{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:QCRDJSEUFA4TPZEGSJNTSK6RLY","short_pith_number":"pith:QCRDJSEU","canonical_record":{"source":{"id":"1706.10173","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-06-30T12:35:46Z","cross_cats_sorted":[],"title_canon_sha256":"dc91b28c9e6a0235d8172b49434477c9bed3d45fd59f94027cc1ff682b67e168","abstract_canon_sha256":"3e407c846e3df56addbd937e87c2185c25fe34c1c4e91ffea04c4313b711167b"},"schema_version":"1.0"},"canonical_sha256":"80a234c894283937e486925b392bd15e29fb44a90b932647e1e8a22c2eca865f","source":{"kind":"arxiv","id":"1706.10173","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.10173","created_at":"2026-05-18T00:41:09Z"},{"alias_kind":"arxiv_version","alias_value":"1706.10173v1","created_at":"2026-05-18T00:41:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.10173","created_at":"2026-05-18T00:41:09Z"},{"alias_kind":"pith_short_12","alias_value":"QCRDJSEUFA4T","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_16","alias_value":"QCRDJSEUFA4TPZEG","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_8","alias_value":"QCRDJSEU","created_at":"2026-05-18T12:31:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:QCRDJSEUFA4TPZEGSJNTSK6RLY","target":"record","payload":{"canonical_record":{"source":{"id":"1706.10173","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-06-30T12:35:46Z","cross_cats_sorted":[],"title_canon_sha256":"dc91b28c9e6a0235d8172b49434477c9bed3d45fd59f94027cc1ff682b67e168","abstract_canon_sha256":"3e407c846e3df56addbd937e87c2185c25fe34c1c4e91ffea04c4313b711167b"},"schema_version":"1.0"},"canonical_sha256":"80a234c894283937e486925b392bd15e29fb44a90b932647e1e8a22c2eca865f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:41:09.258607Z","signature_b64":"is9DWpN4gkbnaTO2DS6jjGKZ+G0u89/nDzBG0vFQJ9R9oj7lv+6qkTHnTh5qP6KfaS54nJ6B7UeH3kGKwgEpDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"80a234c894283937e486925b392bd15e29fb44a90b932647e1e8a22c2eca865f","last_reissued_at":"2026-05-18T00:41:09.258046Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:41:09.258046Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1706.10173","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":"2026-05-18T00:41:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Yz4BM8lqtBybyKYo11fNIkq13vnrrc5uTX5KfJwcuvlJ19z08A/8N08GiszPbcp1zKXKc48FusNadpt7y6pzCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T05:49:58.414832Z"},"content_sha256":"0ba53995a7fa7ad4aea3aadb4d501e5be253cd4b6441748d401fa06a9824f654","schema_version":"1.0","event_id":"sha256:0ba53995a7fa7ad4aea3aadb4d501e5be253cd4b6441748d401fa06a9824f654"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:QCRDJSEUFA4TPZEGSJNTSK6RLY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Some remarks on the regularity time of Leray solutions to the Navier-Stokes equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jana\\'ina P. Zingano, Pablo Braz e Silva, Paulo R. Zingano","submitted_at":"2017-06-30T12:35:46Z","abstract_excerpt":"In this small note we strengthen the classic result about the regularity time t* of arbitrary Leray solutions to the (incompressible) Navier-Stokes equations in Rn (n = 3, 4), which have the form: t* <= K_{3} nu^{-5} || u(.,0) ||_{L2}^{4} if n = 3, and t* <= K_{4} nu^{-3} || u(.,0) ||_{L2}^{2} if n = 4 (in particular, by reducing the current best known values for the constants K_{3}, K_{4}). Some related results of clear interest are also included (derived) in our discussion."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.10173","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":"2026-05-18T00:41:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PMo5CJI2I/VN+d1aG3d1dKLE4Kx3HSPkjq3Tj5bmlAYjx5uT96m3Srzxkhbg4p7Um9ARS4XI5gvTvJLVUipMBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T05:49:58.415529Z"},"content_sha256":"e3c5ea75b6f9144f652a1788b951c19cf5e5eb22581439d9bb846f0ae97c5c06","schema_version":"1.0","event_id":"sha256:e3c5ea75b6f9144f652a1788b951c19cf5e5eb22581439d9bb846f0ae97c5c06"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QCRDJSEUFA4TPZEGSJNTSK6RLY/bundle.json","state_url":"https://