{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:WPPVDM5VE7ELY5B7APBQQT7Y4Y","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":"8e8fa258e4831190ca52c43e177842408227d5b8526bc2bb7e1eb56c3760d198","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2019-07-11T01:58:44Z","title_canon_sha256":"94cf9598847a8d32b1e534feca61685a9a8399d011f53ffe28f9367608138ddf"},"schema_version":"1.0","source":{"id":"1907.05566","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.05566","created_at":"2026-05-17T23:40:47Z"},{"alias_kind":"arxiv_version","alias_value":"1907.05566v1","created_at":"2026-05-17T23:40:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.05566","created_at":"2026-05-17T23:40:47Z"},{"alias_kind":"pith_short_12","alias_value":"WPPVDM5VE7EL","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_16","alias_value":"WPPVDM5VE7ELY5B7","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_8","alias_value":"WPPVDM5V","created_at":"2026-05-18T12:33:30Z"}],"graph_snapshots":[{"event_id":"sha256:d11aca1fc6a133ccb960ce2144d2948c5afd47f5feb3e1221633784d666c1533","target":"graph","created_at":"2026-05-17T23:40:47Z","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 propose models describing the collective dynamics of two opposing groups of individuals with stochastic communication. Individuals from the same group are assumed to align in a stochastic manner, while individuals from different groups are assumed to anti-align. Under reasonable assumptions, we prove the large time behavior of separation, in the sense that the variation inside a group is much less than the distance between the two groups. The separation phenomena are verified by numerical simulations.","authors_text":"Ruiwen Shu, Shi Jin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2019-07-11T01:58:44Z","title":"Collective dynamics of opposing groups with stochastic communication"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.05566","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":"sha256:72adbb362555ea92467c15f5c6f9bbaacfa0721cb1ec0c41385181f261261757","target":"record","created_at":"2026-05-17T23:40:47Z","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":"8e8fa258e4831190ca52c43e177842408227d5b8526bc2bb7e1eb56c3760d198","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2019-07-11T01:58:44Z","title_canon_sha256":"94cf9598847a8d32b1e534feca61685a9a8399d011f53ffe28f9367608138ddf"},"schema_version":"1.0","source":{"id":"1907.05566","kind":"arxiv","version":1}},"canonical_sha256":"b3df51b3b527c8bc743f03c3084ff8e62966be4b39ff0dbba8757171cf5871e4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b3df51b3b527c8bc743f03c3084ff8e62966be4b39ff0dbba8757171cf5871e4","first_computed_at":"2026-05-17T23:40:47.905524Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:40:47.905524Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fg9k1MuPv3oQIzzCk0vDSb4o/XsKFvXXiJWANosZpNVN8Y28DGHAQ/HJcSnwgCMj/unY+m960R6Wy8W9atZ9CQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:40:47.906207Z","signed_message":"canonical_sha256_bytes"},"source_id":"1907.05566","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:72adbb362555ea92467c15f5c6f9bbaacfa0721cb1ec0c41385181f261261757","sha256:d11aca1fc6a133ccb960ce2144d2948c5afd47f5feb3e1221633784d666c1533"],"state_sha256":"5344779753187d6d2cbe5d8067ceb754336d32c2ba1d867392e4037f87e96a9c"}