{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:KH2VB4OWG7CM3QSKWYLEU4F44C","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":"a893ea4156db536a920e8e55d9d817ff370f51ef9cb762b67dbbeafb25b3a5e6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2021-05-03T10:27:48Z","title_canon_sha256":"c8cd6e6785e5c8cfec03bb6f6a3b249e251defa28779a1dae2bd45be3a644281"},"schema_version":"1.0","source":{"id":"2105.00737","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2105.00737","created_at":"2026-07-05T02:36:57Z"},{"alias_kind":"arxiv_version","alias_value":"2105.00737v1","created_at":"2026-07-05T02:36:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2105.00737","created_at":"2026-07-05T02:36:57Z"},{"alias_kind":"pith_short_12","alias_value":"KH2VB4OWG7CM","created_at":"2026-07-05T02:36:57Z"},{"alias_kind":"pith_short_16","alias_value":"KH2VB4OWG7CM3QSK","created_at":"2026-07-05T02:36:57Z"},{"alias_kind":"pith_short_8","alias_value":"KH2VB4OW","created_at":"2026-07-05T02:36:57Z"}],"graph_snapshots":[{"event_id":"sha256:867cc89726ecbcc33866f99b0efb24967fe013f13beef7d37af407805d9a0869","target":"graph","created_at":"2026-07-05T02:36:57Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2105.00737/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In the present study, we find that the surface quasi-geostrophic equation admits exact solutions, which evolve with time in quasi-stationary states. The solutions presented are available for any dissipation effect $\\kappa (-\\Delta)^\\alpha$ ($\\kappa >0$, $0\\le \\alpha <1$), involved in the equation. When the equation is supercritical ($0\\le \\alpha <\\frac12$), the problem on the existence of large global regular solutions remains open. This study, however, provides explicit sample solutions for the understanding of the uncertain problem.","authors_text":"Zhi-Min Chen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2021-05-03T10:27:48Z","title":"Quasi-stationary solutions of the surface quasi-geostrophic equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2105.00737","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:d17aad2ad8f917378edde0e424bd0f2b5d408e08c48ded3fad15b9024b132089","target":"record","created_at":"2026-07-05T02:36:57Z","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":"a893ea4156db536a920e8e55d9d817ff370f51ef9cb762b67dbbeafb25b3a5e6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2021-05-03T10:27:48Z","title_canon_sha256":"c8cd6e6785e5c8cfec03bb6f6a3b249e251defa28779a1dae2bd45be3a644281"},"schema_version":"1.0","source":{"id":"2105.00737","kind":"arxiv","version":1}},"canonical_sha256":"51f550f1d637c4cdc24ab6164a70bce09ed16043e02f3ff9eb1418a714c656ae","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"51f550f1d637c4cdc24ab6164a70bce09ed16043e02f3ff9eb1418a714c656ae","first_computed_at":"2026-07-05T02:36:57.331845Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:36:57.331845Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"M5zarwwXcMOTxPwvNEFEydhTb9wOeofuJi/i/49YjjgbKSzflBsTxKQEtUTho+vq70SuNZ7jnoLv57ICBAYHCg==","signature_status":"signed_v1","signed_at":"2026-07-05T02:36:57.332198Z","signed_message":"canonical_sha256_bytes"},"source_id":"2105.00737","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d17aad2ad8f917378edde0e424bd0f2b5d408e08c48ded3fad15b9024b132089","sha256:867cc89726ecbcc33866f99b0efb24967fe013f13beef7d37af407805d9a0869"],"state_sha256":"a74803aa55f9abf01557166d41d67180780448d97efdaf8cdfdcc7e4df7c1a6e"}