{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:RZOFB2FGDDCDFGSQKMICUUBZG3","short_pith_number":"pith:RZOFB2FG","canonical_record":{"source":{"id":"1605.03864","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-05-12T15:50:24Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"595c4c52ff5d7905753cc44c926bb6041775e746d43527b582a7d66a493a7649","abstract_canon_sha256":"db8a0bb5db7540a17ea3710071bdb644d2d71212d0ffeb2c22ab6c39384c0c48"},"schema_version":"1.0"},"canonical_sha256":"8e5c50e8a618c4329a5053102a503936f2de6c75d37dc562084a6f4f7bf279b9","source":{"kind":"arxiv","id":"1605.03864","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.03864","created_at":"2026-05-18T00:48:28Z"},{"alias_kind":"arxiv_version","alias_value":"1605.03864v1","created_at":"2026-05-18T00:48:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.03864","created_at":"2026-05-18T00:48:28Z"},{"alias_kind":"pith_short_12","alias_value":"RZOFB2FGDDCD","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_16","alias_value":"RZOFB2FGDDCDFGSQ","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_8","alias_value":"RZOFB2FG","created_at":"2026-05-18T12:30:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:RZOFB2FGDDCDFGSQKMICUUBZG3","target":"record","payload":{"canonical_record":{"source":{"id":"1605.03864","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-05-12T15:50:24Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"595c4c52ff5d7905753cc44c926bb6041775e746d43527b582a7d66a493a7649","abstract_canon_sha256":"db8a0bb5db7540a17ea3710071bdb644d2d71212d0ffeb2c22ab6c39384c0c48"},"schema_version":"1.0"},"canonical_sha256":"8e5c50e8a618c4329a5053102a503936f2de6c75d37dc562084a6f4f7bf279b9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:48:28.294467Z","signature_b64":"BmPX7yHaIikh6CvVS+8wJsHR5vWwGdnHuyVsyrY1fLwZV6dWru9Ul5N2MrUT2ieBRCAWhEu4x08TfirdWrKTBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8e5c50e8a618c4329a5053102a503936f2de6c75d37dc562084a6f4f7bf279b9","last_reissued_at":"2026-05-18T00:48:28.293911Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:48:28.293911Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1605.03864","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":"2026-05-18T00:48:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"J+x47rFjnkBWTqvnX9P9aW2FLNuMkdnk0oz88pcmrmmsmoCK1acrEG9iErCRgj5RmOpgZbzzET4mxsBy0nL2Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T00:36:56.763307Z"},"content_sha256":"3e54918423589f63cbf520d1eeea4870d697c3674f3864eaf319efedd7265458","schema_version":"1.0","event_id":"sha256:3e54918423589f63cbf520d1eeea4870d697c3674f3864eaf319efedd7265458"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:RZOFB2FGDDCDFGSQKMICUUBZG3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the asymptotic stability of steady flows with nonzero flux in two-dimensional exterior domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Julien Guillod","submitted_at":"2016-05-12T15:50:24Z","abstract_excerpt":"The Navier-Stokes equations in a two-dimensional exterior domain are considered. The asymptotic stability of stationary solutions satisfying a general hypothesis is proven under any $L^2$-perturbation. In particular the general hypothesis is valid if the steady solution is the sum of the critically decaying flux carrier with flux $|\\Phi| < 2\\pi$ and a small subcritically decaying term. Under the central symmetry assumption, the general hypothesis is also proven for any critically decaying steady solutions under a suitable smallness condition."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.03864","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":"2026-05-18T00:48:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"m4Mhvc/qRC0D7ZX4RK6c00H0kpaSLADu5Ek9jBSc7bKTqpHgPNPo8oQPyNjK1LabtuJGcp6/SXpVr3PN0X7mBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T00:36:56.764023Z"},"content_sha256":"cfdf5262e284d679c9a9ae0c718d9fc4b7054c0ee913ee0c1a6f8dd56ada13ed","schema_version":"1.0","event_id":"sha256:cfdf5262e284d679c9a9ae0c718d9fc4b7054c0ee913ee0c1a6f8dd56ada13ed"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RZOFB2FGDDCDFGSQKMICUUBZG3/bundle.json","state_url":"https://pith.