pith.science/pith/QCRDJSEUFA4TPZEGSJNTSK6RLY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QCRDJSEUFA4TPZEGSJNTSK6RLY/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":"2026-06-04T05:49:58Z","links":{"resolver":"https://pith.science/pith/QCRDJSEUFA4TPZEGSJNTSK6RLY","bundle":"https://pith.science/pith/QCRDJSEUFA4TPZEGSJNTSK6RLY/bundle.json","state":"https://pith.science/pith/QCRDJSEUFA4TPZEGSJNTSK6RLY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QCRDJSEUFA4TPZEGSJNTSK6RLY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:QCRDJSEUFA4TPZEGSJNTSK6RLY","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":"3e407c846e3df56addbd937e87c2185c25fe34c1c4e91ffea04c4313b711167b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-06-30T12:35:46Z","title_canon_sha256":"dc91b28c9e6a0235d8172b49434477c9bed3d45fd59f94027cc1ff682b67e168"},"schema_version":"1.0","source":{"id":"1706.10173","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.10173","created_at":"2026-05-18T00:41:09Z"},{"alias_kind":"arxiv_version","alias_value":"1706.10173v1","created_at":"2026-05-18T00:41:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.10173","created_at":"2026-05-18T00:41:09Z"},{"alias_kind":"pith_short_12","alias_value":"QCRDJSEUFA4T","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_16","alias_value":"QCRDJSEUFA4TPZEG","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_8","alias_value":"QCRDJSEU","created_at":"2026-05-18T12:31:37Z"}],"graph_snapshots":[{"event_id":"sha256:e3c5ea75b6f9144f652a1788b951c19cf5e5eb22581439d9bb846f0ae97c5c06","target":"graph","created_at":"2026-05-18T00:41:09Z","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 small note we strengthen the classic result about the regularity time t* of arbitrary Leray solutions to the (incompressible) Navier-Stokes equations in Rn (n = 3, 4), which have the form: t* <= K_{3} nu^{-5} || u(.,0) ||_{L2}^{4} if n = 3, and t* <= K_{4} nu^{-3} || u(.,0) ||_{L2}^{2} if n = 4 (in particular, by reducing the current best known values for the constants K_{3}, K_{4}). Some related results of clear interest are also included (derived) in our discussion.","authors_text":"Jana\\'ina P. Zingano, Pablo Braz e Silva, Paulo R. Zingano","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-06-30T12:35:46Z","title":"Some remarks on the regularity time of Leray solutions to the Navier-Stokes equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.10173","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":"sha256:0ba53995a7fa7ad4aea3aadb4d501e5be253cd4b6441748d401fa06a9824f654","target":"record","created_at":"2026-05-18T00:41:09Z","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":"3e407c846e3df56addbd937e87c2185c25fe34c1c4e91ffea04c4313b711167b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-06-30T12:35:46Z","title_canon_sha256":"dc91b28c9e6a0235d8172b49434477c9bed3d45fd59f94027cc1ff682b67e168"},"schema_version":"1.0","source":{"id":"1706.10173","kind":"arxiv","version":1}},"canonical_sha256":"80a234c894283937e486925b392bd15e29fb44a90b932647e1e8a22c2eca865f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"80a234c894283937e486925b392bd15e29fb44a90b932647e1e8a22c2eca865f","first_computed_at":"2026-05-18T00:41:09.258046Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:41:09.258046Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"is9DWpN4gkbnaTO2DS6jjGKZ+G0u89/nDzBG0vFQJ9R9oj7lv+6qkTHnTh5qP6KfaS54nJ6B7UeH3kGKwgEpDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:41:09.258607Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.10173","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0ba53995a7fa7ad4aea3aadb4d501e5be253cd4b6441748d401fa06a9824f654","sha256:e3c5ea75b6f9144f652a1788b951c19cf5e5eb22581439d9bb846f0ae97c5c06"],"state_sha256":"af85ae10437eb3dfaddae2fabdc750e621509f9b852c1cdc86fbda6119997d1b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ov0/r6C8xxDN0mbVn2R43hCNBJtPPmR2PkT3S2qBuMIisvjt8wwdC1cCHfsv+kbQ+tm/1HpRdVf3OhyozJRlCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T05:49:58.419013Z","bundle_sha256":"567c2d6efec1e8f39fb3fdb69b949b5abd6ff9afa87f5a5a57a6c2349d438387"}}