{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:2AYLO3CUTQJ45PF4XU63N52CEH","short_pith_number":"pith:2AYLO3CU","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"},"canonical_sha256":"d030b76c549c13cebcbcbd3db6f74221da9041abfaa3d27e22b2ad61dfe24861","source":{"kind":"arxiv","id":"1409.0652","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.0652","created_at":"2026-05-18T02:41:52Z"},{"alias_kind":"arxiv_version","alias_value":"1409.0652v2","created_at":"2026-05-18T02:41:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.0652","created_at":"2026-05-18T02:41:52Z"},{"alias_kind":"pith_short_12","alias_value":"2AYLO3CUTQJ4","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"2AYLO3CUTQJ45PF4","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"2AYLO3CU","created_at":"2026-05-18T12:28:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:2AYLO3CUTQJ45PF4XU63N52CEH","target":"record","payload":{"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"},"canonical_sha256":"d030b76c549c13cebcbcbd3db6f74221da9041abfaa3d27e22b2ad61dfe24861","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"},"source_kind":"arxiv","source_id":"1409.0652","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:41:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+6YFotwfxZW4r7QFA832rN/xhb4bs2ClgdQSqtl5lhK7yoF4OCu8mY4DH7A2yW5cnB3S80DBcgu3wE0eGsY/Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T09:59:46.775678Z"},"content_sha256":"270d9470a6bc990b2bb2b35551bb9018dad07536a6d7e6bc125b4f71afa205a8","schema_version":"1.0","event_id":"sha256:270d9470a6bc990b2bb2b35551bb9018dad07536a6d7e6bc125b4f71afa205a8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:2AYLO3CUTQJ45PF4XU63N52CEH","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:41:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"89iTctPGKTyWDOn85cesKiWgTYGFE22AZbmlshhYixJoF49qBT4KmTKoUd4DvyaLZMaiCo3u4sMdz6CsK9RFBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T09:59:46.776033Z"},"content_sha256":"5114e6c5be4141172d62cdba82390fd5073efe025376749c825d3e653fd787f9","schema_version":"1.0","event_id":"sha256:5114e6c5be4141172d62cdba82390fd5073efe025376749c825d3e653fd787f9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2AYLO3CUTQJ45PF4XU63N52CEH/bundle.json","state_url":"https://pith.science/pith/2AYLO3CUTQJ45PF4XU63N52CEH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2AYLO3CUTQJ45PF4XU63N52CEH/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-08T09:59:46Z","links":{"resolver":"https://pith.science/pith/2AYLO3CUTQJ45PF4XU63N52CEH","bundle":"https://pith.science/pith/2AYLO3CUTQJ45PF4XU63N52CEH/bundle.json","state":"https://pith.science/pith/2AYLO3CUTQJ45PF4XU63N52CEH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2AYLO3CUTQJ45PF4XU63N52CEH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:2AYLO3CUTQJ45PF4XU63N52CEH","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":"e1cee5dbf3d9609209508bf02ed8aaf5e74d7cad626b013ae22b79c7fb82826c","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-09-02T10:10:28Z","title_canon_sha256":"130bd48f5fedd65f888f01f1fbcf4ea3e6d057bc53214073e08893c25860cf33"},"schema_version":"1.0","source":{"id":"1409.0652","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.0652","created_at":"2026-05-18T02:41:52Z"},{"alias_kind":"arxiv_version","alias_value":"1409.0652v2","created_at":"2026-05-18T02:41:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.0652","created_at":"2026-05-18T02:41:52Z"},{"alias_kind":"pith_short_12","alias_value":"2AYLO3CUTQJ4","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"2AYLO3CUTQJ45PF4","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"2AYLO3CU","created_at":"2026-05-18T12:28:09Z"}],"graph_snapshots":[{"event_id":"sha256:5114e6c5be4141172d62cdba82390fd5073efe025376749c825d3e653fd787f9","target":"graph","created_at":"2026-05-18T02:41:52Z","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 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 $\\beta\\to\\infty$","authors_text":"Alberto Maiocchi, Sergei Kuksin","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-09-02T10:10:28Z","title":"The limit of small Rossby numbers for randomly forced quasi-geostrophic equation on $\\beta$-plane"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.0652","kind":"arxiv","version":2},"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":"sha256:270d9470a6bc990b2bb2b35551bb9018dad07536a6d7e6bc125b4f71afa205a8","target":"record","created_at":"2026-05-18T02:41:52Z","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":"e1cee5dbf3d9609209508bf02ed8aaf5e74d7cad626b013ae22b79c7fb82826c","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-09-02T10:10:28Z","title_canon_sha256":"130bd48f5fedd65f888f01f1fbcf4ea3e6d057bc53214073e08893c25860cf33"},"schema_version":"1.0","source":{"id":"1409.0652","kind":"arxiv","version":2}},"canonical_sha256":"d030b76c549c13cebcbcbd3db6f74221da9041abfaa3d27e22b2ad61dfe24861","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d030b76c549c13cebcbcbd3db6f74221da9041abfaa3d27e22b2ad61dfe24861","first_computed_at":"2026-05-18T02:41:52.886585Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:41:52.886585Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rxLcewvYOTnlADDKhJt7hBBnAGlE8AkrV6DWZRKgJ4RPHDBusdiI5D9K0F5xIXJpYyamdkrwnFpdv1LlUj3ZDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:41:52.887049Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.0652","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:270d9470a6bc990b2bb2b35551bb9018dad07536a6d7e6bc125b4f71afa205a8","sha256:5114e6c5be4141172d62cdba82390fd5073efe025376749c825d3e653fd787f9"],"state_sha256":"1ff89b3daba475dc3713d0499e81627809272c039718b8071596d0d1b5ca53db"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CXSjy+4riSXzrzhqLw09f8XvIZyxWIljyxfbNu2D5qcbKeUTZHtT+Ol+gZDKNca1bdp4XC8HFcXXLwzu6JHfBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T09:59:46.778227Z","bundle_sha256":"f67397d72d3816455506f49f610e72639a87c7007f1c6810315eafa1505db4d6"}}