{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:M2UQBRQB2KWUWYN4CD4JM3GDW7","short_pith_number":"pith:M2UQBRQB","schema_version":"1.0","canonical_sha256":"66a900c601d2ad4b61bc10f8966cc3b7ca4dfca9a5de0231fc34ac6688fde153","source":{"kind":"arxiv","id":"2405.12181","version":3},"attestation_state":"computed","paper":{"title":"Regularization by rough Kraichnan noise for the generalised SQG equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.PR","authors_text":"Lucio Galeati, Marco Bagnara, Mario Maurelli","submitted_at":"2024-05-20T17:06:52Z","abstract_excerpt":"We consider the generalised Surface Quasi-Geostrophic (gSQG) equations in $\\mathbb R^2$ with parameter $\\beta\\in (0,1)$, an active scalar model interpolating between SQG ($\\beta=1$) and the 2D Euler equations ($\\beta=0$) in vorticity form. Existence of weak $(L^1\\cap L^p)$-valued solutions in the deterministic setting is known, but their uniqueness is open. We show that the addition of a rough Stratonovich transport noise of Kraichnan type regularizes the PDE, providing strong existence and pathwise uniqueness of solutions for initial data $\\theta_0\\in L^1\\cap L^p$, for suitable values $p\\in[2"},"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":"2405.12181","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2024-05-20T17:06:52Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"be86c2fb9324985bfe335bba05a17da067e354e4e1d20b8ac9e9b2c787a65448","abstract_canon_sha256":"0bc655d76b2b08dbcb4071305392697b45db2eb7b1c546bbd7d6b2403b13e480"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:40:01.110515Z","signature_b64":"AQdPXL10b0ito08a3Ov+2+lhZB5L13LNj7nuEddceqhqk2sc0Be+vbEbc2V4AVdeJHe+mtqgkMRQevsI/i6KDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"66a900c601d2ad4b61bc10f8966cc3b7ca4dfca9a5de0231fc34ac6688fde153","last_reissued_at":"2026-07-05T10:40:01.110043Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:40:01.110043Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Regularization by rough Kraichnan noise for the generalised SQG equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.PR","authors_text":"Lucio Galeati, Marco Bagnara, Mario Maurelli","submitted_at":"2024-05-20T17:06:52Z","abstract_excerpt":"We consider the generalised Surface Quasi-Geostrophic (gSQG) equations in $\\mathbb R^2$ with parameter $\\beta\\in (0,1)$, an active scalar model interpolating between SQG ($\\beta=1$) and the 2D Euler equations ($\\beta=0$) in vorticity form. Existence of weak $(L^1\\cap L^p)$-valued solutions in the deterministic setting is known, but their uniqueness is open. We show that the addition of a rough Stratonovich transport noise of Kraichnan type regularizes the PDE, providing strong existence and pathwise uniqueness of solutions for initial data $\\theta_0\\in L^1\\cap L^p$, for suitable values $p\\in[2"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.12181","kind":"arxiv","version":3},"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/2405.12181/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":"2405.12181","created_at":"2026-07-05T10:40:01.110097+00:00"},{"alias_kind":"arxiv_version","alias_value":"2405.12181v3","created_at":"2026-07-05T10:40:01.110097+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2405.12181","created_at":"2026-07-05T10:40:01.110097+00:00"},{"alias_kind":"pith_short_12","alias_value":"M2UQBRQB2KWU","created_at":"2026-07-05T10:40:01.110097+00:00"},{"alias_kind":"pith_short_16","alias_value":"M2UQBRQB2KWUWYN4","created_at":"2026-07-05T10:40:01.110097+00:00"},{"alias_kind":"pith_short_8","alias_value":"M2UQBRQB","created_at":"2026-07-05T10:40:01.110097+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2506.06947","citing_title":"Zero-noise selection and Large Deviations in $L^\\infty_t L^p_x$ for the stochastic transport equation beyond DiPerna-Lions","ref_index":2017,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/M2UQBRQB2KWUWYN4CD4JM3GDW7","json":"https://pith.science/pith/M2UQBRQB2KWUWYN4CD4JM3GDW7.json","graph_json":"https://pith.science/api/pith-number/M2UQBRQB2KWUWYN4CD4JM3GDW7/graph.json","events_json":"https://pith.science/api/pith-number/M2UQBRQB2KWUWYN4CD4JM3GDW7/events.json","paper":"https://pith.science/paper/M2UQBRQB"},"agent_actions":{"view_html":"https://pith.science/pith/M2UQBRQB2KWUWYN4CD4JM3GDW7","download_json":"https://pith.science/pith/M2UQBRQB2KWUWYN4CD4JM3GDW7.json","view_paper":"https://pith.science/paper/M2UQBRQB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2405.12181&json=true","fetch_graph":"https://pith.science/api/pith-number/M2UQBRQB2KWUWYN4CD4JM3GDW7/graph.json","fetch_events":"https://pith.science/api/pith-number/M2UQBRQB2KWUWYN4CD4JM3GDW7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/M2UQBRQB2KWUWYN4CD4JM3GDW7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/M2UQBRQB2KWUWYN4CD4JM3GDW7/action/storage_attestation","attest_author":"https://pith.science/pith/M2UQBRQB2KWUWYN4CD4JM3GDW7/action/author_attestation","sign_citation":"https://pith.science/pith/M2UQBRQB2KWUWYN4CD4JM3GDW7/action/citation_signature","submit_replication":"https://pith.science/pith/M2UQBRQB2KWUWYN4CD4JM3GDW7/action/replication_record"}},"created_at":"2026-07-05T10:40:01.110097+00:00","updated_at":"2026-07-05T10:40:01.110097+00:00"}