{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:RJJYK633ZFM5V5SBU33OPD4Q6R","short_pith_number":"pith:RJJYK633","schema_version":"1.0","canonical_sha256":"8a53857b7bc959daf641a6f6e78f90f47d53be053a5afbc40a4f8fbcebf52932","source":{"kind":"arxiv","id":"2505.08443","version":1},"attestation_state":"computed","paper":{"title":"A nonlocal-to-local approach to aggregation-diffusion equations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"q-bio.CB","authors_text":"Carles Falc\\'o, Jos\\'e A. Carrillo, Ruth E. Baker","submitted_at":"2025-05-13T11:09:43Z","abstract_excerpt":"Over the past decades, nonlocal models have been widely used to describe aggregation phenomena in biology, physics, engineering, and the social sciences. These are often derived as mean-field limits of attraction-repulsion agent-based models, and consist of systems of nonlocal partial differential equations. Using differential adhesion between cells as a biological case study, we introduce a novel local model of aggregation-diffusion phenomena. This system of local aggregation-diffusion equations is fourth-order, resembling thin-film or Cahn-Hilliard type equations. In this framework, cell sor"},"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":"2505.08443","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"q-bio.CB","submitted_at":"2025-05-13T11:09:43Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"1e9bce97e37b62075a268073934a643b74d7262c7531e6b44160f6f4bda7f5da","abstract_canon_sha256":"4e3d43fa98d1446b8ba8b2d4c2df4d7ee4d1cb85c9154e7a7d5042d6a7477731"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:02:30.509851Z","signature_b64":"XY/4JXWiLmq28znjhDPTd6koWh1TRKy4TQpIEJGo050t3A5H0z1X4BqwTPpvog2VzqxJyuQtgahtR85dwzoxDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8a53857b7bc959daf641a6f6e78f90f47d53be053a5afbc40a4f8fbcebf52932","last_reissued_at":"2026-07-05T11:02:30.509341Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:02:30.509341Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A nonlocal-to-local approach to aggregation-diffusion equations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"q-bio.CB","authors_text":"Carles Falc\\'o, Jos\\'e A. Carrillo, Ruth E. Baker","submitted_at":"2025-05-13T11:09:43Z","abstract_excerpt":"Over the past decades, nonlocal models have been widely used to describe aggregation phenomena in biology, physics, engineering, and the social sciences. These are often derived as mean-field limits of attraction-repulsion agent-based models, and consist of systems of nonlocal partial differential equations. Using differential adhesion between cells as a biological case study, we introduce a novel local model of aggregation-diffusion phenomena. This system of local aggregation-diffusion equations is fourth-order, resembling thin-film or Cahn-Hilliard type equations. In this framework, cell sor"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.08443","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/2505.08443/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":"2505.08443","created_at":"2026-07-05T11:02:30.509409+00:00"},{"alias_kind":"arxiv_version","alias_value":"2505.08443v1","created_at":"2026-07-05T11:02:30.509409+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.08443","created_at":"2026-07-05T11:02:30.509409+00:00"},{"alias_kind":"pith_short_12","alias_value":"RJJYK633ZFM5","created_at":"2026-07-05T11:02:30.509409+00:00"},{"alias_kind":"pith_short_16","alias_value":"RJJYK633ZFM5V5SB","created_at":"2026-07-05T11:02:30.509409+00:00"},{"alias_kind":"pith_short_8","alias_value":"RJJYK633","created_at":"2026-07-05T11:02:30.509409+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/RJJYK633ZFM5V5SBU33OPD4Q6R","json":"https://pith.science/pith/RJJYK633ZFM5V5SBU33OPD4Q6R.json","graph_json":"https://pith.science/api/pith-number/RJJYK633ZFM5V5SBU33OPD4Q6R/graph.json","events_json":"https://pith.science/api/pith-number/RJJYK633ZFM5V5SBU33OPD4Q6R/events.json","paper":"https://pith.science/paper/RJJYK633"},"agent_actions":{"view_html":"https://pith.science/pith/RJJYK633ZFM5V5SBU33OPD4Q6R","download_json":"https://pith.science/pith/RJJYK633ZFM5V5SBU33OPD4Q6R.json","view_paper":"https://pith.science/paper/RJJYK633","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2505.08443&json=true","fetch_graph":"https://pith.science/api/pith-number/RJJYK633ZFM5V5SBU33OPD4Q6R/graph.json","fetch_events":"https://pith.science/api/pith-number/RJJYK633ZFM5V5SBU33OPD4Q6R/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RJJYK633ZFM5V5SBU33OPD4Q6R/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RJJYK633ZFM5V5SBU33OPD4Q6R/action/storage_attestation","attest_author":"https://pith.science/pith/RJJYK633ZFM5V5SBU33OPD4Q6R/action/author_attestation","sign_citation":"https://pith.science/pith/RJJYK633ZFM5V5SBU33OPD4Q6R/action/citation_signature","submit_replication":"https://pith.science/pith/RJJYK633ZFM5V5SBU33OPD4Q6R/action/replication_record"}},"created_at":"2026-07-05T11:02:30.509409+00:00","updated_at":"2026-07-05T11:02:30.509409+00:00"}