{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:JLT7DYCW3BQXEKUPCXU2JWFG4H","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":"d46b16359d2ac6741cc794237dcba6848dd24d582b341e7c3cc3a54e3704d08a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2021-07-08T05:36:11Z","title_canon_sha256":"1052f98caf39cafb3fdeb2f778f9473744431b74a14537e5c45dd22eaaef6974"},"schema_version":"1.0","source":{"id":"2107.03616","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2107.03616","created_at":"2026-07-05T06:06:51Z"},{"alias_kind":"arxiv_version","alias_value":"2107.03616v4","created_at":"2026-07-05T06:06:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2107.03616","created_at":"2026-07-05T06:06:51Z"},{"alias_kind":"pith_short_12","alias_value":"JLT7DYCW3BQX","created_at":"2026-07-05T06:06:51Z"},{"alias_kind":"pith_short_16","alias_value":"JLT7DYCW3BQXEKUP","created_at":"2026-07-05T06:06:51Z"},{"alias_kind":"pith_short_8","alias_value":"JLT7DYCW","created_at":"2026-07-05T06:06:51Z"}],"graph_snapshots":[{"event_id":"sha256:60d03b04a0aa1e291f698909222df48caf09b13f48910f9124efa70c0e539004","target":"graph","created_at":"2026-07-05T06:06:51Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2107.03616/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider moderately interacting particle systems with singular interaction kernel and environmental noise. It is shown that the mollified empirical measures converge in strong norms to the unique (local) solutions of nonlinear Fokker-Planck equations. The approach works for the Biot-Savart and repulsive Poisson kernels.","authors_text":"Dejun Luo, Shuchen Guo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2021-07-08T05:36:11Z","title":"Scaling Limit of Moderately Interacting Particle Systems with Singular Interaction and Environmental Noise"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2107.03616","kind":"arxiv","version":4},"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":"sha256:3c0728b97a5263acd9c8585bc81443443407f0085908fd1e117e3633d61b0140","target":"record","created_at":"2026-07-05T06:06:51Z","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":"d46b16359d2ac6741cc794237dcba6848dd24d582b341e7c3cc3a54e3704d08a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2021-07-08T05:36:11Z","title_canon_sha256":"1052f98caf39cafb3fdeb2f778f9473744431b74a14537e5c45dd22eaaef6974"},"schema_version":"1.0","source":{"id":"2107.03616","kind":"arxiv","version":4}},"canonical_sha256":"4ae7f1e056d861722a8f15e9a4d8a6e1d5b9ded5238ef2f616a9bcb825a2c9f2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4ae7f1e056d861722a8f15e9a4d8a6e1d5b9ded5238ef2f616a9bcb825a2c9f2","first_computed_at":"2026-07-05T06:06:51.883236Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:06:51.883236Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bEwitHaNDB6t+FlrRJVN+bd4fv1koN1veQWZklo4V0PY/p8ygYASdka5dnWwvdIueEe1WfHvG1Xv6A/p019NAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T06:06:51.883622Z","signed_message":"canonical_sha256_bytes"},"source_id":"2107.03616","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3c0728b97a5263acd9c8585bc81443443407f0085908fd1e117e3633d61b0140","sha256:60d03b04a0aa1e291f698909222df48caf09b13f48910f9124efa70c0e539004"],"state_sha256":"bdebddd6acb247c1d9c6e48f28030ec0a87b28be2efec2e301a1973c6648391b"}