{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:KT6DSMTBZMNWOKWGRTEH2YQ4XI","short_pith_number":"pith:KT6DSMTB","canonical_record":{"source":{"id":"1212.1582","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-12-07T10:58:09Z","cross_cats_sorted":[],"title_canon_sha256":"a8c2ef2b70a0b9aa405a4984c737548936b9fa15ded1b516ae132040e8c80941","abstract_canon_sha256":"b4968838b81ca5001fbc8b0ef7b0c65c3d4fc41cec544621ea01795d1d1f3744"},"schema_version":"1.0"},"canonical_sha256":"54fc393261cb1b672ac68cc87d621cba0a75c6bd1eba0f06b656ab07362a4178","source":{"kind":"arxiv","id":"1212.1582","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.1582","created_at":"2026-05-18T03:38:56Z"},{"alias_kind":"arxiv_version","alias_value":"1212.1582v1","created_at":"2026-05-18T03:38:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.1582","created_at":"2026-05-18T03:38:56Z"},{"alias_kind":"pith_short_12","alias_value":"KT6DSMTBZMNW","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_16","alias_value":"KT6DSMTBZMNWOKWG","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_8","alias_value":"KT6DSMTB","created_at":"2026-05-18T12:27:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:KT6DSMTBZMNWOKWGRTEH2YQ4XI","target":"record","payload":{"canonical_record":{"source":{"id":"1212.1582","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-12-07T10:58:09Z","cross_cats_sorted":[],"title_canon_sha256":"a8c2ef2b70a0b9aa405a4984c737548936b9fa15ded1b516ae132040e8c80941","abstract_canon_sha256":"b4968838b81ca5001fbc8b0ef7b0c65c3d4fc41cec544621ea01795d1d1f3744"},"schema_version":"1.0"},"canonical_sha256":"54fc393261cb1b672ac68cc87d621cba0a75c6bd1eba0f06b656ab07362a4178","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:38:56.864866Z","signature_b64":"bdOwJYEJeE6V04k1ZcFNIuD4XWwaaxtsDE9GQ4qSl30nSEmXThfPZ3B1dHMYk3sr0CY9G4FIstMlB39qtXPEDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"54fc393261cb1b672ac68cc87d621cba0a75c6bd1eba0f06b656ab07362a4178","last_reissued_at":"2026-05-18T03:38:56.864343Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:38:56.864343Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1212.1582","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":"2026-05-18T03:38:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fk89d9aQJBWnW3SQ0TDIzWFRwjB0KpcDshMrgyV5dyKalT8v7NHzMVZo+gI7Frib2RbVYrDC6gCUsGbgusTuBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T14:00:37.559404Z"},"content_sha256":"c39ef31f960d4596b9baf4a46715807f93b7225418c6140f199f7b6fb090d7c2","schema_version":"1.0","event_id":"sha256:c39ef31f960d4596b9baf4a46715807f93b7225418c6140f199f7b6fb090d7c2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:KT6DSMTBZMNWOKWGRTEH2YQ4XI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Long-Time Asymptotics for the Navier-Stokes Equation in a Two-Dimensional Exterior Domain","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Thierry Gallay","submitted_at":"2012-12-07T10:58:09Z","abstract_excerpt":"We study the long-time behavior of infinite-energy solutions to the incompressible Navier-Stokes equations in a two-dimensional exterior domain, with no-slip boundary conditions. The initial data we consider are finite-energy perturbations of a smooth vortex with small circulation at infinity, but are otherwise arbitrarily large. Using a logarithmic energy estimate and some interpolation arguments, we prove that the solution approaches a self-similar Oseen vortex as $t \\to \\infty$. This result was obtained in collaboration with Yasunori Maekawa (Kobe University)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.1582","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":"2026-05-18T03:38:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aNleVR4pmpN+qeK26bfXetkLnNEv1vhMmqXuTY1f24aCt8RgB2zpKPkjHvpqlKpy8gLuuqvGriHxoxqMKGV5Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T14:00:37.560086Z"},"content_sha256":"0cf9afb272a1379c446a0e49942a34c6348d347528d7376007da803dadc7373c","schema_version":"1.0","event_id":"sha256:0cf9afb272a1379c446a0e49942a34c6348d347528d7376007da803dadc7373c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KT6DSMTBZMNWOKWGRTEH2YQ4XI/bundle.json","state_url":"https://pith.science