{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:D7C6HLE75LPL4VHRYYENIQPRWJ","short_pith_number":"pith:D7C6HLE7","schema_version":"1.0","canonical_sha256":"1fc5e3ac9feadebe54f1c608d441f1b25bd36ebb79c3de16ffccb90a1ff6f5d2","source":{"kind":"arxiv","id":"0912.0594","version":3},"attestation_state":"computed","paper":{"title":"A continuum model for alignment of self-propelled particles with anisotropy and density-dependent parameters","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.MP"],"primary_cat":"math-ph","authors_text":"Amic Frouvelle (IMT)","submitted_at":"2009-12-03T08:23:07Z","abstract_excerpt":"We consider the macroscopic model derived by Degond and Motsch from a time-continuous version of the Vicsek model, describing the interaction orientation in a large number of self-propelled particles. In this article, we study the influence of a slight modification at the individual level, letting the relaxation parameter depend on the local density and taking in account some anisotropy in the observation kernel (which can model an angle of vision). The main result is a certain robustness of this macroscopic limit and of the methodology used to derive it. With some adaptations to the concept o"},"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":"0912.0594","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2009-12-03T08:23:07Z","cross_cats_sorted":["math.AP","math.MP"],"title_canon_sha256":"c26b2fd4996708323abfcd0b59ea78445839c8f84ac7551069f848138ca78cdd","abstract_canon_sha256":"9efe9f6f46be51502b3c0cf1b2aa430a57b31a7ed01dbb38f6d196b48a4d0ea4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:36:16.451605Z","signature_b64":"BvJ0+v4wBVtaoSatK9bw3vkJdcEc36VGgU8qDuJOjRasm5VnIk0C+bHXVPROZTzYPVo3IQ4XlH5ZO1+DRRRXAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1fc5e3ac9feadebe54f1c608d441f1b25bd36ebb79c3de16ffccb90a1ff6f5d2","last_reissued_at":"2026-05-18T03:36:16.450799Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:36:16.450799Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A continuum model for alignment of self-propelled particles with anisotropy and density-dependent parameters","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.MP"],"primary_cat":"math-ph","authors_text":"Amic Frouvelle (IMT)","submitted_at":"2009-12-03T08:23:07Z","abstract_excerpt":"We consider the macroscopic model derived by Degond and Motsch from a time-continuous version of the Vicsek model, describing the interaction orientation in a large number of self-propelled particles. In this article, we study the influence of a slight modification at the individual level, letting the relaxation parameter depend on the local density and taking in account some anisotropy in the observation kernel (which can model an angle of vision). The main result is a certain robustness of this macroscopic limit and of the methodology used to derive it. With some adaptations to the concept o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0912.0594","kind":"arxiv","version":3},"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":"0912.0594","created_at":"2026-05-18T03:36:16.450934+00:00"},{"alias_kind":"arxiv_version","alias_value":"0912.0594v3","created_at":"2026-05-18T03:36:16.450934+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0912.0594","created_at":"2026-05-18T03:36:16.450934+00:00"},{"alias_kind":"pith_short_12","alias_value":"D7C6HLE75LPL","created_at":"2026-05-18T12:25:59.703012+00:00"},{"alias_kind":"pith_short_16","alias_value":"D7C6HLE75LPL4VHR","created_at":"2026-05-18T12:25:59.703012+00:00"},{"alias_kind":"pith_short_8","alias_value":"D7C6HLE7","created_at":"2026-05-18T12:25:59.703012+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/D7C6HLE75LPL4VHRYYENIQPRWJ","json":"https://pith.science/pith/D7C6HLE75LPL4VHRYYENIQPRWJ.json","graph_json":"https://pith.science/api/pith-number/D7C6HLE75LPL4VHRYYENIQPRWJ/graph.json","events_json":"https://pith.science/api/pith-number/D7C6HLE75LPL4VHRYYENIQPRWJ/events.json","paper":"https://pith.science/paper/D7C6HLE7"},"agent_actions":{"view_html":"https://pith.science/pith/D7C6HLE75LPL4VHRYYENIQPRWJ","download_json":"https://pith.science/pith/D7C6HLE75LPL4VHRYYENIQPRWJ.json","view_paper":"https://pith.science/paper/D7C6HLE7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0912.0594&json=true","fetch_graph":"https://pith.science/api/pith-number/D7C6HLE75LPL4VHRYYENIQPRWJ/graph.json","fetch_events":"https://pith.science/api/pith-number/D7C6HLE75LPL4VHRYYENIQPRWJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/D7C6HLE75LPL4VHRYYENIQPRWJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/D7C6HLE75LPL4VHRYYENIQPRWJ/action/storage_attestation","attest_author":"https://pith.science/pith/D7C6HLE75LPL4VHRYYENIQPRWJ/action/author_attestation","sign_citation":"https://pith.science/pith/D7C6HLE75LPL4VHRYYENIQPRWJ/action/citation_signature","submit_replication":"https://pith.science/pith/D7C6HLE75LPL4VHRYYENIQPRWJ/action/replication_record"}},"created_at":"2026-05-18T03:36:16.450934+00:00","updated_at":"2026-05-18T03:36:16.450934+00:00"}