{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:SF3DIMPFZU4GTJR3ILKJVAVF2N","short_pith_number":"pith:SF3DIMPF","schema_version":"1.0","canonical_sha256":"91763431e5cd3869a63b42d49a82a5d34e63fe93dd38e51bae2caf2318ebfa50","source":{"kind":"arxiv","id":"1507.04259","version":2},"attestation_state":"computed","paper":{"title":"Biological aggregation driven by social and environmental factors: A nonlocal model and its degenerate Cahn-Hilliard approximation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["nlin.AO","q-bio.PE"],"primary_cat":"nlin.PS","authors_text":"Andrew J. Bernoff, Chad M. Topaz","submitted_at":"2015-07-15T15:37:57Z","abstract_excerpt":"Biological aggregations such as insect swarms and bird flocks may arise from a combination of social interactions and environmental cues. We focus on nonlocal continuum equations, which are often used to model aggregations, and yet which pose significant analytical and computational challenges. Beginning with a particular nonlocal aggregation model [Topaz et al., Bull. Math. Bio., 2006], we derive the minimal well-posed long-wave approximation, which is a degenerate Cahn-Hilliard equation. Energy minimizers of this reduced, local model retain many salient features of those of the nonlocal mode"},"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":"1507.04259","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2015-07-15T15:37:57Z","cross_cats_sorted":["nlin.AO","q-bio.PE"],"title_canon_sha256":"57d4b87a189a10cb3233d20dc4e403905560f9b992e44afde98ddd8dd1862eda","abstract_canon_sha256":"e5799e60b873620414aaec6dd5bc394ac86209463442cb0d5615d652d610ceee"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:14:58.897669Z","signature_b64":"pMfsZYbLZXHjMUGrZTNVEf8nhlIMAyYZ15nz06+rrdQsqqLviAYKOog3bwZpwZui63z2FPP0eoPLsfm2tsXJDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"91763431e5cd3869a63b42d49a82a5d34e63fe93dd38e51bae2caf2318ebfa50","last_reissued_at":"2026-05-18T01:14:58.897115Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:14:58.897115Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Biological aggregation driven by social and environmental factors: A nonlocal model and its degenerate Cahn-Hilliard approximation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["nlin.AO","q-bio.PE"],"primary_cat":"nlin.PS","authors_text":"Andrew J. Bernoff, Chad M. Topaz","submitted_at":"2015-07-15T15:37:57Z","abstract_excerpt":"Biological aggregations such as insect swarms and bird flocks may arise from a combination of social interactions and environmental cues. We focus on nonlocal continuum equations, which are often used to model aggregations, and yet which pose significant analytical and computational challenges. Beginning with a particular nonlocal aggregation model [Topaz et al., Bull. Math. Bio., 2006], we derive the minimal well-posed long-wave approximation, which is a degenerate Cahn-Hilliard equation. Energy minimizers of this reduced, local model retain many salient features of those of the nonlocal mode"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.04259","kind":"arxiv","version":2},"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":"1507.04259","created_at":"2026-05-18T01:14:58.897185+00:00"},{"alias_kind":"arxiv_version","alias_value":"1507.04259v2","created_at":"2026-05-18T01:14:58.897185+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.04259","created_at":"2026-05-18T01:14:58.897185+00:00"},{"alias_kind":"pith_short_12","alias_value":"SF3DIMPFZU4G","created_at":"2026-05-18T12:29:39.896362+00:00"},{"alias_kind":"pith_short_16","alias_value":"SF3DIMPFZU4GTJR3","created_at":"2026-05-18T12:29:39.896362+00:00"},{"alias_kind":"pith_short_8","alias_value":"SF3DIMPF","created_at":"2026-05-18T12:29:39.896362+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/SF3DIMPFZU4GTJR3ILKJVAVF2N","json":"https://pith.science/pith/SF3DIMPFZU4GTJR3ILKJVAVF2N.json","graph_json":"https://pith.science/api/pith-number/SF3DIMPFZU4GTJR3ILKJVAVF2N/graph.json","events_json":"https://pith.science/api/pith-number/SF3DIMPFZU4GTJR3ILKJVAVF2N/events.json","paper":"https://pith.science/paper/SF3DIMPF"},"agent_actions":{"view_html":"https://pith.science/pith/SF3DIMPFZU4GTJR3ILKJVAVF2N","download_json":"https://pith.science/pith/SF3DIMPFZU4GTJR3ILKJVAVF2N.json","view_paper":"https://pith.science/paper/SF3DIMPF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1507.04259&json=true","fetch_graph":"https://pith.science/api/pith-number/SF3DIMPFZU4GTJR3ILKJVAVF2N/graph.json","fetch_events":"https://pith.science/api/pith-number/SF3DIMPFZU4GTJR3ILKJVAVF2N/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SF3DIMPFZU4GTJR3ILKJVAVF2N/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SF3DIMPFZU4GTJR3ILKJVAVF2N/action/storage_attestation","attest_author":"https://pith.science/pith/SF3DIMPFZU4GTJR3ILKJVAVF2N/action/author_attestation","sign_citation":"https://pith.science/pith/SF3DIMPFZU4GTJR3ILKJVAVF2N/action/citation_signature","submit_replication":"https://pith.science/pith/SF3DIMPFZU4GTJR3ILKJVAVF2N/action/replication_record"}},"created_at":"2026-05-18T01:14:58.897185+00:00","updated_at":"2026-05-18T01:14:58.897185+00:00"}