/pith/KT6DSMTBZMNWOKWGRTEH2YQ4XI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KT6DSMTBZMNWOKWGRTEH2YQ4XI/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":"2026-05-30T14:00:37Z","links":{"resolver":"https://pith.science/pith/KT6DSMTBZMNWOKWGRTEH2YQ4XI","bundle":"https://pith.science/pith/KT6DSMTBZMNWOKWGRTEH2YQ4XI/bundle.json","state":"https://pith.science/pith/KT6DSMTBZMNWOKWGRTEH2YQ4XI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KT6DSMTBZMNWOKWGRTEH2YQ4XI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:KT6DSMTBZMNWOKWGRTEH2YQ4XI","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":"b4968838b81ca5001fbc8b0ef7b0c65c3d4fc41cec544621ea01795d1d1f3744","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-12-07T10:58:09Z","title_canon_sha256":"a8c2ef2b70a0b9aa405a4984c737548936b9fa15ded1b516ae132040e8c80941"},"schema_version":"1.0","source":{"id":"1212.1582","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.1582","created_at":"2026-05-18T03:38:56Z"},{"alias_kind":"arxiv_version","alias_value":"1212.1582v1","created_at":"2026-05-18T03:38:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.1582","created_at":"2026-05-18T03:38:56Z"},{"alias_kind":"pith_short_12","alias_value":"KT6DSMTBZMNW","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_16","alias_value":"KT6DSMTBZMNWOKWG","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_8","alias_value":"KT6DSMTB","created_at":"2026-05-18T12:27:11Z"}],"graph_snapshots":[{"event_id":"sha256:0cf9afb272a1379c446a0e49942a34c6348d347528d7376007da803dadc7373c","target":"graph","created_at":"2026-05-18T03:38:56Z","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 study the long-time behavior of infinite-energy solutions to the incompressible Navier-Stokes equations in a two-dimensional exterior domain, with no-slip boundary conditions. The initial data we consider are finite-energy perturbations of a smooth vortex with small circulation at infinity, but are otherwise arbitrarily large. Using a logarithmic energy estimate and some interpolation arguments, we prove that the solution approaches a self-similar Oseen vortex as $t \\to \\infty$. This result was obtained in collaboration with Yasunori Maekawa (Kobe University).","authors_text":"Thierry Gallay","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-12-07T10:58:09Z","title":"Long-Time Asymptotics for the Navier-Stokes Equation in a Two-Dimensional Exterior Domain"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.1582","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:c39ef31f960d4596b9baf4a46715807f93b7225418c6140f199f7b6fb090d7c2","target":"record","created_at":"2026-05-18T03:38:56Z","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":"b4968838b81ca5001fbc8b0ef7b0c65c3d4fc41cec544621ea01795d1d1f3744","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-12-07T10:58:09Z","title_canon_sha256":"a8c2ef2b70a0b9aa405a4984c737548936b9fa15ded1b516ae132040e8c80941"},"schema_version":"1.0","source":{"id":"1212.1582","kind":"arxiv","version":1}},"canonical_sha256":"54fc393261cb1b672ac68cc87d621cba0a75c6bd1eba0f06b656ab07362a4178","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"54fc393261cb1b672ac68cc87d621cba0a75c6bd1eba0f06b656ab07362a4178","first_computed_at":"2026-05-18T03:38:56.864343Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:38:56.864343Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bdOwJYEJeE6V04k1ZcFNIuD4XWwaaxtsDE9GQ4qSl30nSEmXThfPZ3B1dHMYk3sr0CY9G4FIstMlB39qtXPEDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:38:56.864866Z","signed_message":"canonical_sha256_bytes"},"source_id":"1212.1582","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c39ef31f960d4596b9baf4a46715807f93b7225418c6140f199f7b6fb090d7c2","sha256:0cf9afb272a1379c446a0e49942a34c6348d347528d7376007da803dadc7373c"],"state_sha256":"b6b902c0f6c13e816cd9d8c18ee438f10d6e799f3b63df29870c139d546f6604"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fT2Rme4IG6DH57PVU22W4SBNGla0TZLByS49XNYqtvWMQzpSpYh7fCBX4Qu3N6McRECglhKNQ+OGLogsKHxIDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T14:00:37.564036Z","bundle_sha256":"537e08e0e8de12c5eb2e17465a6d9933a55c7e6a5ee61514bfe53eca6b8bc5a9"}}