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For typical values of the horizontal period $L$ we prove that the law of the action-vector of a solution for $(*)$ (formed by the halves of the squared norms of its complex Fourier coefficients) converges, as $\\beta\\to\\infty$"},"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":"1409.0652","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-09-02T10:10:28Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"130bd48f5fedd65f888f01f1fbcf4ea3e6d057bc53214073e08893c25860cf33","abstract_canon_sha256":"e1cee5dbf3d9609209508bf02ed8aaf5e74d7cad626b013ae22b79c7fb82826c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:41:52.887049Z","signature_b64":"rxLcewvYOTnlADDKhJt7hBBnAGlE8AkrV6DWZRKgJ4RPHDBusdiI5D9K0F5xIXJpYyamdkrwnFpdv1LlUj3ZDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d030b76c549c13cebcbcbd3db6f74221da9041abfaa3d27e22b2ad61dfe24861","last_reissued_at":"2026-05-18T02:41:52.886585Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:41:52.886585Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The limit of small Rossby numbers for randomly forced quasi-geostrophic equation on $\\beta$-plane","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Alberto Maiocchi, Sergei Kuksin","submitted_at":"2014-09-02T10:10:28Z","abstract_excerpt":"We consider the 2d quasigeostrophic equation on the $\\beta$-plane for the stream function $\\psi$, with dissipation and a random force: $$ (*)\\qquad (-\\Delta +K)\\psi_t - \\rho J(\\psi, \\Delta\\psi) -\\beta\\psi_x= \\langle \\text{random force}\\rangle -\\kappa\\Delta^2\\psi +\\Delta\\psi, $$ where $\\psi=\\psi(t,x,y), \\ x\\in\\mathbb{R}/2\\pi L\\mathbb{Z}, \\ y\\in \\mathbb{R}/2\\pi \\mathbb{Z}$. For typical values of the horizontal period $L$ we prove that the law of the action-vector of a solution for $(*)$ (formed by the halves of the squared norms of its complex Fourier coefficients) converges, as $\\beta\\to\\infty$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.0652","kind":"arxiv","version":2},"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":"1409.0652","created_at":"2026-05-18T02:41:52.886649+00:00"},{"alias_kind":"arxiv_version","alias_value":"1409.0652v2","created_at":"2026-05-18T02:41:52.886649+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.0652","created_at":"2026-05-18T02:41:52.886649+00:00"},{"alias_kind":"pith_short_12","alias_value":"2AYLO3CUTQJ4","created_at":"2026-05-18T12:28:09.283467+00:00"},{"alias_kind":"pith_short_16","alias_value":"2AYLO3CUTQJ45PF4","created_at":"2026-05-18T12:28:09.283467+00:00"},{"alias_kind":"pith_short_8","alias_value":"2AYLO3CU","created_at":"2026-05-18T12:28:09.283467+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/2AYLO3CUTQJ45PF4XU63N52CEH","json":"https://pith.science/pith/2AYLO3CUTQJ45PF4XU63N52CEH.json","graph_json":"https://pith.science/api/pith-number/2AYLO3CUTQJ45PF4XU63N52CEH/graph.json","events_json":"https://pith.science/api/pith-number/2AYLO3CUTQJ45PF4XU63N52CEH/events.json","paper":"https://pith.science/paper/2AYLO3CU"},"agent_actions":{"view_html":"https://pith.science/pith/2AYLO3CUTQJ45PF4XU63N52CEH","download_json":"https://pith.science/pith/2AYLO3CUTQJ45PF4XU63N52CEH.json","view_paper":"https://pith.science/paper/2AYLO3CU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1409.0652&json=true","fetch_graph":"https://pith.science/api/pith-number/2AYLO3CUTQJ45PF4XU63N52CEH/graph.json","fetch_events":"https://pith.science/api/pith-number/2AYLO3CUTQJ45PF4XU63N52CEH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2AYLO3CUTQJ45PF4XU63N52CEH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2AYLO3CUTQJ45PF4XU63N52CEH/action/storage_attestation","attest_author":"https://pith.science/pith/2AYLO3CUTQJ45PF4XU63N52CEH/action/author_attestation","sign_citation":"https://pith.science/pith/2AYLO3CUTQJ45PF4XU63N52CEH/action/citation_signature","submit_replication":"https://pith.science/pith/2AYLO3CUTQJ45PF4XU63N52CEH/action/replication_record"}},"created_at":"2026-05-18T02:41:52.886649+00:00","updated_at":"2026-05-18T02:41:52.886649+00:00"}