{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:5CUPVGW7AH34BJHHSNX2PUO6ZP","short_pith_number":"pith:5CUPVGW7","schema_version":"1.0","canonical_sha256":"e8a8fa9adf01f7c0a4e7936fa7d1decbf520739d8ade9d830d51039d5eee4de3","source":{"kind":"arxiv","id":"1805.02950","version":1},"attestation_state":"computed","paper":{"title":"Weak-strong uniqueness of renormalized solutions to reaction-cross-diffusion systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ansgar J\\\"ungel, Xiuqing Chen","submitted_at":"2018-05-08T11:28:59Z","abstract_excerpt":"The weak-strong uniqueness for solutions to reaction-cross-diffusion systems in a bounded domain with no-flux boundary conditions is proved. The system generalizes the Shigesada-Kawasaki-Teramoto population model to an arbitrary number of species. The diffusion matrix is neither symmetric nor positive definite, but the system possesses a formal gradient-flow or entropy structure. No growth conditions on the source terms are imposed. It is shown that any renormalized solution coincides with a strong solution with the same initial data, as long as the strong solution exists. The proof is based o"},"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":"1805.02950","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-05-08T11:28:59Z","cross_cats_sorted":[],"title_canon_sha256":"0a0a20f11535a1532732ff42cbefcd8436dc3ba9517be1ed023bc5ade85aebcd","abstract_canon_sha256":"2fc8a9e1e0ecfb8e386b2dd7efba9ea594d5f03e9245b825dcc27daf74e739fc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:16:35.141978Z","signature_b64":"Y1+epbeS03qWVaawTGHDW2qYUmeAas2MDw03Xfev5mWdwssnGgPRnnx2Y1q7Hbu/LdFokf+5KIJFc3XDGso+AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e8a8fa9adf01f7c0a4e7936fa7d1decbf520739d8ade9d830d51039d5eee4de3","last_reissued_at":"2026-05-18T00:16:35.141433Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:16:35.141433Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Weak-strong uniqueness of renormalized solutions to reaction-cross-diffusion systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ansgar J\\\"ungel, Xiuqing Chen","submitted_at":"2018-05-08T11:28:59Z","abstract_excerpt":"The weak-strong uniqueness for solutions to reaction-cross-diffusion systems in a bounded domain with no-flux boundary conditions is proved. The system generalizes the Shigesada-Kawasaki-Teramoto population model to an arbitrary number of species. The diffusion matrix is neither symmetric nor positive definite, but the system possesses a formal gradient-flow or entropy structure. No growth conditions on the source terms are imposed. It is shown that any renormalized solution coincides with a strong solution with the same initial data, as long as the strong solution exists. The proof is based o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.02950","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":""},"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":"1805.02950","created_at":"2026-05-18T00:16:35.141514+00:00"},{"alias_kind":"arxiv_version","alias_value":"1805.02950v1","created_at":"2026-05-18T00:16:35.141514+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.02950","created_at":"2026-05-18T00:16:35.141514+00:00"},{"alias_kind":"pith_short_12","alias_value":"5CUPVGW7AH34","created_at":"2026-05-18T12:32:08.215937+00:00"},{"alias_kind":"pith_short_16","alias_value":"5CUPVGW7AH34BJHH","created_at":"2026-05-18T12:32:08.215937+00:00"},{"alias_kind":"pith_short_8","alias_value":"5CUPVGW7","created_at":"2026-05-18T12:32:08.215937+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/5CUPVGW7AH34BJHHSNX2PUO6ZP","json":"https://pith.science/pith/5CUPVGW7AH34BJHHSNX2PUO6ZP.json","graph_json":"https://pith.science/api/pith-number/5CUPVGW7AH34BJHHSNX2PUO6ZP/graph.json","events_json":"https://pith.science/api/pith-number/5CUPVGW7AH34BJHHSNX2PUO6ZP/events.json","paper":"https://pith.science/paper/5CUPVGW7"},"agent_actions":{"view_html":"https://pith.science/pith/5CUPVGW7AH34BJHHSNX2PUO6ZP","download_json":"https://pith.science/pith/5CUPVGW7AH34BJHHSNX2PUO6ZP.json","view_paper":"https://pith.science/paper/5CUPVGW7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1805.02950&json=true","fetch_graph":"https://pith.science/api/pith-number/5CUPVGW7AH34BJHHSNX2PUO6ZP/graph.json","fetch_events":"https://pith.science/api/pith-number/5CUPVGW7AH34BJHHSNX2PUO6ZP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5CUPVGW7AH34BJHHSNX2PUO6ZP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5CUPVGW7AH34BJHHSNX2PUO6ZP/action/storage_attestation","attest_author":"https://pith.science/pith/5CUPVGW7AH34BJHHSNX2PUO6ZP/action/author_attestation","sign_citation":"https://pith.science/pith/5CUPVGW7AH34BJHHSNX2PUO6ZP/action/citation_signature","submit_replication":"https://pith.science/pith/5CUPVGW7AH34BJHHSNX2PUO6ZP/action/replication_record"}},"created_at":"2026-05-18T00:16:35.141514+00:00","updated_at":"2026-05-18T00:16:35.141514+00:00"}