{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:P4WDPDQCY4QQ4Z7N5SOM4FT3JP","short_pith_number":"pith:P4WDPDQC","canonical_record":{"source":{"id":"1002.2489","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-02-12T07:35:34Z","cross_cats_sorted":[],"title_canon_sha256":"ad01ea56a4f8ce3997215fbfe391ddee6863de5bfec7e57017fae6c74c3c10f7","abstract_canon_sha256":"a61ccd9e3f5dc2023d1f3c889918b7d103a6aa3a6b5061ed68c245acf9a7c812"},"schema_version":"1.0"},"canonical_sha256":"7f2c378e02c7210e67edec9cce167b4be0f734c4a97aaad31a21def57122ecf5","source":{"kind":"arxiv","id":"1002.2489","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1002.2489","created_at":"2026-05-18T02:09:08Z"},{"alias_kind":"arxiv_version","alias_value":"1002.2489v1","created_at":"2026-05-18T02:09:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1002.2489","created_at":"2026-05-18T02:09:08Z"},{"alias_kind":"pith_short_12","alias_value":"P4WDPDQCY4QQ","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_16","alias_value":"P4WDPDQCY4QQ4Z7N","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_8","alias_value":"P4WDPDQC","created_at":"2026-05-18T12:26:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:P4WDPDQCY4QQ4Z7N5SOM4FT3JP","target":"record","payload":{"canonical_record":{"source":{"id":"1002.2489","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-02-12T07:35:34Z","cross_cats_sorted":[],"title_canon_sha256":"ad01ea56a4f8ce3997215fbfe391ddee6863de5bfec7e57017fae6c74c3c10f7","abstract_canon_sha256":"a61ccd9e3f5dc2023d1f3c889918b7d103a6aa3a6b5061ed68c245acf9a7c812"},"schema_version":"1.0"},"canonical_sha256":"7f2c378e02c7210e67edec9cce167b4be0f734c4a97aaad31a21def57122ecf5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:09:08.956842Z","signature_b64":"3nEegMZINxxFsuA7rHAr+iPQw01hUdZvXIpDtZjKsoybUfkmbEQ9dlHHMY3RXve2oLtGTJR9Sbjgb2uV1A69DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7f2c378e02c7210e67edec9cce167b4be0f734c4a97aaad31a21def57122ecf5","last_reissued_at":"2026-05-18T02:09:08.956272Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:09:08.956272Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1002.2489","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":"2026-05-18T02:09:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2Hvw2Om+4n9uZv4xgDskOTAIoCWivUPJrzUZzpWSqqMkTDWuuaPR4maRx0C0wFpC7bAIVoYw9PKrYYgxMVHuBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T12:09:34.524516Z"},"content_sha256":"56dc20ef851f1908e9c17d947654c81b4812eeac60a52792d2c1dfea5036dfaa","schema_version":"1.0","event_id":"sha256:56dc20ef851f1908e9c17d947654c81b4812eeac60a52792d2c1dfea5036dfaa"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:P4WDPDQCY4QQ4Z7N5SOM4FT3JP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Three-dimensional stability of Burgers vortices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Thierry Gallay, Yasunori Maekawa","submitted_at":"2010-02-12T07:35:34Z","abstract_excerpt":"Burgers vortices are explicit stationary solutions of the Navier-Stokes equations which are often used to describe the vortex tubes observed in numerical simulations of three-dimensional turbulence. In this model, the velocity field is a two-dimensional perturbation of a linear straining flow with axial symmetry. The only free parameter is the Reynolds number $Re = \\Gamma/\\nu$, where $\\Gamma$ is the total circulation of the vortex and $\\nu$ is the kinematic viscosity. The purpose of this paper is to show that Burgers vortex is asymptotically stable with respect to general three-dimensional per"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1002.2489","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":"2026-05-18T02:09:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"c/6mzqDTOzx6F+DXimbs9oJIjXf4hi2JK52D235cfr4HS4JFxAa6XDtEA0W5voUcdkuCnP1QrsqFwfpIk4Q6CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T12:09:34.524864Z"},"content_sha256":"3ef7792b10cad790fa51767f35e6d066a44130b72d9d086271b06c18b534a109","schema_version":"1.0","event_id":"sha256:3ef7792b10cad790fa51767f35e6d066a44130b72d9d086271b06c18b534a109"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/P4WDPDQCY4QQ4Z7N5SOM4FT3JP/bundle.json","state_url":"https://pith.science/pith/P4WDPDQCY4QQ4Z7N5SOM4FT3JP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/P4WDPDQCY4QQ4Z7N5SOM4FT3JP/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":"2026-05-28T12:09:34Z","links":{"resolver":"https://pith.science/pith/P4WDPDQCY4QQ4Z7N5SOM4FT3JP","bundle":"https://pith.science/pith/P4WDPDQCY4QQ4Z7N5SOM4FT3JP/bundle.json","state":"https://pith.science/pith/P4WDPDQCY4QQ4Z7N5SOM4FT3JP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/P4WDPDQCY4QQ4Z7N5SOM4FT3JP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:P4WDPDQCY4QQ4Z7N5SOM4FT3JP","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":"a61ccd9e3f5dc2023d1f3c889918b7d103a6aa3a6b5061ed68c245acf9a7c812","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-02-12T07:35:34Z","title_canon_sha256":"ad01ea56a4f8ce3997215fbfe391ddee6863de5bfec7e57017fae6c74c3c10f7"},"schema_version":"1.0","source":{"id":"1002.2489","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1002.2489","created_at":"2026-05-18T02:09:08Z"},{"alias_kind":"arxiv_version","alias_value":"1002.2489v1","created_at":"2026-05-18T02:09:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1002.2489","created_at":"2026-05-18T02:09:08Z"},{"alias_kind":"pith_short_12","alias_value":"P4WDPDQCY4QQ","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_16","alias_value":"P4WDPDQCY4QQ4Z7N","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_8","alias_value":"P4WDPDQC","created_at":"2026-05-18T12:26:12Z"}],"graph_snapshots":[{"event_id":"sha256:3ef7792b10cad790fa51767f35e6d066a44130b72d9d086271b06c18b534a109","target":"graph","created_at":"2026-05-18T02:09:08Z","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":"Burgers vortices are explicit stationary solutions of the Navier-Stokes equations which are often used to describe the vortex tubes observed in numerical simulations of three-dimensional turbulence. In this model, the velocity field is a two-dimensional perturbation of a linear straining flow with axial symmetry. The only free parameter is the Reynolds number $Re = \\Gamma/\\nu$, where $\\Gamma$ is the total circulation of the vortex and $\\nu$ is the kinematic viscosity. The purpose of this paper is to show that Burgers vortex is asymptotically stable with respect to general three-dimensional per","authors_text":"Thierry Gallay, Yasunori Maekawa","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-02-12T07:35:34Z","title":"Three-dimensional stability of Burgers vortices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1002.2489","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":"sha256:56dc20ef851f1908e9c17d947654c81b4812eeac60a52792d2c1dfea5036dfaa","target":"record","created_at":"2026-05-18T02:09:08Z","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":"a61ccd9e3f5dc2023d1f3c889918b7d103a6aa3a6b5061ed68c245acf9a7c812","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-02-12T07:35:34Z","title_canon_sha256":"ad01ea56a4f8ce3997215fbfe391ddee6863de5bfec7e57017fae6c74c3c10f7"},"schema_version":"1.0","source":{"id":"1002.2489","kind":"arxiv","version":1}},"canonical_sha256":"7f2c378e02c7210e67edec9cce167b4be0f734c4a97aaad31a21def57122ecf5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7f2c378e02c7210e67edec9cce167b4be0f734c4a97aaad31a21def57122ecf5","first_computed_at":"2026-05-18T02:09:08.956272Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:09:08.956272Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3nEegMZINxxFsuA7rHAr+iPQw01hUdZvXIpDtZjKsoybUfkmbEQ9dlHHMY3RXve2oLtGTJR9Sbjgb2uV1A69DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:09:08.956842Z","signed_message":"canonical_sha256_bytes"},"source_id":"1002.2489","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:56dc20ef851f1908e9c17d947654c81b4812eeac60a52792d2c1dfea5036dfaa","sha256:3ef7792b10cad790fa51767f35e6d066a44130b72d9d086271b06c18b534a109"],"state_sha256":"d8f806b0395b0bdcd2664e37eead99278c24da07f7fb7b98d23be07d286a7de6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"j0aFGmqNtlGKXUTjIwvifZfxEvvGh5MD7RqUZ7sQpkSrERuzUD+OjIyVuIlG95QkyecLpbNVN2iMJm1dp8nECA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T12:09:34.526833Z","bundle_sha256":"defcd82ff685ebb524a28b39ceb08e1a83fc5f635154e1d6aca1542fa3d8d29f"}}