{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:GPGBVHS4ZXD2HDPDM32SR3CTC7","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":"c203f21917bc2de76f6ddcb0135c88f59080cb5abb16b98775579716385196dd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-10-04T15:27:21Z","title_canon_sha256":"caa4d6d03e3544bb2b40d675ab1fc50057c9cd54a5a73044f2e127d747e9df8a"},"schema_version":"1.0","source":{"id":"1710.01653","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.01653","created_at":"2026-05-18T00:33:40Z"},{"alias_kind":"arxiv_version","alias_value":"1710.01653v1","created_at":"2026-05-18T00:33:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.01653","created_at":"2026-05-18T00:33:40Z"},{"alias_kind":"pith_short_12","alias_value":"GPGBVHS4ZXD2","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_16","alias_value":"GPGBVHS4ZXD2HDPD","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_8","alias_value":"GPGBVHS4","created_at":"2026-05-18T12:31:18Z"}],"graph_snapshots":[{"event_id":"sha256:0bd1f9d74b7b590f5dea8671c8e5ae3940b885ef963a4207b8f4c2ec5c537a71","target":"graph","created_at":"2026-05-18T00:33:40Z","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":"We investigate a class of systems of partial differential equations with nonlinear cross-diffusion and nonlocal interactions, which are of interest in several contexts in social sciences, finance, biology, and real world applications. Assuming a uniform \"coerciveness\" assumption on the diffusion part, which allows to consider a large class of systems with degenerate cross-diffusion (i.e. of porous medium type) and relaxes sets of assumptions previously considered in the literature, we prove global-in-time existence of weak solutions by means of a semi-implicit version of the Jordan-Kinderlehre","authors_text":"A. Esposito, M. Di Francesco, S. Fagioli","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-10-04T15:27:21Z","title":"Nonlinear degenerate cross-diffusion systems with nonlocal interaction"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.01653","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":"sha256:45a94c776eb1d9e44b2e4a478b4f4e8b11ef7f22031c7023357ff3de5fabaa2f","target":"record","created_at":"2026-05-18T00:33:40Z","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":"c203f21917bc2de76f6ddcb0135c88f59080cb5abb16b98775579716385196dd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-10-04T15:27:21Z","title_canon_sha256":"caa4d6d03e3544bb2b40d675ab1fc50057c9cd54a5a73044f2e127d747e9df8a"},"schema_version":"1.0","source":{"id":"1710.01653","kind":"arxiv","version":1}},"canonical_sha256":"33cc1a9e5ccdc7a38de366f528ec5317ca0f27b68bbdf3f47d2c775e07138180","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"33cc1a9e5ccdc7a38de366f528ec5317ca0f27b68bbdf3f47d2c775e07138180","first_computed_at":"2026-05-18T00:33:40.282458Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:33:40.282458Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CNyqZL0VQgqvd5R+C+YAMmouy+BfCnuVXhZNmjOoXew14t7sEE/gc8h4YKqLOPYong0YguM9nnIJEP+j/n4jAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:33:40.283089Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.01653","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:45a94c776eb1d9e44b2e4a478b4f4e8b11ef7f22031c7023357ff3de5fabaa2f","sha256:0bd1f9d74b7b590f5dea8671c8e5ae3940b885ef963a4207b8f4c2ec5c537a71"],"state_sha256":"27dc822e80d2e848365bcbd6c5e6d053ef794b9ac773e3bc5aff5ce32ad50aab"}