{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:PYJ7CB2P4X5F5UGVI7SRER7VXI","short_pith_number":"pith:PYJ7CB2P","schema_version":"1.0","canonical_sha256":"7e13f1074fe5fa5ed0d547e51247f5ba1ce106fb19fc492312fef5a4b9f0e7a8","source":{"kind":"arxiv","id":"2412.20188","version":1},"attestation_state":"computed","paper":{"title":"Nonlocal approximation of an anisotropic cross-diffusion system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Markus Schmidtchen, Tomasz D\\k{e}biec","submitted_at":"2024-12-28T16:01:46Z","abstract_excerpt":"Localisation limits and nonlocal approximations of degenerate parabolic systems have experienced a renaissance in recent years. However, only few results cover anisotropic systems. This work addresses this gap by establishing the nonlocal-to-limit for a specific anisotropic cross-diffusion system encountered in population dynamics featuring phase-separation phenomena, i.e., internal layers between different species. A critical element of the proof is an entropy dissipation identity, which we show to hold for any weak solution."},"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":"2412.20188","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-12-28T16:01:46Z","cross_cats_sorted":[],"title_canon_sha256":"34a76006d963926f685a8e3e5299c1f2db349caead40b46d396906652c70574b","abstract_canon_sha256":"e14e6c0b6b6d37694f6fbe353fb26019bf0597337b861f15549349ca8c6611ad"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:54:55.740361Z","signature_b64":"MGz4XsQcMrtEx70xtnPANIJ8syJo1IPs/6o45HbpuTlHoWggg/ZylWgvsDOPgTDWUbxxQkqSo41ZhuR+Y3FzAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7e13f1074fe5fa5ed0d547e51247f5ba1ce106fb19fc492312fef5a4b9f0e7a8","last_reissued_at":"2026-07-05T09:54:55.739863Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:54:55.739863Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Nonlocal approximation of an anisotropic cross-diffusion system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Markus Schmidtchen, Tomasz D\\k{e}biec","submitted_at":"2024-12-28T16:01:46Z","abstract_excerpt":"Localisation limits and nonlocal approximations of degenerate parabolic systems have experienced a renaissance in recent years. However, only few results cover anisotropic systems. This work addresses this gap by establishing the nonlocal-to-limit for a specific anisotropic cross-diffusion system encountered in population dynamics featuring phase-separation phenomena, i.e., internal layers between different species. A critical element of the proof is an entropy dissipation identity, which we show to hold for any weak solution."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.20188","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/2412.20188/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":"2412.20188","created_at":"2026-07-05T09:54:55.739924+00:00"},{"alias_kind":"arxiv_version","alias_value":"2412.20188v1","created_at":"2026-07-05T09:54:55.739924+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.20188","created_at":"2026-07-05T09:54:55.739924+00:00"},{"alias_kind":"pith_short_12","alias_value":"PYJ7CB2P4X5F","created_at":"2026-07-05T09:54:55.739924+00:00"},{"alias_kind":"pith_short_16","alias_value":"PYJ7CB2P4X5F5UGV","created_at":"2026-07-05T09:54:55.739924+00:00"},{"alias_kind":"pith_short_8","alias_value":"PYJ7CB2P","created_at":"2026-07-05T09:54:55.739924+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/PYJ7CB2P4X5F5UGVI7SRER7VXI","json":"https://pith.science/pith/PYJ7CB2P4X5F5UGVI7SRER7VXI.json","graph_json":"https://pith.science/api/pith-number/PYJ7CB2P4X5F5UGVI7SRER7VXI/graph.json","events_json":"https://pith.science/api/pith-number/PYJ7CB2P4X5F5UGVI7SRER7VXI/events.json","paper":"https://pith.science/paper/PYJ7CB2P"},"agent_actions":{"view_html":"https://pith.science/pith/PYJ7CB2P4X5F5UGVI7SRER7VXI","download_json":"https://pith.science/pith/PYJ7CB2P4X5F5UGVI7SRER7VXI.json","view_paper":"https://pith.science/paper/PYJ7CB2P","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2412.20188&json=true","fetch_graph":"https://pith.science/api/pith-number/PYJ7CB2P4X5F5UGVI7SRER7VXI/graph.json","fetch_events":"https://pith.science/api/pith-number/PYJ7CB2P4X5F5UGVI7SRER7VXI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PYJ7CB2P4X5F5UGVI7SRER7VXI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PYJ7CB2P4X5F5UGVI7SRER7VXI/action/storage_attestation","attest_author":"https://pith.science/pith/PYJ7CB2P4X5F5UGVI7SRER7VXI/action/author_attestation","sign_citation":"https://pith.science/pith/PYJ7CB2P4X5F5UGVI7SRER7VXI/action/citation_signature","submit_replication":"https://pith.science/pith/PYJ7CB2P4X5F5UGVI7SRER7VXI/action/replication_record"}},"created_at":"2026-07-05T09:54:55.739924+00:00","updated_at":"2026-07-05T09:54:55.739924+00:00"}