science/pith/RZOFB2FGDDCDFGSQKMICUUBZG3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RZOFB2FGDDCDFGSQKMICUUBZG3/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":"2026-06-11T00:36:56Z","links":{"resolver":"https://pith.science/pith/RZOFB2FGDDCDFGSQKMICUUBZG3","bundle":"https://pith.science/pith/RZOFB2FGDDCDFGSQKMICUUBZG3/bundle.json","state":"https://pith.science/pith/RZOFB2FGDDCDFGSQKMICUUBZG3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RZOFB2FGDDCDFGSQKMICUUBZG3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:RZOFB2FGDDCDFGSQKMICUUBZG3","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":"db8a0bb5db7540a17ea3710071bdb644d2d71212d0ffeb2c22ab6c39384c0c48","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-05-12T15:50:24Z","title_canon_sha256":"595c4c52ff5d7905753cc44c926bb6041775e746d43527b582a7d66a493a7649"},"schema_version":"1.0","source":{"id":"1605.03864","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.03864","created_at":"2026-05-18T00:48:28Z"},{"alias_kind":"arxiv_version","alias_value":"1605.03864v1","created_at":"2026-05-18T00:48:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.03864","created_at":"2026-05-18T00:48:28Z"},{"alias_kind":"pith_short_12","alias_value":"RZOFB2FGDDCD","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_16","alias_value":"RZOFB2FGDDCDFGSQ","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_8","alias_value":"RZOFB2FG","created_at":"2026-05-18T12:30:41Z"}],"graph_snapshots":[{"event_id":"sha256:cfdf5262e284d679c9a9ae0c718d9fc4b7054c0ee913ee0c1a6f8dd56ada13ed","target":"graph","created_at":"2026-05-18T00:48:28Z","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":"The Navier-Stokes equations in a two-dimensional exterior domain are considered. The asymptotic stability of stationary solutions satisfying a general hypothesis is proven under any $L^2$-perturbation. In particular the general hypothesis is valid if the steady solution is the sum of the critically decaying flux carrier with flux $|\\Phi| < 2\\pi$ and a small subcritically decaying term. Under the central symmetry assumption, the general hypothesis is also proven for any critically decaying steady solutions under a suitable smallness condition.","authors_text":"Julien Guillod","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-05-12T15:50:24Z","title":"On the asymptotic stability of steady flows with nonzero flux in two-dimensional exterior domains"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.03864","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":"sha256:3e54918423589f63cbf520d1eeea4870d697c3674f3864eaf319efedd7265458","target":"record","created_at":"2026-05-18T00:48:28Z","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":"db8a0bb5db7540a17ea3710071bdb644d2d71212d0ffeb2c22ab6c39384c0c48","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-05-12T15:50:24Z","title_canon_sha256":"595c4c52ff5d7905753cc44c926bb6041775e746d43527b582a7d66a493a7649"},"schema_version":"1.0","source":{"id":"1605.03864","kind":"arxiv","version":1}},"canonical_sha256":"8e5c50e8a618c4329a5053102a503936f2de6c75d37dc562084a6f4f7bf279b9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8e5c50e8a618c4329a5053102a503936f2de6c75d37dc562084a6f4f7bf279b9","first_computed_at":"2026-05-18T00:48:28.293911Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:48:28.293911Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BmPX7yHaIikh6CvVS+8wJsHR5vWwGdnHuyVsyrY1fLwZV6dWru9Ul5N2MrUT2ieBRCAWhEu4x08TfirdWrKTBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:48:28.294467Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.03864","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3e54918423589f63cbf520d1eeea4870d697c3674f3864eaf319efedd7265458","sha256:cfdf5262e284d679c9a9ae0c718d9fc4b7054c0ee913ee0c1a6f8dd56ada13ed"],"state_sha256":"d037d25b1bc3682dd9bdb6e404c70fb8e8d00b499fe93ff6245e368ef04d1d27"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ebX6e4rQWq9EelcE4orJQqu4wZ1Pov7UX03n6F8SA5o2plEbOcKGL6N4mDOj2lz3n3f0FWhcLx5eCUcn7Rr3BQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T00:36:56.768864Z","bundle_sha256":"09447c5262a903bee4e0c5f6b16f7c7fafef9dc50042a1084bee1b61d9634aa0"}}