{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:LSYDZ5UY6AU5UWG5MFNDCID4ES","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":"43df9b62d81e44f78d62c2e46ef532069ea4d810804fd5e2cb22357efa56ab48","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-10-11T10:03:33Z","title_canon_sha256":"f8ac7daa78bb5bddeb3f986ff3302748c9287ddec237b9607d09d63870252ad9"},"schema_version":"1.0","source":{"id":"1610.03261","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.03261","created_at":"2026-05-18T00:44:42Z"},{"alias_kind":"arxiv_version","alias_value":"1610.03261v2","created_at":"2026-05-18T00:44:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.03261","created_at":"2026-05-18T00:44:42Z"},{"alias_kind":"pith_short_12","alias_value":"LSYDZ5UY6AU5","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"LSYDZ5UY6AU5UWG5","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"LSYDZ5UY","created_at":"2026-05-18T12:30:29Z"}],"graph_snapshots":[{"event_id":"sha256:ee49264d1c21b8bafc24444d3a260f7b70c0baecd13f85f13abc6ad2c68ba293","target":"graph","created_at":"2026-05-18T00:44:42Z","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 $N$-particle interacting particle system with the vision geometrical constraints and reflected noises, proposed as a model for collective behavior of individuals. We rigorously derive a continuity-type of mean-field equation with discontinuous kernels and the normal reflecting boundary conditions from that stochastic particle system as the number of particles $N$ goes to infinity. More precisely, we provide a quantitative estimate of the convergence in law of the empirical measure associated to the particle system to a probability measure which possesses a density which is a weak","authors_text":"Samir Salem, Young-Pil Choi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-10-11T10:03:33Z","title":"Propagation of chaos for aggregation equations with no-flux boundary conditions and sharp sensing zones"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.03261","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":"sha256:5de9a03c6a8590729a685aa86e2fee53849cbb67b608d52cee5cbfd23dfd0632","target":"record","created_at":"2026-05-18T00:44:42Z","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":"43df9b62d81e44f78d62c2e46ef532069ea4d810804fd5e2cb22357efa56ab48","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-10-11T10:03:33Z","title_canon_sha256":"f8ac7daa78bb5bddeb3f986ff3302748c9287ddec237b9607d09d63870252ad9"},"schema_version":"1.0","source":{"id":"1610.03261","kind":"arxiv","version":2}},"canonical_sha256":"5cb03cf698f029da58dd615a31207c24b2765cb642b681516fafc09738e513a9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5cb03cf698f029da58dd615a31207c24b2765cb642b681516fafc09738e513a9","first_computed_at":"2026-05-18T00:44:42.353670Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:44:42.353670Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uwxIuqWXiuciYQWa822vqVQpainavNqK2u0zA4GAj7MZ5LTUls0B+hMKElclgPZxXpieX09AvQgLlN7eryO7AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:44:42.354234Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.03261","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5de9a03c6a8590729a685aa86e2fee53849cbb67b608d52cee5cbfd23dfd0632","sha256:ee49264d1c21b8bafc24444d3a260f7b70c0baecd13f85f13abc6ad2c68ba293"],"state_sha256":"5d9a017ec981ba37ae733cf9b702035f93beb0230a3a1dc5577d434c7b1a99d8"}