{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:ZN3EWSTR5ODK2VZNAOQ7GDNBRV","short_pith_number":"pith:ZN3EWSTR","schema_version":"1.0","canonical_sha256":"cb764b4a71eb86ad572d03a1f30da18d598737b6571718ac5d04b1b4e3e80fc2","source":{"kind":"arxiv","id":"1808.05717","version":1},"attestation_state":"computed","paper":{"title":"Analysis of a Singular Boussinesq Model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alexander Kiselev, Hang Yang","submitted_at":"2018-08-17T00:32:31Z","abstract_excerpt":"Recently, a new singularity formation scenario for the 3D axi-symmetric Euler equation and the 2D inviscid Boussinesq system has been proposed by Hu and Luo based on extensive numerical simulations [15, 16]. As the firrst step to understand the scenario, models with simplified sign-definite Biot-Savart law and forcing have recently been studied in [7, 6, 8, 12, 14, 18]. In this paper, we aim to bring back one of the complications encountered in the original equation - the sign changing kernel in the Biot-Savart law. This makes analysis harder, as there are two competing terms in the fluid velo"},"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":"1808.05717","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-08-17T00:32:31Z","cross_cats_sorted":[],"title_canon_sha256":"2e4e5d9a6371d5897ae4c8078ebb72e1c9db4813b8549f2708975582c501399d","abstract_canon_sha256":"83cdffa6897626df85264e849bf05bb0753f105d2777232354cae3a990e4e3e2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:07:52.388738Z","signature_b64":"GNrV8YMhXkTeQBxxEskZ1svtSHx/DNOqINWrny18+dZyar9hXpLoFVmr4bkunC1oAgBuoxPGDDYMNh9U/aaHCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cb764b4a71eb86ad572d03a1f30da18d598737b6571718ac5d04b1b4e3e80fc2","last_reissued_at":"2026-05-18T00:07:52.388098Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:07:52.388098Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Analysis of a Singular Boussinesq Model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alexander Kiselev, Hang Yang","submitted_at":"2018-08-17T00:32:31Z","abstract_excerpt":"Recently, a new singularity formation scenario for the 3D axi-symmetric Euler equation and the 2D inviscid Boussinesq system has been proposed by Hu and Luo based on extensive numerical simulations [15, 16]. As the firrst step to understand the scenario, models with simplified sign-definite Biot-Savart law and forcing have recently been studied in [7, 6, 8, 12, 14, 18]. In this paper, we aim to bring back one of the complications encountered in the original equation - the sign changing kernel in the Biot-Savart law. This makes analysis harder, as there are two competing terms in the fluid velo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.05717","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1808.05717","created_at":"2026-05-18T00:07:52.388177+00:00"},{"alias_kind":"arxiv_version","alias_value":"1808.05717v1","created_at":"2026-05-18T00:07:52.388177+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.05717","created_at":"2026-05-18T00:07:52.388177+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZN3EWSTR5ODK","created_at":"2026-05-18T12:33:07.085635+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZN3EWSTR5ODK2VZN","created_at":"2026-05-18T12:33:07.085635+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZN3EWSTR","created_at":"2026-05-18T12:33:07.085635+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/ZN3EWSTR5ODK2VZNAOQ7GDNBRV","json":"https://pith.science/pith/ZN3EWSTR5ODK2VZNAOQ7GDNBRV.json","graph_json":"https://pith.science/api/pith-number/ZN3EWSTR5ODK2VZNAOQ7GDNBRV/graph.json","events_json":"https://pith.science/api/pith-number/ZN3EWSTR5ODK2VZNAOQ7GDNBRV/events.json","paper":"https://pith.science/paper/ZN3EWSTR"},"agent_actions":{"view_html":"https://pith.science/pith/ZN3EWSTR5ODK2VZNAOQ7GDNBRV","download_json":"https://pith.science/pith/ZN3EWSTR5ODK2VZNAOQ7GDNBRV.json","view_paper":"https://pith.science/paper/ZN3EWSTR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1808.05717&json=true","fetch_graph":"https://pith.science/api/pith-number/ZN3EWSTR5ODK2VZNAOQ7GDNBRV/graph.json","fetch_events":"https://pith.science/api/pith-number/ZN3EWSTR5ODK2VZNAOQ7GDNBRV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZN3EWSTR5ODK2VZNAOQ7GDNBRV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZN3EWSTR5ODK2VZNAOQ7GDNBRV/action/storage_attestation","attest_author":"https://pith.science/pith/ZN3EWSTR5ODK2VZNAOQ7GDNBRV/action/author_attestation","sign_citation":"https://pith.science/pith/ZN3EWSTR5ODK2VZNAOQ7GDNBRV/action/citation_signature","submit_replication":"https://pith.science/pith/ZN3EWSTR5ODK2VZNAOQ7GDNBRV/action/replication_record"}},"created_at":"2026-05-18T00:07:52.388177+00:00","updated_at":"2026-05-18T00:07:52.388177+00:00"}