{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:LAO2X243VQ4GMQA52MFFCG722I","short_pith_number":"pith:LAO2X243","schema_version":"1.0","canonical_sha256":"581dabeb9bac3866401dd30a511bfad238c7a5e94877e2e62f1c94d034a8e7d0","source":{"kind":"arxiv","id":"1606.06932","version":1},"attestation_state":"computed","paper":{"title":"Pattern formation for a volume-filling chemotaxis model with logistic growth","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jicheng Tao, Manjun Ma, Yazhou Han, Zhongfang Li","submitted_at":"2016-06-22T13:02:28Z","abstract_excerpt":"This paper is devoted to investigate the pattern formation of a volume-filling chemotaxis model with logistic cell growth. We first apply the local stability analysis to establish sufficient conditions of destabilization for uniform steady-state solution. Then, weakly nonlinear analysis with multi-scales is used to deal with the emerging process of patterns near the bifurcation point. For the single unstable mode case, we derive the Stuart-Landau equations describing the evolution of the amplitude, and thus the asymptotic expressions of patterns are obtained in both supercritical case and subc"},"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":"1606.06932","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-06-22T13:02:28Z","cross_cats_sorted":[],"title_canon_sha256":"332f8d5a3ff00583da7bfff7e79a613814e3eb9fa95b551c44fb58a383c92c67","abstract_canon_sha256":"3e7a0b71c476d7683353da483bda4d77d9f6b0c3b6433de5ecee3dc2686bbfe5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:57:37.772335Z","signature_b64":"EuEki36E0OV85e5sRdk7W9vxE+kGA+KwhNOGuN4/9h2gR5YmKzB2XXCfCzdPqGrj+KVDLA7mOuHQWRoz5hXPDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"581dabeb9bac3866401dd30a511bfad238c7a5e94877e2e62f1c94d034a8e7d0","last_reissued_at":"2026-05-18T00:57:37.771626Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:57:37.771626Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Pattern formation for a volume-filling chemotaxis model with logistic growth","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jicheng Tao, Manjun Ma, Yazhou Han, Zhongfang Li","submitted_at":"2016-06-22T13:02:28Z","abstract_excerpt":"This paper is devoted to investigate the pattern formation of a volume-filling chemotaxis model with logistic cell growth. We first apply the local stability analysis to establish sufficient conditions of destabilization for uniform steady-state solution. Then, weakly nonlinear analysis with multi-scales is used to deal with the emerging process of patterns near the bifurcation point. For the single unstable mode case, we derive the Stuart-Landau equations describing the evolution of the amplitude, and thus the asymptotic expressions of patterns are obtained in both supercritical case and subc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.06932","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":"1606.06932","created_at":"2026-05-18T00:57:37.771740+00:00"},{"alias_kind":"arxiv_version","alias_value":"1606.06932v1","created_at":"2026-05-18T00:57:37.771740+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.06932","created_at":"2026-05-18T00:57:37.771740+00:00"},{"alias_kind":"pith_short_12","alias_value":"LAO2X243VQ4G","created_at":"2026-05-18T12:30:29.479603+00:00"},{"alias_kind":"pith_short_16","alias_value":"LAO2X243VQ4GMQA5","created_at":"2026-05-18T12:30:29.479603+00:00"},{"alias_kind":"pith_short_8","alias_value":"LAO2X243","created_at":"2026-05-18T12:30:29.479603+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/LAO2X243VQ4GMQA52MFFCG722I","json":"https://pith.science/pith/LAO2X243VQ4GMQA52MFFCG722I.json","graph_json":"https://pith.science/api/pith-number/LAO2X243VQ4GMQA52MFFCG722I/graph.json","events_json":"https://pith.science/api/pith-number/LAO2X243VQ4GMQA52MFFCG722I/events.json","paper":"https://pith.science/paper/LAO2X243"},"agent_actions":{"view_html":"https://pith.science/pith/LAO2X243VQ4GMQA52MFFCG722I","download_json":"https://pith.science/pith/LAO2X243VQ4GMQA52MFFCG722I.json","view_paper":"https://pith.science/paper/LAO2X243","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1606.06932&json=true","fetch_graph":"https://pith.science/api/pith-number/LAO2X243VQ4GMQA52MFFCG722I/graph.json","fetch_events":"https://pith.science/api/pith-number/LAO2X243VQ4GMQA52MFFCG722I/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LAO2X243VQ4GMQA52MFFCG722I/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LAO2X243VQ4GMQA52MFFCG722I/action/storage_attestation","attest_author":"https://pith.science/pith/LAO2X243VQ4GMQA52MFFCG722I/action/author_attestation","sign_citation":"https://pith.science/pith/LAO2X243VQ4GMQA52MFFCG722I/action/citation_signature","submit_replication":"https://pith.science/pith/LAO2X243VQ4GMQA52MFFCG722I/action/replication_record"}},"created_at":"2026-05-18T00:57:37.771740+00:00","updated_at":"2026-05-18T00:57:37.771740+00:00"}