{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:YUAS7N4NH6HYZG2GZAFB2AKK6L","short_pith_number":"pith:YUAS7N4N","schema_version":"1.0","canonical_sha256":"c5012fb78d3f8f8c9b46c80a1d014af2d467904ac70aace0ae7cf43e00d2a904","source":{"kind":"arxiv","id":"2606.25783","version":1},"attestation_state":"computed","paper":{"title":"Non-uniqueness of weak solutions to cross-diffusion systems with advection","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ansgar J\\\"ungel, Jakub Skrzeczkowski, Jos\\'e A. Carrillo, Yao Yao","submitted_at":"2026-06-24T13:00:38Z","abstract_excerpt":"A cross-diffusion system with advection is considered on the whole line, describing the dynamics of two segregating population species. Starting from two initial densities supported on the half-lines $x\\leq 0$ and $x\\geq 0$, respectively, we construct two distinct solutions of the system: one pair of densities remains confined to their initial supports and stay completely segregated, while the second pair of densities begins to invade the opposite half-line after a finite time (mixing). To the best of our knowledge, this provides one of the first examples of non-uniqueness for this class of eq"},"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":"2606.25783","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-06-24T13:00:38Z","cross_cats_sorted":[],"title_canon_sha256":"5db7b3ca4fc7bc57b4234eb9634fd062fc8adce5b66fbafff5134950922cea00","abstract_canon_sha256":"dbe580528fe94e2e890eb844b787c763ac6304fcd435b4d3aec79dc83d656d27"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-25T01:18:15.042241Z","signature_b64":"0wHHiu+x/rrFULO6I7wdxkEVtcIPmh5s6f3u76psDuF6Q1bsaBYv7aLdZihRqyrab4QkhJ+IYwATqVfDpxxiBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c5012fb78d3f8f8c9b46c80a1d014af2d467904ac70aace0ae7cf43e00d2a904","last_reissued_at":"2026-06-25T01:18:15.041892Z","signature_status":"signed_v1","first_computed_at":"2026-06-25T01:18:15.041892Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Non-uniqueness of weak solutions to cross-diffusion systems with advection","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ansgar J\\\"ungel, Jakub Skrzeczkowski, Jos\\'e A. Carrillo, Yao Yao","submitted_at":"2026-06-24T13:00:38Z","abstract_excerpt":"A cross-diffusion system with advection is considered on the whole line, describing the dynamics of two segregating population species. Starting from two initial densities supported on the half-lines $x\\leq 0$ and $x\\geq 0$, respectively, we construct two distinct solutions of the system: one pair of densities remains confined to their initial supports and stay completely segregated, while the second pair of densities begins to invade the opposite half-line after a finite time (mixing). To the best of our knowledge, this provides one of the first examples of non-uniqueness for this class of eq"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.25783","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.25783/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2606.25783","created_at":"2026-06-25T01:18:15.041958+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.25783v1","created_at":"2026-06-25T01:18:15.041958+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.25783","created_at":"2026-06-25T01:18:15.041958+00:00"},{"alias_kind":"pith_short_12","alias_value":"YUAS7N4NH6HY","created_at":"2026-06-25T01:18:15.041958+00:00"},{"alias_kind":"pith_short_16","alias_value":"YUAS7N4NH6HYZG2G","created_at":"2026-06-25T01:18:15.041958+00:00"},{"alias_kind":"pith_short_8","alias_value":"YUAS7N4N","created_at":"2026-06-25T01:18:15.041958+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/YUAS7N4NH6HYZG2GZAFB2AKK6L","json":"https://pith.science/pith/YUAS7N4NH6HYZG2GZAFB2AKK6L.json","graph_json":"https://pith.science/api/pith-number/YUAS7N4NH6HYZG2GZAFB2AKK6L/graph.json","events_json":"https://pith.science/api/pith-number/YUAS7N4NH6HYZG2GZAFB2AKK6L/events.json","paper":"https://pith.science/paper/YUAS7N4N"},"agent_actions":{"view_html":"https://pith.science/pith/YUAS7N4NH6HYZG2GZAFB2AKK6L","download_json":"https://pith.science/pith/YUAS7N4NH6HYZG2GZAFB2AKK6L.json","view_paper":"https://pith.science/paper/YUAS7N4N","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.25783&json=true","fetch_graph":"https://pith.science/api/pith-number/YUAS7N4NH6HYZG2GZAFB2AKK6L/graph.json","fetch_events":"https://pith.science/api/pith-number/YUAS7N4NH6HYZG2GZAFB2AKK6L/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YUAS7N4NH6HYZG2GZAFB2AKK6L/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YUAS7N4NH6HYZG2GZAFB2AKK6L/action/storage_attestation","attest_author":"https://pith.science/pith/YUAS7N4NH6HYZG2GZAFB2AKK6L/action/author_attestation","sign_citation":"https://pith.science/pith/YUAS7N4NH6HYZG2GZAFB2AKK6L/action/citation_signature","submit_replication":"https://pith.science/pith/YUAS7N4NH6HYZG2GZAFB2AKK6L/action/replication_record"}},"created_at":"2026-06-25T01:18:15.041958+00:00","updated_at":"2026-06-25T01:18:15.041958+00:00"}