{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:IPPP77P4S3H2LYIYE2374A754Z","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":"7b6cedb00c4840ac05027d63fa889cd4acf70cd5f79aef7b8f5964794d2bbf6c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-05-14T01:05:11Z","title_canon_sha256":"d14177673ace747c82671a335f2064389be48aa088937cb05b0083aef619dfa6"},"schema_version":"1.0","source":{"id":"1305.2987","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.2987","created_at":"2026-05-18T03:03:32Z"},{"alias_kind":"arxiv_version","alias_value":"1305.2987v2","created_at":"2026-05-18T03:03:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.2987","created_at":"2026-05-18T03:03:32Z"},{"alias_kind":"pith_short_12","alias_value":"IPPP77P4S3H2","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_16","alias_value":"IPPP77P4S3H2LYIY","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_8","alias_value":"IPPP77P4","created_at":"2026-05-18T12:27:46Z"}],"graph_snapshots":[{"event_id":"sha256:19a401f88fcfc448f25c307fed6b85b350503f67459f3264d17dda3ef3d5f538","target":"graph","created_at":"2026-05-18T03:03:32Z","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 a family of dissipative active scalar equations outside the $L^{2}$-space. This was introduced in [D. Chae, P. Constantin, J. Wu, to appear in IUMJ (2014)] and its velocity fields are coupled with the active scalar via a class of multiplier operators which morally behave as derivatives of positive order. We prove global well-posedness and time decay of solutions, without smallness assumptions, for initial data belonging to the critical Lebesgue space $L^{\\frac{n}{\\gamma-\\beta}}(\\mathbb{R}^{n})$ which is a class larger than that of the above reference. Symmetry properties of solutio","authors_text":"Lidiane S. M. Lima, Lucas C. F. Ferreira","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-05-14T01:05:11Z","title":"Global well-posedness and symmetries for dissipative active scalar equations with positive-order couplings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.2987","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":"sha256:91a210f82aa69210620070f8bb634f70c8807f2a2128145aac807b2a57b874c5","target":"record","created_at":"2026-05-18T03:03:32Z","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":"7b6cedb00c4840ac05027d63fa889cd4acf70cd5f79aef7b8f5964794d2bbf6c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-05-14T01:05:11Z","title_canon_sha256":"d14177673ace747c82671a335f2064389be48aa088937cb05b0083aef619dfa6"},"schema_version":"1.0","source":{"id":"1305.2987","kind":"arxiv","version":2}},"canonical_sha256":"43defffdfc96cfa5e11826b7fe03fde6411fc886ef65d827644dd53870fe541d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"43defffdfc96cfa5e11826b7fe03fde6411fc886ef65d827644dd53870fe541d","first_computed_at":"2026-05-18T03:03:32.189228Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:03:32.189228Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zHjZZjAOzKnyXbUIywih8svTFIt85lcngSp9DjH2GdvZfniY+GNgjJatC88q4GHACeoz1UARN/Z+85nOMg/jDg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:03:32.189847Z","signed_message":"canonical_sha256_bytes"},"source_id":"1305.2987","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:91a210f82aa69210620070f8bb634f70c8807f2a2128145aac807b2a57b874c5","sha256:19a401f88fcfc448f25c307fed6b85b350503f67459f3264d17dda3ef3d5f538"],"state_sha256":"cc94acacbd80dc981f402e6f5059c0dc7c635d8241ad09fc5b521ee0caca4dd4"}