{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:CXJHVNJHKVKGFBY5YPAPPNQGFB","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":"b7084cd604433b75596d915352d2d714db63853897070447830e544cc5a45640","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-12-09T04:44:52Z","title_canon_sha256":"0aa1fca5c7a118f71ac135df66eabb66452a43b1f5d00aa5dd977ac173c5206c"},"schema_version":"1.0","source":{"id":"1212.1857","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.1857","created_at":"2026-05-18T03:38:54Z"},{"alias_kind":"arxiv_version","alias_value":"1212.1857v1","created_at":"2026-05-18T03:38:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.1857","created_at":"2026-05-18T03:38:54Z"},{"alias_kind":"pith_short_12","alias_value":"CXJHVNJHKVKG","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"CXJHVNJHKVKGFBY5","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"CXJHVNJH","created_at":"2026-05-18T12:27:01Z"}],"graph_snapshots":[{"event_id":"sha256:3ba426fff2e8ba24d5581fb6f45e6dcd4aed0b7aa7866cc2d1633b26e31ba542","target":"graph","created_at":"2026-05-18T03:38:54Z","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 related to the mean field type equation. First, we show that this flow exists for all time. Next, we prove a compactness result for this flow allowing us to get, under suitable hypothesis on its energy, the convergence of the flow to a solution of the mean field type equation. We also get a divergence result if the energy of the initial data is largely negative.","authors_text":"Jean-Baptiste Cast\\'eras","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-12-09T04:44:52Z","title":"A mean field type flow"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.1857","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:bf3150bdf9ab8cd0dd66bdb10c626f6f12379edaa57b6b6cf840dd04800ae11e","target":"record","created_at":"2026-05-18T03:38:54Z","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":"b7084cd604433b75596d915352d2d714db63853897070447830e544cc5a45640","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-12-09T04:44:52Z","title_canon_sha256":"0aa1fca5c7a118f71ac135df66eabb66452a43b1f5d00aa5dd977ac173c5206c"},"schema_version":"1.0","source":{"id":"1212.1857","kind":"arxiv","version":1}},"canonical_sha256":"15d27ab527555462871dc3c0f7b606285364c27af6e58dad459c99ace95a988f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"15d27ab527555462871dc3c0f7b606285364c27af6e58dad459c99ace95a988f","first_computed_at":"2026-05-18T03:38:54.932013Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:38:54.932013Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4IOmVSDRiYFjWK75XMPKU1EZqW6lrUNc7qSX2A0La2KxPob8UpsiAMqZnQggGoayr6qd1eqMw24Q52Yshs0BAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:38:54.932665Z","signed_message":"canonical_sha256_bytes"},"source_id":"1212.1857","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bf3150bdf9ab8cd0dd66bdb10c626f6f12379edaa57b6b6cf840dd04800ae11e","sha256:3ba426fff2e8ba24d5581fb6f45e6dcd4aed0b7aa7866cc2d1633b26e31ba542"],"state_sha256":"0430b06d7bf099e65a3721ec1a03898c654fba9b715575ab1468e063b137a99b"}