{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:HX6ODR62DCJF77JI7BLANYKVVC","short_pith_number":"pith:HX6ODR62","canonical_record":{"source":{"id":"1706.10070","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-06-30T08:56:58Z","cross_cats_sorted":[],"title_canon_sha256":"d4052257bd8654178acf4a1ae0ee8e59b0494c3fd5f07a57ad9518f7931e29fa","abstract_canon_sha256":"2a7fd14f0de6cd6ad101dcff548b3d9f1b47c34acdb87717ef41d9b011fa1262"},"schema_version":"1.0"},"canonical_sha256":"3dfce1c7da18925ffd28f85606e155a8aa61e9c85e105377c43eec669a255e5d","source":{"kind":"arxiv","id":"1706.10070","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.10070","created_at":"2026-05-17T23:43:18Z"},{"alias_kind":"arxiv_version","alias_value":"1706.10070v2","created_at":"2026-05-17T23:43:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.10070","created_at":"2026-05-17T23:43:18Z"},{"alias_kind":"pith_short_12","alias_value":"HX6ODR62DCJF","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_16","alias_value":"HX6ODR62DCJF77JI","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_8","alias_value":"HX6ODR62","created_at":"2026-05-18T12:31:21Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:HX6ODR62DCJF77JI7BLANYKVVC","target":"record","payload":{"canonical_record":{"source":{"id":"1706.10070","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-06-30T08:56:58Z","cross_cats_sorted":[],"title_canon_sha256":"d4052257bd8654178acf4a1ae0ee8e59b0494c3fd5f07a57ad9518f7931e29fa","abstract_canon_sha256":"2a7fd14f0de6cd6ad101dcff548b3d9f1b47c34acdb87717ef41d9b011fa1262"},"schema_version":"1.0"},"canonical_sha256":"3dfce1c7da18925ffd28f85606e155a8aa61e9c85e105377c43eec669a255e5d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:43:18.587232Z","signature_b64":"KHuKMxLuIZ8Mdrm4sHppbDE3XYdT68jNsGO4B/IJKGPDy6/xhEiYh91h2L7En68Msqxa8nIh0L53kSO+5W4jBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3dfce1c7da18925ffd28f85606e155a8aa61e9c85e105377c43eec669a255e5d","last_reissued_at":"2026-05-17T23:43:18.586635Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:43:18.586635Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1706.10070","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:43:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+UpqhprE3jnXTAdeKKNXrjh13t7mCNrVXhbgprSdc+rGzEvU4aDnz0xO6GglUb0YbAX9WZ89xnGk+me/9bnCCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T07:11:27.573779Z"},"content_sha256":"2faf83d5e531a82f2374003c9d8b9c9a9b04d0feea9d4704c4fc7f11796de1e5","schema_version":"1.0","event_id":"sha256:2faf83d5e531a82f2374003c9d8b9c9a9b04d0feea9d4704c4fc7f11796de1e5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:HX6ODR62DCJF77JI7BLANYKVVC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Nonlinear Stability of Planar Vortex Patches in an ideal fluid","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Daomin Cao, Guodong Wang","submitted_at":"2017-06-30T08:56:58Z","abstract_excerpt":"In this paper, we prove nonlinear stability of planar vortex patches concentrated near an isolated minimum point of the Robin function in a general bounded domain. These vortex patches are stationary solutions of the two-dimensinal incompressible Euler equations. The result is obtained by showing that these concentrated vortex patches are in fact isolated maximizers of the kinetic energy among isovortical patches."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.10070","kind":"arxiv","version":2},"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":"2026-05-17T23:43:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YBBWg2J5uSbChlU0V6m8H7a9bPCc9Q+B2g9z6ihxepeBsqXZvB0zyMvdg3+lk5gPS3L1fCZKa3Jh/mOEBLYkAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T07:11:27.574121Z"},"content_sha256":"77ddbeb23053de6284f1805a909fa76d845a646abf86f5c64d71a13f572ff546","schema_version":"1.0","event_id":"sha256:77ddbeb23053de6284f1805a909fa76d845a646abf86f5c64d71a13f572ff546"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HX6ODR62DCJF77JI7BLANYKVVC/bundle.json","state_url":"https://pith.science