{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:7EC3MWFBL4UYQRVGZNNGRT4X3L","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":"346ebf3df67aeedb2c0d9b0229c44156a9f56972a3c89d75237b699b4ee01f1b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-12-09T04:22:55Z","title_canon_sha256":"754951021f890be028d108287bf6292a04d091170bef11434c333a455a5439a2"},"schema_version":"1.0","source":{"id":"1212.1854","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.1854","created_at":"2026-05-18T01:52:46Z"},{"alias_kind":"arxiv_version","alias_value":"1212.1854v1","created_at":"2026-05-18T01:52:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.1854","created_at":"2026-05-18T01:52:46Z"},{"alias_kind":"pith_short_12","alias_value":"7EC3MWFBL4UY","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"7EC3MWFBL4UYQRVG","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"7EC3MWFB","created_at":"2026-05-18T12:26:56Z"}],"graph_snapshots":[{"event_id":"sha256:7227b1e395c4cee08371feb6656704605bffc7510f898aae82b46e436f922c00","target":"graph","created_at":"2026-05-18T01:52:46Z","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 gradient flow associated to the mean field equation on $(M,g)$ a compact riemanniann surface without boundary. We prove that this flow exists for all time. Moreover, letting $G$ be a group of isometry acting on $(M,g)$, we obtain the convergence of the flow to a solution of the mean field equation under suitable hypothesis on the orbits of points of $M$ under the action of $G$.","authors_text":"Jean-Baptiste Cast\\'eras","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-12-09T04:22:55Z","title":"Equivariant mean field flow"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.1854","kind":"arxiv","version":1},"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":"sha256:449546efd38f2b14a845411ecb09bf891fd47191d502da2268fa6d68bf8e498f","target":"record","created_at":"2026-05-18T01:52:46Z","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":"346ebf3df67aeedb2c0d9b0229c44156a9f56972a3c89d75237b699b4ee01f1b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-12-09T04:22:55Z","title_canon_sha256":"754951021f890be028d108287bf6292a04d091170bef11434c333a455a5439a2"},"schema_version":"1.0","source":{"id":"1212.1854","kind":"arxiv","version":1}},"canonical_sha256":"f905b658a15f298846a6cb5a68cf97dad4b31157b3345d1f263c15be52937651","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f905b658a15f298846a6cb5a68cf97dad4b31157b3345d1f263c15be52937651","first_computed_at":"2026-05-18T01:52:46.185773Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:52:46.185773Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YGgEynXqRLI7vERqmphWU6TbQ5YkVsOPwKgZf5FtGcJDtUZ/uBN8f8scS+JjP1YaMFOnLScz/GVji+f3/aTMDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:52:46.186365Z","signed_message":"canonical_sha256_bytes"},"source_id":"1212.1854","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:449546efd38f2b14a845411ecb09bf891fd47191d502da2268fa6d68bf8e498f","sha256:7227b1e395c4cee08371feb6656704605bffc7510f898aae82b46e436f922c00"],"state_sha256":"d4dafb1b46e0bfe841005439c70c618372db995c4ddfba242fcff1a42db0e5d1"}