{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:IS23ZA7DCWBZGSQOUETAHAPUUJ","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":"212ec3c2ad09885d72a8b9ec3450064eddbbb7845aa4633a3800aa227013343b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-06-02T14:04:25Z","title_canon_sha256":"5bc8de46dbb8b873af659ff4ac1ff54840efea6dcfbf352949b6c7d71b19d917"},"schema_version":"1.0","source":{"id":"2606.03680","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.03680","created_at":"2026-06-03T01:06:04Z"},{"alias_kind":"arxiv_version","alias_value":"2606.03680v1","created_at":"2026-06-03T01:06:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.03680","created_at":"2026-06-03T01:06:04Z"},{"alias_kind":"pith_short_12","alias_value":"IS23ZA7DCWBZ","created_at":"2026-06-03T01:06:04Z"},{"alias_kind":"pith_short_16","alias_value":"IS23ZA7DCWBZGSQO","created_at":"2026-06-03T01:06:04Z"},{"alias_kind":"pith_short_8","alias_value":"IS23ZA7D","created_at":"2026-06-03T01:06:04Z"}],"graph_snapshots":[{"event_id":"sha256:deaefcf2cc23391f121e949051c91c73b93b693b8ced4547e9818376f020ac48","target":"graph","created_at":"2026-06-03T01:06:04Z","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/2606.03680/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper studies the global regularity problem for the two-dimensional incompressible Boussinesq equations with fractional dissipation given by $(-\\Delta)^{\\frac\\alpha2}u$ and $(-\\Delta)^{\\frac\\beta2} \\theta$. Attention is focused on the subcritical regime where $\\alpha+ \\beta>1$. The case $\\alpha >\\frac23$ was recently settled in a joint work of the authors [Math. Ann., \\textbf{391} (2025), 5965-6012], which established global regularity under this condition. This paper addresses the remaining case $\\alpha \\leq \\frac23$. We obtain the sharpest regularity result by minimizing assumptions on ","authors_text":"Atanas Stefanov, Jiahong Wu, Xiaojing Xu, Zhuan Ye","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-06-02T14:04:25Z","title":"Global regularity of the 2D fractional Boussinesq equations with subcritical dissipation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.03680","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":"sha256:44c753e4305d37e4615547f2d6661031612ace85ebd03bd41a8d1662971a985a","target":"record","created_at":"2026-06-03T01:06:04Z","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":"212ec3c2ad09885d72a8b9ec3450064eddbbb7845aa4633a3800aa227013343b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-06-02T14:04:25Z","title_canon_sha256":"5bc8de46dbb8b873af659ff4ac1ff54840efea6dcfbf352949b6c7d71b19d917"},"schema_version":"1.0","source":{"id":"2606.03680","kind":"arxiv","version":1}},"canonical_sha256":"44b5bc83e31583934a0ea1260381f4a26932acb25fff13600f5ada5a755a07d4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"44b5bc83e31583934a0ea1260381f4a26932acb25fff13600f5ada5a755a07d4","first_computed_at":"2026-06-03T01:06:04.386939Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-03T01:06:04.386939Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"laIP3yyJm514MLrFlv2O5pABcG55BJtqu7B/XonfTSxlkAc8GUq1IxOoMQZKPLG/otDPC/sdjA0HwPI8W1uTBg==","signature_status":"signed_v1","signed_at":"2026-06-03T01:06:04.387389Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.03680","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:44c753e4305d37e4615547f2d6661031612ace85ebd03bd41a8d1662971a985a","sha256:deaefcf2cc23391f121e949051c91c73b93b693b8ced4547e9818376f020ac48"],"state_sha256":"6dd85b4f012d8c9dc546582b3db4074811d70fa6ae24b87715c5efed2b6579c7"}