{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:2IOU5LH44YI5IV52J7JD2I3FUD","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":"7deb27fa40d7fdaacc39a040fa5205a5c89c2257d84c8f6dacbf5ad1612d6155","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-04-29T02:20:37Z","title_canon_sha256":"f24000d402a7f4ea007152a031d2271da23154b258a88f2d762ae58ca4246a8d"},"schema_version":"1.0","source":{"id":"1604.08668","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.08668","created_at":"2026-05-17T23:47:31Z"},{"alias_kind":"arxiv_version","alias_value":"1604.08668v2","created_at":"2026-05-17T23:47:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.08668","created_at":"2026-05-17T23:47:31Z"},{"alias_kind":"pith_short_12","alias_value":"2IOU5LH44YI5","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_16","alias_value":"2IOU5LH44YI5IV52","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_8","alias_value":"2IOU5LH4","created_at":"2026-05-18T12:29:55Z"}],"graph_snapshots":[{"event_id":"sha256:c22090a3b0d7efa41187e40c8f84b1a9218c06a3bb6366182666aad352ce6c55","target":"graph","created_at":"2026-05-17T23:47:31Z","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 study a system of interacting diffusions that models chemotaxis of biological cells or microorganisms (referred to as particles) in a chemical field that is dynamically modified through the collective contributions from the particles. Such systems of reinforced diffusions have been widely studied and their hydrodynamic limits that are nonlinear non-local partial differential equations are usually referred to as Patlak-Keller-Segel (PKS) equations. Under the so-called \"quasi-stationary hypothesis\" on the chemical field the limit PDE is closely related to granular media equations that have be","authors_text":"Amarjit Budhiraja, Wai-Tong Louis Fan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-04-29T02:20:37Z","title":"Uniform in Time Interacting Particle Approximations for Nonlinear Equations of Patlak-Keller-Segel type"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.08668","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":"sha256:83c73bb859adc058215403a5a6e96266440528c14d87bf5cd7190a4c24377d1b","target":"record","created_at":"2026-05-17T23:47:31Z","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":"7deb27fa40d7fdaacc39a040fa5205a5c89c2257d84c8f6dacbf5ad1612d6155","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-04-29T02:20:37Z","title_canon_sha256":"f24000d402a7f4ea007152a031d2271da23154b258a88f2d762ae58ca4246a8d"},"schema_version":"1.0","source":{"id":"1604.08668","kind":"arxiv","version":2}},"canonical_sha256":"d21d4eacfce611d457ba4fd23d2365a0db49a963e9d09814126617434a7ebb11","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d21d4eacfce611d457ba4fd23d2365a0db49a963e9d09814126617434a7ebb11","first_computed_at":"2026-05-17T23:47:31.928431Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:47:31.928431Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JNjfIo/iSv5i0xO50iTRnLg1XvbXXSRFEkfUOIRGxK18OeRZ7UX1kedk6KQfUP8PpD/vXkTh13gt4ToDVLdBBQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:47:31.929151Z","signed_message":"canonical_sha256_bytes"},"source_id":"1604.08668","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:83c73bb859adc058215403a5a6e96266440528c14d87bf5cd7190a4c24377d1b","sha256:c22090a3b0d7efa41187e40c8f84b1a9218c06a3bb6366182666aad352ce6c55"],"state_sha256":"80a728cda92ef8c373e5e82435abfbddc8b49a564fcf60723a330394e9b26272"}