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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1705.10842","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-05-30T19:51:42Z","cross_cats_sorted":[],"title_canon_sha256":"b38d223183fb5374f5b506ad79dfa520fc25468d13dfdf8fab27cd258c04105d","abstract_canon_sha256":"435a0842e18d391f046af9774ae7e38d920e7a4369d0c5fee7280e3d87f4b86f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:43:20.092600Z","signature_b64":"gQu6ymUTqQQ8QOoNs3r/faq6VnYvIJEFvuSQWOZeY39x4K4zxYRJ25E38/OMJEhM0GOB1LTYdKVOeHXWISqzDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9abf08f5413648b3e5deb95fb70df0a7456855f80c0b8b096ff6501702e7889d","last_reissued_at":"2026-05-18T00:43:20.092126Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:43:20.092126Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Global solutions for the generalized SQG patch equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alexandru D. 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