{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:C72CS3VQJBSRMBMLIQL5HQ3WHC","short_pith_number":"pith:C72CS3VQ","schema_version":"1.0","canonical_sha256":"17f4296eb0486516058b4417d3c37638a19f04470a1c6ca08450e5389a84640a","source":{"kind":"arxiv","id":"2407.02582","version":1},"attestation_state":"computed","paper":{"title":"An Onsager-type theorem for SQG","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Mimi Dai, Razvan-Octavian Radu, Vikram Giri","submitted_at":"2024-07-02T18:05:01Z","abstract_excerpt":"We construct non-trivial weak solutions $\\theta\\in C_t^0C_x^{0-}$ to the surface quasi-geostrophic (SQG) equations, which have compact support in time and, thus, violate the conservation of the Hamiltonian. The result is sharp in view of the fact that such a conservation law holds for all weak solutions in the class $C_{t,x}^0 \\subset L_{t,x}^3$ (Isett-Vicol, 2015) and resolves the Onsager conjecture for SQG. The construction is achieved by means of a Nash iteration together with the linear decoupling method recently introduced in Giri-Radu (2023)."},"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":"2407.02582","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-07-02T18:05:01Z","cross_cats_sorted":[],"title_canon_sha256":"863953619055892b57acb1b09684a65128fd6c61ce9d8593653b5826fd3aa973","abstract_canon_sha256":"9d24398281b3f905855b6fa1d8bddea895416245525b668405f4f7b3b7131433"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:39:38.674126Z","signature_b64":"A3lqIoUDSq2i+BSAe7GbMeel9FdVZjBGS+Ighrq4HWbOklNAsfE5Fq1dFjGuHVxgN5XulJ4WzezphEGfE6fcBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"17f4296eb0486516058b4417d3c37638a19f04470a1c6ca08450e5389a84640a","last_reissued_at":"2026-07-05T08:39:38.673707Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:39:38.673707Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An Onsager-type theorem for SQG","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Mimi Dai, Razvan-Octavian Radu, Vikram Giri","submitted_at":"2024-07-02T18:05:01Z","abstract_excerpt":"We construct non-trivial weak solutions $\\theta\\in C_t^0C_x^{0-}$ to the surface quasi-geostrophic (SQG) equations, which have compact support in time and, thus, violate the conservation of the Hamiltonian. The result is sharp in view of the fact that such a conservation law holds for all weak solutions in the class $C_{t,x}^0 \\subset L_{t,x}^3$ (Isett-Vicol, 2015) and resolves the Onsager conjecture for SQG. The construction is achieved by means of a Nash iteration together with the linear decoupling method recently introduced in Giri-Radu (2023)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.02582","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2407.02582/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2407.02582","created_at":"2026-07-05T08:39:38.673763+00:00"},{"alias_kind":"arxiv_version","alias_value":"2407.02582v1","created_at":"2026-07-05T08:39:38.673763+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2407.02582","created_at":"2026-07-05T08:39:38.673763+00:00"},{"alias_kind":"pith_short_12","alias_value":"C72CS3VQJBSR","created_at":"2026-07-05T08:39:38.673763+00:00"},{"alias_kind":"pith_short_16","alias_value":"C72CS3VQJBSRMBML","created_at":"2026-07-05T08:39:38.673763+00:00"},{"alias_kind":"pith_short_8","alias_value":"C72CS3VQ","created_at":"2026-07-05T08:39:38.673763+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":3,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.26788","citing_title":"Mixed Third-Order Flux Laws for Dual Cascade in the Stochastic SQG Equation","ref_index":14,"is_internal_anchor":false},{"citing_arxiv_id":"2606.26788","citing_title":"Mixed Third-Order Flux Laws for Dual Cascade in the Stochastic SQG Equation","ref_index":14,"is_internal_anchor":false},{"citing_arxiv_id":"2604.19732","citing_title":"Hamiltonian compactness and dissipation for the generalized SQG equation in the inviscid limit","ref_index":23,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/C72CS3VQJBSRMBMLIQL5HQ3WHC","json":"https://pith.science/pith/C72CS3VQJBSRMBMLIQL5HQ3WHC.json","graph_json":"https://pith.science/api/pith-number/C72CS3VQJBSRMBMLIQL5HQ3WHC/graph.json","events_json":"https://pith.science/api/pith-number/C72CS3VQJBSRMBMLIQL5HQ3WHC/events.json","paper":"https://pith.science/paper/C72CS3VQ"},"agent_actions":{"view_html":"https://pith.science/pith/C72CS3VQJBSRMBMLIQL5HQ3WHC","download_json":"https://pith.science/pith/C72CS3VQJBSRMBMLIQL5HQ3WHC.json","view_paper":"https://pith.science/paper/C72CS3VQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2407.02582&json=true","fetch_graph":"https://pith.science/api/pith-number/C72CS3VQJBSRMBMLIQL5HQ3WHC/graph.json","fetch_events":"https://pith.science/api/pith-number/C72CS3VQJBSRMBMLIQL5HQ3WHC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/C72CS3VQJBSRMBMLIQL5HQ3WHC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/C72CS3VQJBSRMBMLIQL5HQ3WHC/action/storage_attestation","attest_author":"https://pith.science/pith/C72CS3VQJBSRMBMLIQL5HQ3WHC/action/author_attestation","sign_citation":"https://pith.science/pith/C72CS3VQJBSRMBMLIQL5HQ3WHC/action/citation_signature","submit_replication":"https://pith.science/pith/C72CS3VQJBSRMBMLIQL5HQ3WHC/action/replication_record"}},"created_at":"2026-07-05T08:39:38.673763+00:00","updated_at":"2026-07-05T08:39:38.673763+00:00"}