{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:ZRLUX5RMLSFIEAEKE4SLH5JCJA","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":"20e184538448ac4ab73d125b4b3789c793b7c6f64fdcae0e63cf310024bebbc3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-06-09T21:14:58Z","title_canon_sha256":"2bda62bf9ecf248cb9c57d30372d68bc6224ee8c3b434474b41d110ddc30f226"},"schema_version":"1.0","source":{"id":"1906.03712","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1906.03712","created_at":"2026-05-17T23:43:45Z"},{"alias_kind":"arxiv_version","alias_value":"1906.03712v1","created_at":"2026-05-17T23:43:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.03712","created_at":"2026-05-17T23:43:45Z"},{"alias_kind":"pith_short_12","alias_value":"ZRLUX5RMLSFI","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_16","alias_value":"ZRLUX5RMLSFIEAEK","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_8","alias_value":"ZRLUX5RM","created_at":"2026-05-18T12:33:33Z"}],"graph_snapshots":[{"event_id":"sha256:74fe5569fc1cfff7c8248fb56b65da69d510316a64ff405618ddec16fd0aec41","target":"graph","created_at":"2026-05-17T23:43:45Z","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":"In this paper we analyse a class of nonlinear cross-diffusion systems for two species with local repulsive interactions that exhibit a formal gradient flow structure with respect to the Wasserstein metric. We show that systems where the population pressure is given by a function of the total population are critical with respect to cross-diffusion perturbations. This criticality is showcased by proving that adding an extra cross-diffusion term that breaks the symmetry of the population pressure in the system leads to completely different behaviours, namely segregation or mixing, depending on th","authors_text":"J. A. Carrillo, J.-F. Pietschmann, M. Burger, M. Schmidtchen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-06-09T21:14:58Z","title":"Segregation and Gap Formation in Cross-Diffusion Models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.03712","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:daab56aded90445307f3ccf1e3d7c624b94fcbd9d3e48385daff7ddf85edd028","target":"record","created_at":"2026-05-17T23:43:45Z","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":"20e184538448ac4ab73d125b4b3789c793b7c6f64fdcae0e63cf310024bebbc3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-06-09T21:14:58Z","title_canon_sha256":"2bda62bf9ecf248cb9c57d30372d68bc6224ee8c3b434474b41d110ddc30f226"},"schema_version":"1.0","source":{"id":"1906.03712","kind":"arxiv","version":1}},"canonical_sha256":"cc574bf62c5c8a82008a2724b3f5224832643d66ef464a6246c0d4a8dba6a293","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cc574bf62c5c8a82008a2724b3f5224832643d66ef464a6246c0d4a8dba6a293","first_computed_at":"2026-05-17T23:43:45.227036Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:43:45.227036Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YJjKvLLRbnqFuYCYYByn/LUTAi5iFAlcmPyUoR4mxYV1pJNchh0k+A406TG7oefvJfXuW7C6Jp33sEw60fVUDg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:43:45.227677Z","signed_message":"canonical_sha256_bytes"},"source_id":"1906.03712","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:daab56aded90445307f3ccf1e3d7c624b94fcbd9d3e48385daff7ddf85edd028","sha256:74fe5569fc1cfff7c8248fb56b65da69d510316a64ff405618ddec16fd0aec41"],"state_sha256":"f02eec89baa31ba4e3e990c0cf78bd0e3e41a0ce79c2387ae9efd3be9949e1bc"}