/pith/HX6ODR62DCJF77JI7BLANYKVVC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HX6ODR62DCJF77JI7BLANYKVVC/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":"2026-06-12T07:11:27Z","links":{"resolver":"https://pith.science/pith/HX6ODR62DCJF77JI7BLANYKVVC","bundle":"https://pith.science/pith/HX6ODR62DCJF77JI7BLANYKVVC/bundle.json","state":"https://pith.science/pith/HX6ODR62DCJF77JI7BLANYKVVC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HX6ODR62DCJF77JI7BLANYKVVC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:HX6ODR62DCJF77JI7BLANYKVVC","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":"2a7fd14f0de6cd6ad101dcff548b3d9f1b47c34acdb87717ef41d9b011fa1262","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-06-30T08:56:58Z","title_canon_sha256":"d4052257bd8654178acf4a1ae0ee8e59b0494c3fd5f07a57ad9518f7931e29fa"},"schema_version":"1.0","source":{"id":"1706.10070","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.10070","created_at":"2026-05-17T23:43:18Z"},{"alias_kind":"arxiv_version","alias_value":"1706.10070v2","created_at":"2026-05-17T23:43:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.10070","created_at":"2026-05-17T23:43:18Z"},{"alias_kind":"pith_short_12","alias_value":"HX6ODR62DCJF","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_16","alias_value":"HX6ODR62DCJF77JI","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_8","alias_value":"HX6ODR62","created_at":"2026-05-18T12:31:21Z"}],"graph_snapshots":[{"event_id":"sha256:77ddbeb23053de6284f1805a909fa76d845a646abf86f5c64d71a13f572ff546","target":"graph","created_at":"2026-05-17T23:43:18Z","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 paper, we prove nonlinear stability of planar vortex patches concentrated near an isolated minimum point of the Robin function in a general bounded domain. These vortex patches are stationary solutions of the two-dimensinal incompressible Euler equations. The result is obtained by showing that these concentrated vortex patches are in fact isolated maximizers of the kinetic energy among isovortical patches.","authors_text":"Daomin Cao, Guodong Wang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-06-30T08:56:58Z","title":"Nonlinear Stability of Planar Vortex Patches in an ideal fluid"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.10070","kind":"arxiv","version":2},"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":"sha256:2faf83d5e531a82f2374003c9d8b9c9a9b04d0feea9d4704c4fc7f11796de1e5","target":"record","created_at":"2026-05-17T23:43:18Z","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":"2a7fd14f0de6cd6ad101dcff548b3d9f1b47c34acdb87717ef41d9b011fa1262","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-06-30T08:56:58Z","title_canon_sha256":"d4052257bd8654178acf4a1ae0ee8e59b0494c3fd5f07a57ad9518f7931e29fa"},"schema_version":"1.0","source":{"id":"1706.10070","kind":"arxiv","version":2}},"canonical_sha256":"3dfce1c7da18925ffd28f85606e155a8aa61e9c85e105377c43eec669a255e5d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3dfce1c7da18925ffd28f85606e155a8aa61e9c85e105377c43eec669a255e5d","first_computed_at":"2026-05-17T23:43:18.586635Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:43:18.586635Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KHuKMxLuIZ8Mdrm4sHppbDE3XYdT68jNsGO4B/IJKGPDy6/xhEiYh91h2L7En68Msqxa8nIh0L53kSO+5W4jBA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:43:18.587232Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.10070","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2faf83d5e531a82f2374003c9d8b9c9a9b04d0feea9d4704c4fc7f11796de1e5","sha256:77ddbeb23053de6284f1805a909fa76d845a646abf86f5c64d71a13f572ff546"],"state_sha256":"c969bcf0ccf4eae0bec3f05a7ee8c0c361f5f1dfe045dcaf0fb86a22f745e043"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0AwiCAVxYW1W+bIHoA6Bvrkfk5nOz0CcTelThSox7AnX0BeGbJJW9ZeSpcRKmXiqn4ZSaKym4uKcoO6b1dRMCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-12T07:11:27.576105Z","bundle_sha256":"7d890e53bfc26fb2f06e540a0c95a7f9f58c4eb3592837b1b621708ec6e2aaa2"}}