-Majda. Some of the proofs make use of a stochastic approach involving Feynman-Kac like inequalities. As part of the our methods, we give a different approach to a priori estimates of Foias, Guillope and Temam.","authors_text":"Stephen Montgomery-Smith","cross_cats":["math.PR"],"headline":"","license":"","primary_cat":"math.AP","submitted_at":"2003-01-20T05:44:25Z","title":"Conditions implying regularity of the three dimensional Navier-Stokes equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0301207","kind":"arxiv","version":6},"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:b94e0aad1bea0fcf262d5e9385b0da1eb51fea0e57c154c64ec6affb74cd9506","target":"record","created_at":"2026-05-18T03:21:55Z","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":"9321b004bc7b209ea9b7a589c459c0bf8978311beb9aeaf7e8f07d99766ce480","cross_cats_sorted":["math.PR"],"license":"","primary_cat":"math.AP","submitted_at":"2003-01-20T05:44:25Z","title_canon_sha256":"8a532b3911ce74f93be6feef4806abd3140096f032379d9dd8e9f05724a673d4"},"schema_version":"1.0","source":{"id":"math/0301207","kind":"arxiv","version":6}},"canonical_sha256":"b926a515441896307f7f8b602a2b83a80cfc309498a29e91f3c18d60f0a395eb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b926a515441896307f7f8b602a2b83a80cfc309498a29e91f3c18d60f0a395eb","first_computed_at":"2026-05-18T03:21:55.070253Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:21:55.070253Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oxKcppxcm3xDzDhSJBHkhnOXGdPjT3/fu8IxGGL/22DVLVPDzZsBzMly0dkZ9ArlR7B86NDrLGHRz+egBatCDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:21:55.070678Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0301207","source_kind":"arxiv","source_version":6}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b94e0aad1bea0fcf262d5e9385b0da1eb51fea0e57c154c64ec6affb74cd9506","sha256:c974c5db17a89d7f6f36441d4d4ed5eadcdb63e2b79e544dc7119fcaf07a7cd0"],"state_sha256":"1ed91897c6e64d88cec7a3936d2c5e247389014e3488059005b31bd1fb5f7086"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pybVPMYyRPDAkwW+WDIfdFQrxhElFE8OUwKIXMTAOn9QkGVwERXKMJ7gJu0zBMCbkBpToazDWa/6bpRFnNgxDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T20:23:34.986238Z","bundle_sha256":"0da3d29eb3d919140dc9a4f006286974bf54b78f59428a119c13a6d0c6bba8d4"}}