{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:GUDD3LESMP3Y22PMH5SRD5CPG6","short_pith_number":"pith:GUDD3LES","schema_version":"1.0","canonical_sha256":"35063dac9263f78d69ec3f6511f44f37bb701662a6a1cfc869d4275c2929c6d4","source":{"kind":"arxiv","id":"1109.5001","version":1},"attestation_state":"computed","paper":{"title":"Blow-up analysis for some mean field equations involving probability measures from statistical hydrodynamics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Gabriella Zecca, Tonia Ricciardi","submitted_at":"2011-09-23T05:37:53Z","abstract_excerpt":"Motivated by the mean field equations with probability measure derived by Sawada-Suzuki and by Neri in the context of the statistical mechanics description of two-dimensional turbulence, we study the semilinear elliptic equation with probability measure: {equation*} -\\Delta v=\\lambda\\int_I V(\\alpha,x,v)e^{\\alpha v}\\,\\Pda -\\frac{\\lambda}{|\\Omega|}\\iint_{I\\times\\Om}V(\\alpha,x,v)e^{\\alpha v}\\,\\Pda dx, {equation*} defined on a compact Riemannian surface. This equation includes the above mentioned equations of physical interest as special cases. For such an equation we study the blow-up properties "},"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":"1109.5001","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-09-23T05:37:53Z","cross_cats_sorted":[],"title_canon_sha256":"544a6979e94ae4fa809deeb95dc18abae9de89240d8e33738e11c7e0839ef892","abstract_canon_sha256":"0c586347cf45cc28f5a30dcc34923d82f0382654062118ee9c9e5f50b8f2bbfe"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:12:31.756034Z","signature_b64":"kfF4svNv9slU20Zroz0WD2tDU+xjJfglIPHSB45WF+hib8DwNyqw0UJD1QZr49wzF/8+wF6eJK0VTxwr2MLPCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"35063dac9263f78d69ec3f6511f44f37bb701662a6a1cfc869d4275c2929c6d4","last_reissued_at":"2026-05-18T04:12:31.755362Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:12:31.755362Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Blow-up analysis for some mean field equations involving probability measures from statistical hydrodynamics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Gabriella Zecca, Tonia Ricciardi","submitted_at":"2011-09-23T05:37:53Z","abstract_excerpt":"Motivated by the mean field equations with probability measure derived by Sawada-Suzuki and by Neri in the context of the statistical mechanics description of two-dimensional turbulence, we study the semilinear elliptic equation with probability measure: {equation*} -\\Delta v=\\lambda\\int_I V(\\alpha,x,v)e^{\\alpha v}\\,\\Pda -\\frac{\\lambda}{|\\Omega|}\\iint_{I\\times\\Om}V(\\alpha,x,v)e^{\\alpha v}\\,\\Pda dx, {equation*} defined on a compact Riemannian surface. This equation includes the above mentioned equations of physical interest as special cases. For such an equation we study the blow-up properties "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.5001","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":""},"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":"1109.5001","created_at":"2026-05-18T04:12:31.755464+00:00"},{"alias_kind":"arxiv_version","alias_value":"1109.5001v1","created_at":"2026-05-18T04:12:31.755464+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.5001","created_at":"2026-05-18T04:12:31.755464+00:00"},{"alias_kind":"pith_short_12","alias_value":"GUDD3LESMP3Y","created_at":"2026-05-18T12:26:30.835961+00:00"},{"alias_kind":"pith_short_16","alias_value":"GUDD3LESMP3Y22PM","created_at":"2026-05-18T12:26:30.835961+00:00"},{"alias_kind":"pith_short_8","alias_value":"GUDD3LES","created_at":"2026-05-18T12:26:30.835961+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/GUDD3LESMP3Y22PMH5SRD5CPG6","json":"https://pith.science/pith/GUDD3LESMP3Y22PMH5SRD5CPG6.json","graph_json":"https://pith.science/api/pith-number/GUDD3LESMP3Y22PMH5SRD5CPG6/graph.json","events_json":"https://pith.science/api/pith-number/GUDD3LESMP3Y22PMH5SRD5CPG6/events.json","paper":"https://pith.science/paper/GUDD3LES"},"agent_actions":{"view_html":"https://pith.science/pith/GUDD3LESMP3Y22PMH5SRD5CPG6","download_json":"https://pith.science/pith/GUDD3LESMP3Y22PMH5SRD5CPG6.json","view_paper":"https://pith.science/paper/GUDD3LES","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1109.5001&json=true","fetch_graph":"https://pith.science/api/pith-number/GUDD3LESMP3Y22PMH5SRD5CPG6/graph.json","fetch_events":"https://pith.science/api/pith-number/GUDD3LESMP3Y22PMH5SRD5CPG6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GUDD3LESMP3Y22PMH5SRD5CPG6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GUDD3LESMP3Y22PMH5SRD5CPG6/action/storage_attestation","attest_author":"https://pith.science/pith/GUDD3LESMP3Y22PMH5SRD5CPG6/action/author_attestation","sign_citation":"https://pith.science/pith/GUDD3LESMP3Y22PMH5SRD5CPG6/action/citation_signature","submit_replication":"https://pith.science/pith/GUDD3LESMP3Y22PMH5SRD5CPG6/action/replication_record"}},"created_at":"2026-05-18T04:12:31.755464+00:00","updated_at":"2026-05-18T04:12:31.755464+00:00"}