{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:TK7QR5KBGZELHZO6XFP3ODPQU5","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":"435a0842e18d391f046af9774ae7e38d920e7a4369d0c5fee7280e3d87f4b86f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-05-30T19:51:42Z","title_canon_sha256":"b38d223183fb5374f5b506ad79dfa520fc25468d13dfdf8fab27cd258c04105d"},"schema_version":"1.0","source":{"id":"1705.10842","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.10842","created_at":"2026-05-18T00:43:20Z"},{"alias_kind":"arxiv_version","alias_value":"1705.10842v1","created_at":"2026-05-18T00:43:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.10842","created_at":"2026-05-18T00:43:20Z"},{"alias_kind":"pith_short_12","alias_value":"TK7QR5KBGZEL","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_16","alias_value":"TK7QR5KBGZELHZO6","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_8","alias_value":"TK7QR5KB","created_at":"2026-05-18T12:31:46Z"}],"graph_snapshots":[{"event_id":"sha256:0ae08ecf76e4644d0b797018fbdbb3ffebfb0c3e394ee01c09f4704c85a7dbff","target":"graph","created_at":"2026-05-18T00:43:20Z","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 consider the inviscid generalized surface quasi-geostrophic equation (gSQG) in a patch setting, where the parameter $\\alpha \\in (1,2)$. The cases $\\alpha = 0$ and $\\alpha = 1$ correspond to 2d Euler and SQG respectively, and our choice of the parameter $\\alpha$ results in a velocity more singular than in the SQG case.\n  Our main result concerns the global stability of the half-plane patch stationary solution, under small and localized perturbations. Our theorem appears to be the first construction of stable global solutions for the gSQG-patch equations. The only other nontrivial global solu","authors_text":"Alexandru D. Ionescu, Diego C\\'ordoba, Javier G\\'omez-Serrano","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-05-30T19:51:42Z","title":"Global solutions for the generalized SQG patch equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.10842","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":"sha256:612c8b1aec5312a9f575601909f96f6996089a340b13d7b077102d39e4fb87e3","target":"record","created_at":"2026-05-18T00:43:20Z","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":"435a0842e18d391f046af9774ae7e38d920e7a4369d0c5fee7280e3d87f4b86f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-05-30T19:51:42Z","title_canon_sha256":"b38d223183fb5374f5b506ad79dfa520fc25468d13dfdf8fab27cd258c04105d"},"schema_version":"1.0","source":{"id":"1705.10842","kind":"arxiv","version":1}},"canonical_sha256":"9abf08f5413648b3e5deb95fb70df0a7456855f80c0b8b096ff6501702e7889d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9abf08f5413648b3e5deb95fb70df0a7456855f80c0b8b096ff6501702e7889d","first_computed_at":"2026-05-18T00:43:20.092126Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:43:20.092126Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gQu6ymUTqQQ8QOoNs3r/faq6VnYvIJEFvuSQWOZeY39x4K4zxYRJ25E38/OMJEhM0GOB1LTYdKVOeHXWISqzDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:43:20.092600Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.10842","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:612c8b1aec5312a9f575601909f96f6996089a340b13d7b077102d39e4fb87e3","sha256:0ae08ecf76e4644d0b797018fbdbb3ffebfb0c3e394ee01c09f4704c85a7dbff"],"state_sha256":"26ec293af178856256b1663d3147960da476a3af5d9aa9eced9869da5025d679"}