{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:E2YP6RTAJ5QDA6PLCKNWPOK7ZG","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":"53567f6d798e1cb80f4e6fc31cfca4b5af7de16f33b8d06111e9ce3e23e15dae","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-04-03T00:30:07Z","title_canon_sha256":"2f98d84959c6bc3d57b2c98cbc7f50b4561af9d1aa06f703511134f78829bb70"},"schema_version":"1.0","source":{"id":"1504.00716","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.00716","created_at":"2026-05-18T02:19:42Z"},{"alias_kind":"arxiv_version","alias_value":"1504.00716v1","created_at":"2026-05-18T02:19:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.00716","created_at":"2026-05-18T02:19:42Z"},{"alias_kind":"pith_short_12","alias_value":"E2YP6RTAJ5QD","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_16","alias_value":"E2YP6RTAJ5QDA6PL","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_8","alias_value":"E2YP6RTA","created_at":"2026-05-18T12:29:17Z"}],"graph_snapshots":[{"event_id":"sha256:21f50eeb6da081b1ae34e6056eb46f91526033723e23b2dfd0f8388c5c4d8f98","target":"graph","created_at":"2026-05-18T02:19:42Z","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 prove global well-posedness of strong solutions and existence of the global attractor for the 2D Boussinesq system in a periodic channel with fractional Laplacian in subcritical case. The analysis reveals a relation between the Laplacian exponent and the regularity of the spaces of velocity and temperature.","authors_text":"Aimin Huang, Wenru Huo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-04-03T00:30:07Z","title":"The global attractor of the 2D Boussinesq equations with fractional Laplacian in Subcritical case"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.00716","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":"sha256:6b2d76bc404562d567512268a7f72a957866a44e72a953f10cc801915006b5fc","target":"record","created_at":"2026-05-18T02:19:42Z","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":"53567f6d798e1cb80f4e6fc31cfca4b5af7de16f33b8d06111e9ce3e23e15dae","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-04-03T00:30:07Z","title_canon_sha256":"2f98d84959c6bc3d57b2c98cbc7f50b4561af9d1aa06f703511134f78829bb70"},"schema_version":"1.0","source":{"id":"1504.00716","kind":"arxiv","version":1}},"canonical_sha256":"26b0ff46604f603079eb129b67b95fc9b969fd6f6fe952df48a69c57cb18ef38","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"26b0ff46604f603079eb129b67b95fc9b969fd6f6fe952df48a69c57cb18ef38","first_computed_at":"2026-05-18T02:19:42.085406Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:19:42.085406Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zRMgEGDD17nk67UWuTwj3Qn+zajIUDb6Y9hHNbuhxGCemjxaifjK9kdhY9YFDUoVoo8a2jJpzG8/gc3vN+WDAg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:19:42.085921Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.00716","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6b2d76bc404562d567512268a7f72a957866a44e72a953f10cc801915006b5fc","sha256:21f50eeb6da081b1ae34e6056eb46f91526033723e23b2dfd0f8388c5c4d8f98"],"state_sha256":"de3c17f750ee30c4adbc2b6a2049aab5d29f1090e18731196f154f6cce85c713"}