{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:3VPVKJ3WQ7IPGNPJFELOHVLZTL","short_pith_number":"pith:3VPVKJ3W","schema_version":"1.0","canonical_sha256":"dd5f55277687d0f335e92916e3d5799ac1f67b0ad2debaa91c5a0b81de4e1220","source":{"kind":"arxiv","id":"1008.1749","version":1},"attestation_state":"computed","paper":{"title":"Collective motion of active Brownian particles in one dimension","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"Pawel Romanczuk, Udo Erdmann","submitted_at":"2010-08-10T16:18:53Z","abstract_excerpt":"We analyze a model of active Brownian particles with non-linear friction and velocity coupling in one spatial dimension. The model exhibits two modes of motion observed in biological swarms: A disordered phase with vanishing mean velocity and an ordered phase with finite mean velocity. Starting from the microscopic Langevin equations, we derive mean-field equations of the collective dynamics. We identify the fixed points of the mean-field equations corresponding to the two modes and analyze their stability with respect to the model parameters. Finally, we compare our analytical findings with n"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1008.1749","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2010-08-10T16:18:53Z","cross_cats_sorted":[],"title_canon_sha256":"3ceabc6a533e5112a4720a7fa0df773a3cbe244590d6aaba96abd287d68677b0","abstract_canon_sha256":"b8211fe56494d36e65a509a6e9befef94bb44d5042c75e56e010d286f1ffa285"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:05:49.723938Z","signature_b64":"KaJvLI5IhPVP1tp69xnGKaeMqj8oWjrzBi4j2vGXarp4zh+7gSIA3XqucXkKKJ22Ih4mWGemFlkWKQsFemqGDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dd5f55277687d0f335e92916e3d5799ac1f67b0ad2debaa91c5a0b81de4e1220","last_reissued_at":"2026-05-18T02:05:49.723355Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:05:49.723355Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Collective motion of active Brownian particles in one dimension","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"Pawel Romanczuk, Udo Erdmann","submitted_at":"2010-08-10T16:18:53Z","abstract_excerpt":"We analyze a model of active Brownian particles with non-linear friction and velocity coupling in one spatial dimension. The model exhibits two modes of motion observed in biological swarms: A disordered phase with vanishing mean velocity and an ordered phase with finite mean velocity. Starting from the microscopic Langevin equations, we derive mean-field equations of the collective dynamics. We identify the fixed points of the mean-field equations corresponding to the two modes and analyze their stability with respect to the model parameters. Finally, we compare our analytical findings with n"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.1749","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1008.1749","created_at":"2026-05-18T02:05:49.723429+00:00"},{"alias_kind":"arxiv_version","alias_value":"1008.1749v1","created_at":"2026-05-18T02:05:49.723429+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.1749","created_at":"2026-05-18T02:05:49.723429+00:00"},{"alias_kind":"pith_short_12","alias_value":"3VPVKJ3WQ7IP","created_at":"2026-05-18T12:26:03.138858+00:00"},{"alias_kind":"pith_short_16","alias_value":"3VPVKJ3WQ7IPGNPJ","created_at":"2026-05-18T12:26:03.138858+00:00"},{"alias_kind":"pith_short_8","alias_value":"3VPVKJ3W","created_at":"2026-05-18T12:26:03.138858+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/3VPVKJ3WQ7IPGNPJFELOHVLZTL","json":"https://pith.science/pith/3VPVKJ3WQ7IPGNPJFELOHVLZTL.json","graph_json":"https://pith.science/api/pith-number/3VPVKJ3WQ7IPGNPJFELOHVLZTL/graph.json","events_json":"https://pith.science/api/pith-number/3VPVKJ3WQ7IPGNPJFELOHVLZTL/events.json","paper":"https://pith.science/paper/3VPVKJ3W"},"agent_actions":{"view_html":"https://pith.science/pith/3VPVKJ3WQ7IPGNPJFELOHVLZTL","download_json":"https://pith.science/pith/3VPVKJ3WQ7IPGNPJFELOHVLZTL.json","view_paper":"https://pith.science/paper/3VPVKJ3W","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1008.1749&json=true","fetch_graph":"https://pith.science/api/pith-number/3VPVKJ3WQ7IPGNPJFELOHVLZTL/graph.json","fetch_events":"https://pith.science/api/pith-number/3VPVKJ3WQ7IPGNPJFELOHVLZTL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3VPVKJ3WQ7IPGNPJFELOHVLZTL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3VPVKJ3WQ7IPGNPJFELOHVLZTL/action/storage_attestation","attest_author":"https://pith.science/pith/3VPVKJ3WQ7IPGNPJFELOHVLZTL/action/author_attestation","sign_citation":"https://pith.science/pith/3VPVKJ3WQ7IPGNPJFELOHVLZTL/action/citation_signature","submit_replication":"https://pith.science/pith/3VPVKJ3WQ7IPGNPJFELOHVLZTL/action/replication_record"}},"created_at":"2026-05-18T02:05:49.723429+00:00","updated_at":"2026-05-18T02:05:49.723429+00:00"}