{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:LAO2X243VQ4GMQA52MFFCG722I","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":"3e7a0b71c476d7683353da483bda4d77d9f6b0c3b6433de5ecee3dc2686bbfe5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-06-22T13:02:28Z","title_canon_sha256":"332f8d5a3ff00583da7bfff7e79a613814e3eb9fa95b551c44fb58a383c92c67"},"schema_version":"1.0","source":{"id":"1606.06932","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.06932","created_at":"2026-05-18T00:57:37Z"},{"alias_kind":"arxiv_version","alias_value":"1606.06932v1","created_at":"2026-05-18T00:57:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.06932","created_at":"2026-05-18T00:57:37Z"},{"alias_kind":"pith_short_12","alias_value":"LAO2X243VQ4G","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"LAO2X243VQ4GMQA5","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"LAO2X243","created_at":"2026-05-18T12:30:29Z"}],"graph_snapshots":[{"event_id":"sha256:6c53bc96a8d43e6662182c236a711744482d73e339c5418950b32f8e970f0d2a","target":"graph","created_at":"2026-05-18T00:57:37Z","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":"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","authors_text":"Jicheng Tao, Manjun Ma, Yazhou Han, Zhongfang Li","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-06-22T13:02:28Z","title":"Pattern formation for a volume-filling chemotaxis model with logistic growth"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.06932","kind":"arxiv","version":1},"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":"sha256:0f15d2bae0ea6f7b13cac0752c663a23782d81f26a50585501bceb85ad6a609b","target":"record","created_at":"2026-05-18T00:57:37Z","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":"3e7a0b71c476d7683353da483bda4d77d9f6b0c3b6433de5ecee3dc2686bbfe5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-06-22T13:02:28Z","title_canon_sha256":"332f8d5a3ff00583da7bfff7e79a613814e3eb9fa95b551c44fb58a383c92c67"},"schema_version":"1.0","source":{"id":"1606.06932","kind":"arxiv","version":1}},"canonical_sha256":"581dabeb9bac3866401dd30a511bfad238c7a5e94877e2e62f1c94d034a8e7d0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"581dabeb9bac3866401dd30a511bfad238c7a5e94877e2e62f1c94d034a8e7d0","first_computed_at":"2026-05-18T00:57:37.771626Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:57:37.771626Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EuEki36E0OV85e5sRdk7W9vxE+kGA+KwhNOGuN4/9h2gR5YmKzB2XXCfCzdPqGrj+KVDLA7mOuHQWRoz5hXPDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:57:37.772335Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.06932","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0f15d2bae0ea6f7b13cac0752c663a23782d81f26a50585501bceb85ad6a609b","sha256:6c53bc96a8d43e6662182c236a711744482d73e339c5418950b32f8e970f0d2a"],"state_sha256":"7dc866547c43fad5b1f3bf7a46719c0e0ebdc5edd5eb987799e9c13403405e42"}