{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:AMWTAOPCGSNV3RIQ2AMY7ZEINE","short_pith_number":"pith:AMWTAOPC","schema_version":"1.0","canonical_sha256":"032d3039e2349b5dc510d0198fe488693e00cdb1bc7a1dbc3a4bba82ab5af4af","source":{"kind":"arxiv","id":"2411.13969","version":1},"attestation_state":"computed","paper":{"title":"Continuum of coupled Wasserstein gradient flows","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Bernhard Schmitzer, Cl\\'ement Canc\\`es, Daniel Matthes, Ismael Medina","submitted_at":"2024-11-21T09:34:08Z","abstract_excerpt":"We study a system of drift-diffusion PDEs for a potentially infinite number of incompressible phases, subject to a joint pointwise volume constraint. Our analysis is based on the interpretation as a collection of coupled Wasserstein gradient flows or, equivalently, as a gradient flow in the space of couplings under a `fibered' Wasserstein distance. We prove existence of weak solutions, long-time asymptotics, and stability with respect to the mass distribution of the phases, including the discrete to continuous limit. A key step is to establish convergence of the product of pressure gradient an"},"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":"2411.13969","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2024-11-21T09:34:08Z","cross_cats_sorted":[],"title_canon_sha256":"9d16d20d0a22f95e8552e5ea1aea0b8a50e6dad5a7a3bfa23ed24ec381349293","abstract_canon_sha256":"d77a9e4471fdc955b18a8bba71702a42ece1260eeefb4e3ad0410e3dae72e4bc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:38:39.624584Z","signature_b64":"+tq9FHL3qMpykznQEASkf8nXJ33PJ9YmjSMEcai5VwpdkE3oDIcDcLlExP5p3nR4KafBsF4XPY+r+qaBHvlRCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"032d3039e2349b5dc510d0198fe488693e00cdb1bc7a1dbc3a4bba82ab5af4af","last_reissued_at":"2026-07-05T09:38:39.624112Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:38:39.624112Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Continuum of coupled Wasserstein gradient flows","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Bernhard Schmitzer, Cl\\'ement Canc\\`es, Daniel Matthes, Ismael Medina","submitted_at":"2024-11-21T09:34:08Z","abstract_excerpt":"We study a system of drift-diffusion PDEs for a potentially infinite number of incompressible phases, subject to a joint pointwise volume constraint. Our analysis is based on the interpretation as a collection of coupled Wasserstein gradient flows or, equivalently, as a gradient flow in the space of couplings under a `fibered' Wasserstein distance. We prove existence of weak solutions, long-time asymptotics, and stability with respect to the mass distribution of the phases, including the discrete to continuous limit. A key step is to establish convergence of the product of pressure gradient an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.13969","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/2411.13969/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":"2411.13969","created_at":"2026-07-05T09:38:39.624180+00:00"},{"alias_kind":"arxiv_version","alias_value":"2411.13969v1","created_at":"2026-07-05T09:38:39.624180+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.13969","created_at":"2026-07-05T09:38:39.624180+00:00"},{"alias_kind":"pith_short_12","alias_value":"AMWTAOPCGSNV","created_at":"2026-07-05T09:38:39.624180+00:00"},{"alias_kind":"pith_short_16","alias_value":"AMWTAOPCGSNV3RIQ","created_at":"2026-07-05T09:38:39.624180+00:00"},{"alias_kind":"pith_short_8","alias_value":"AMWTAOPC","created_at":"2026-07-05T09:38:39.624180+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/AMWTAOPCGSNV3RIQ2AMY7ZEINE","json":"https://pith.science/pith/AMWTAOPCGSNV3RIQ2AMY7ZEINE.json","graph_json":"https://pith.science/api/pith-number/AMWTAOPCGSNV3RIQ2AMY7ZEINE/graph.json","events_json":"https://pith.science/api/pith-number/AMWTAOPCGSNV3RIQ2AMY7ZEINE/events.json","paper":"https://pith.science/paper/AMWTAOPC"},"agent_actions":{"view_html":"https://pith.science/pith/AMWTAOPCGSNV3RIQ2AMY7ZEINE","download_json":"https://pith.science/pith/AMWTAOPCGSNV3RIQ2AMY7ZEINE.json","view_paper":"https://pith.science/paper/AMWTAOPC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2411.13969&json=true","fetch_graph":"https://pith.science/api/pith-number/AMWTAOPCGSNV3RIQ2AMY7ZEINE/graph.json","fetch_events":"https://pith.science/api/pith-number/AMWTAOPCGSNV3RIQ2AMY7ZEINE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AMWTAOPCGSNV3RIQ2AMY7ZEINE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AMWTAOPCGSNV3RIQ2AMY7ZEINE/action/storage_attestation","attest_author":"https://pith.science/pith/AMWTAOPCGSNV3RIQ2AMY7ZEINE/action/author_attestation","sign_citation":"https://pith.science/pith/AMWTAOPCGSNV3RIQ2AMY7ZEINE/action/citation_signature","submit_replication":"https://pith.science/pith/AMWTAOPCGSNV3RIQ2AMY7ZEINE/action/replication_record"}},"created_at":"2026-07-05T09:38:39.624180+00:00","updated_at":"2026-07-05T09:38:39.624180+00:00"}