{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:5SQWKOO4YPGQUPSBEJSW2KZDRQ","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":"08a9a9199b6bd4b257995eb3cd8b1543d2686ed20856ed79ff1ea5b0ba71402c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.soft","submitted_at":"2016-12-21T21:12:49Z","title_canon_sha256":"26b876dcbe3184c8d575dcf7e9f8abf1fd1a5cd4caf593844505257bcb9b44da"},"schema_version":"1.0","source":{"id":"1612.07336","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.07336","created_at":"2026-05-18T00:45:14Z"},{"alias_kind":"arxiv_version","alias_value":"1612.07336v3","created_at":"2026-05-18T00:45:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.07336","created_at":"2026-05-18T00:45:14Z"},{"alias_kind":"pith_short_12","alias_value":"5SQWKOO4YPGQ","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"5SQWKOO4YPGQUPSB","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"5SQWKOO4","created_at":"2026-05-18T12:30:01Z"}],"graph_snapshots":[{"event_id":"sha256:a1403690dca58fb5146a01cf7d236bd3b9f5cf20328b7cc92fab9dd7b896f706","target":"graph","created_at":"2026-05-18T00:45:14Z","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":"Self-propelled particles with hydrodynamic interactions (microswimmers) have previously been shown to produce long-range ordering phenomena. Many theoretical explanations for these collective phenomena are connected to instabilities in the hydrodynamic or kinetic equations. By incorporating stochastic fluxes into the mean field kinetic equation, we quantify the dynamics of a suspension of microswimmers in the parameter regime where the deterministic equation is stable. We can thereby compute nontrivial collective phenomena concerning spatial correlations of orientation and stress as well as th","authors_text":"Patrick T. Underhill, Peter R. Kramer, Yuzhou Qian","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.soft","submitted_at":"2016-12-21T21:12:49Z","title":"Stochastic Kinetic Theory for Collective Behavior of Hydrodynamically Interacting Active Particles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.07336","kind":"arxiv","version":3},"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:a9aac6e4c3e4048c268ee6d836587378fb25dd701b32661223cc292625332c36","target":"record","created_at":"2026-05-18T00:45:14Z","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":"08a9a9199b6bd4b257995eb3cd8b1543d2686ed20856ed79ff1ea5b0ba71402c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.soft","submitted_at":"2016-12-21T21:12:49Z","title_canon_sha256":"26b876dcbe3184c8d575dcf7e9f8abf1fd1a5cd4caf593844505257bcb9b44da"},"schema_version":"1.0","source":{"id":"1612.07336","kind":"arxiv","version":3}},"canonical_sha256":"eca16539dcc3cd0a3e4122656d2b238c3282c5969241d4147907aa6ea649b085","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eca16539dcc3cd0a3e4122656d2b238c3282c5969241d4147907aa6ea649b085","first_computed_at":"2026-05-18T00:45:14.587067Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:45:14.587067Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QtbEt06WJWTsGQHrsPCzHLHWfaBn36uhlS/wLyHJtPL/cwdeivQN8KdDUSiPIKv+fnj84LLg0Xh3CnOr94oqCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:45:14.587849Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.07336","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a9aac6e4c3e4048c268ee6d836587378fb25dd701b32661223cc292625332c36","sha256:a1403690dca58fb5146a01cf7d236bd3b9f5cf20328b7cc92fab9dd7b896f706"],"state_sha256":"83b8d9961551cb5d3d21c49a77ead94c08db049c2d5ff0b5cb5ed28c2725bdd7"}