{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:SJVSN7T6DKHBYE6NQSG6U4OGRP","short_pith_number":"pith:SJVSN7T6","canonical_record":{"source":{"id":"1807.00197","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-06-30T16:30:38Z","cross_cats_sorted":[],"title_canon_sha256":"b8d647e0206fd28730b27d7e98bd549e6feddb25385a12deb35ca5d00eeda268","abstract_canon_sha256":"a4bc590fc8b10b212f6a898abca472801471c9ec5bcc7f9debdd8121bb8bfffe"},"schema_version":"1.0"},"canonical_sha256":"926b26fe7e1a8e1c13cd848dea71c68bfda120ac97f9ca7f7c84334e7bb7a616","source":{"kind":"arxiv","id":"1807.00197","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.00197","created_at":"2026-05-18T00:11:55Z"},{"alias_kind":"arxiv_version","alias_value":"1807.00197v1","created_at":"2026-05-18T00:11:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.00197","created_at":"2026-05-18T00:11:55Z"},{"alias_kind":"pith_short_12","alias_value":"SJVSN7T6DKHB","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_16","alias_value":"SJVSN7T6DKHBYE6N","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_8","alias_value":"SJVSN7T6","created_at":"2026-05-18T12:32:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:SJVSN7T6DKHBYE6NQSG6U4OGRP","target":"record","payload":{"canonical_record":{"source":{"id":"1807.00197","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-06-30T16:30:38Z","cross_cats_sorted":[],"title_canon_sha256":"b8d647e0206fd28730b27d7e98bd549e6feddb25385a12deb35ca5d00eeda268","abstract_canon_sha256":"a4bc590fc8b10b212f6a898abca472801471c9ec5bcc7f9debdd8121bb8bfffe"},"schema_version":"1.0"},"canonical_sha256":"926b26fe7e1a8e1c13cd848dea71c68bfda120ac97f9ca7f7c84334e7bb7a616","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:11:55.736733Z","signature_b64":"A6H20/KXG4Uiq9uRLSpGLD81kVIBzy+vKkL5wFioX6TyujfRH1XESSUAyWE6fZGsE5aq8N0sOlGrOS87M8zJDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"926b26fe7e1a8e1c13cd848dea71c68bfda120ac97f9ca7f7c84334e7bb7a616","last_reissued_at":"2026-05-18T00:11:55.736086Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:11:55.736086Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1807.00197","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":"2026-05-18T00:11:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"R9MusDjn11VLIXqC83C9IaBKhWsfg/Nn7tnwqn68zI88jJV72c9VC3OMjm/gchOorD5lj0GOvdpyZeqpJVsrAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T11:13:50.578730Z"},"content_sha256":"07d7a26f43d4a7003dc914e0d782ec900a314ad97b6e192d935b9204d4927f4f","schema_version":"1.0","event_id":"sha256:07d7a26f43d4a7003dc914e0d782ec900a314ad97b6e192d935b9204d4927f4f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:SJVSN7T6DKHBYE6NQSG6U4OGRP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the supnorm form of Leray's problem for the incompressible 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, Lineia Schutz, Paulo R. Zingano","submitted_at":"2018-06-30T16:30:38Z","abstract_excerpt":"We show that t^{3/4}|| u(.,t) ||_{sup} --> 0 as t --> infty for all (global) Leray solutions of the incompressible Navier-Stokes equations in R3. It is also shown that t || u(.,t) - v(.,t) ||_{sup} --> 0 as t --> infty, where v(.,t) is the Stokes approximation, as well as other fundamental results. In spite of the difficulty of these questions, our approach is elementary and is based on standard tools like conventional Fourier and energy methods."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.00197","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":"2026-05-18T00:11:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SVJ3aI+65VVlGDlNqR3OnET+eTOsYmpg84575F3AowFzhYbw4x4SM+lnbXXStsbxMvp9oBD89ZiU790blSQ5AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T11:13:50.579075Z"},"content_sha256":"d68c3b39379d28f686511dddf5d7b1cff2e6d5e63653fb53ad2eb91fd1e7e779","schema_version":"1.0","event_id":"sha256:d68c3b39379d28f686511dddf5d7b1cff2e6d5e63653fb53ad2eb91fd1e7e779"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SJVSN7T6DKHBYE6NQSG6U4OGRP/bundle.json","state_url":"https://pith.science/pith/SJVSN7T6DKHBYE6NQSG6U4OGRP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SJVSN7T6DKHBYE6NQSG6U4OGRP/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":"2026-06-05T11:13:50Z","links":{"resolver":"https://pith.science/pith/SJVSN7T6DKHBYE6NQSG6U4OGRP","bundle":"https://pith.science/pith/SJVSN7T6DKHBYE6NQSG6U4OGRP/bundle.json","state":"https://pith.science/pith/SJVSN7T6DKHBYE6NQSG6U4OGRP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SJVSN7T6DKHBYE6NQSG6U4OGRP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:SJVSN7T6DKHBYE6NQSG6U4OGRP","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":"a4bc590fc8b10b212f6a898abca472801471c9ec5bcc7f9debdd8121bb8bfffe","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-06-30T16:30:38Z","title_canon_sha256":"b8d647e0206fd28730b27d7e98bd549e6feddb25385a12deb35ca5d00eeda268"},"schema_version":"1.0","source":{"id":"1807.00197","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.00197","created_at":"2026-05-18T00:11:55Z"},{"alias_kind":"arxiv_version","alias_value":"1807.00197v1","created_at":"2026-05-18T00:11:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.00197","created_at":"2026-05-18T00:11:55Z"},{"alias_kind":"pith_short_12","alias_value":"SJVSN7T6DKHB","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_16","alias_value":"SJVSN7T6DKHBYE6N","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_8","alias_value":"SJVSN7T6","created_at":"2026-05-18T12:32:53Z"}],"graph_snapshots":[{"event_id":"sha256:d68c3b39379d28f686511dddf5d7b1cff2e6d5e63653fb53ad2eb91fd1e7e779","target":"graph","created_at":"2026-05-18T00:11:55Z","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 show that t^{3/4}|| u(.,t) ||_{sup} --> 0 as t --> infty for all (global) Leray solutions of the incompressible Navier-Stokes equations in R3. It is also shown that t || u(.,t) - v(.,t) ||_{sup} --> 0 as t --> infty, where v(.,t) is the Stokes approximation, as well as other fundamental results. In spite of the difficulty of these questions, our approach is elementary and is based on standard tools like conventional Fourier and energy methods.","authors_text":"Jana\\'ina P. Zingano, Lineia Schutz, Paulo R. Zingano","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-06-30T16:30:38Z","title":"On the supnorm form of Leray's problem for the incompressible Navier-Stokes equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.00197","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":"sha256:07d7a26f43d4a7003dc914e0d782ec900a314ad97b6e192d935b9204d4927f4f","target":"record","created_at":"2026-05-18T00:11:55Z","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":"a4bc590fc8b10b212f6a898abca472801471c9ec5bcc7f9debdd8121bb8bfffe","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-06-30T16:30:38Z","title_canon_sha256":"b8d647e0206fd28730b27d7e98bd549e6feddb25385a12deb35ca5d00eeda268"},"schema_version":"1.0","source":{"id":"1807.00197","kind":"arxiv","version":1}},"canonical_sha256":"926b26fe7e1a8e1c13cd848dea71c68bfda120ac97f9ca7f7c84334e7bb7a616","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"926b26fe7e1a8e1c13cd848dea71c68bfda120ac97f9ca7f7c84334e7bb7a616","first_computed_at":"2026-05-18T00:11:55.736086Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:11:55.736086Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"A6H20/KXG4Uiq9uRLSpGLD81kVIBzy+vKkL5wFioX6TyujfRH1XESSUAyWE6fZGsE5aq8N0sOlGrOS87M8zJDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:11:55.736733Z","signed_message":"canonical_sha256_bytes"},"source_id":"1807.00197","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:07d7a26f43d4a7003dc914e0d782ec900a314ad97b6e192d935b9204d4927f4f","sha256:d68c3b39379d28f686511dddf5d7b1cff2e6d5e63653fb53ad2eb91fd1e7e779"],"state_sha256":"e6880e0243a32c78af990a35f76712a7be96470dee12c0ab63b7ac435602a15e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Nv9rCP5D0a+0v92AYe4zfA71NtURaBGNEz004RpgKtqluUdC/9DYHtASPN2RhBLtCj2EzcK1g1xZvSd42zyCBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T11:13:50.581006Z","bundle_sha256":"701c6a3364b89f63af6342e137c6e136e6ea2fbcf32605a021bf8a4f4b4c258e"}}