{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:BSYINHOBWYGIOLQFDD7PJFLZP7","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":"8819c2a3296ee6ed6c661b7f3e559f4c7d86797f63c51258ad75d7b129fb203c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-09-16T12:34:13Z","title_canon_sha256":"3deb0fe1b18ace0988782d7f35f347fb837ca547ef23f196b2dbe63d783f8d72"},"schema_version":"1.0","source":{"id":"1609.05024","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.05024","created_at":"2026-05-18T00:48:26Z"},{"alias_kind":"arxiv_version","alias_value":"1609.05024v2","created_at":"2026-05-18T00:48:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.05024","created_at":"2026-05-18T00:48:26Z"},{"alias_kind":"pith_short_12","alias_value":"BSYINHOBWYGI","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_16","alias_value":"BSYINHOBWYGIOLQF","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_8","alias_value":"BSYINHOB","created_at":"2026-05-18T12:30:09Z"}],"graph_snapshots":[{"event_id":"sha256:cedeef6839061fa8dd72097f7625a5d626f9ca7deb58a898b739a97f74cf093f","target":"graph","created_at":"2026-05-18T00:48:26Z","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":"The aim of this paper is to study a PDE model for two diffusing species interacting by local size exclusion and global attraction. This leads to a nonlinear degenerate cross-diffusion system, for which we provide a global existence result. The analysis is motivated by the formulation of the system as a formal gradient flow for an appropriate energy functional consisting of entropic terms as well as quadratic nonlocal terms. Key ingredients are entropy dissipation methods as well as the recently developed boundedness by entropy principle. Moreover, we investigate phase separation effects inhere","authors_text":"Jan-Frederik Pietschmann, Judith Berendsen, Martin Burger","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-09-16T12:34:13Z","title":"On a cross-diffusion model for multiple species with nonlocal interaction and size exclusion"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.05024","kind":"arxiv","version":2},"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":"sha256:30ee2b610345461bb3644714797796425a323b5ae3795756398c48bcb9ed0c15","target":"record","created_at":"2026-05-18T00:48:26Z","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":"8819c2a3296ee6ed6c661b7f3e559f4c7d86797f63c51258ad75d7b129fb203c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-09-16T12:34:13Z","title_canon_sha256":"3deb0fe1b18ace0988782d7f35f347fb837ca547ef23f196b2dbe63d783f8d72"},"schema_version":"1.0","source":{"id":"1609.05024","kind":"arxiv","version":2}},"canonical_sha256":"0cb0869dc1b60c872e0518fef495797ff8454f1945015a4026f764cb586b3726","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0cb0869dc1b60c872e0518fef495797ff8454f1945015a4026f764cb586b3726","first_computed_at":"2026-05-18T00:48:26.416167Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:48:26.416167Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9+i/RLVFh8tq2zfxG6jYBXFbXY0L4tXLJd4BjvY6AaxlGyK1rJ5tzI0W/C6mc8SFuumO3PvU+G9yolN0SfT8BA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:48:26.416619Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.05024","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:30ee2b610345461bb3644714797796425a323b5ae3795756398c48bcb9ed0c15","sha256:cedeef6839061fa8dd72097f7625a5d626f9ca7deb58a898b739a97f74cf093f"],"state_sha256":"b73076bfa01a6a390dfafd37f617da81d6bef2c3a2f474320bcb0a4ca2437294"}