{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:HUMQBBCKJL25NJ5WAVVMACRQ5F","short_pith_number":"pith:HUMQBBCK","schema_version":"1.0","canonical_sha256":"3d1900844a4af5d6a7b6056ac00a30e962ad428060f92cf9838dd38cbcb6f4c2","source":{"kind":"arxiv","id":"2205.04365","version":1},"attestation_state":"computed","paper":{"title":"Traveling wave solution for a coupled incompressible Darcy's free boundary problem with surface tension","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Martina Magliocca, Nicolas Meunier, Thomas Alazard","submitted_at":"2022-05-09T15:05:32Z","abstract_excerpt":"We study an incompressible Darcy's free boundary problem, recently introduced in [22]. Our goal is to prove the existence of non-trivial traveling wave solutions and thus validate the interest of this model to describe cell motility. The model equations include a convection diffusion equation for the polarity marker concentration and the incompressible Darcy's equation. The mathematical novelty of this problem is the nonlinear destabilizing term in the boundary condition that describes the active character of the cell cytoskeleton. We first study the linear stability of this problem and we sho"},"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":"2205.04365","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2022-05-09T15:05:32Z","cross_cats_sorted":[],"title_canon_sha256":"e5376d8a2719cba3f127c40c8da9a9b8c2fe2ad6b1dc87e228116f94123688a8","abstract_canon_sha256":"0c5fc4871d1de859c8f917a78b8460548bbba31ceaeb03ea85c6234268825130"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:21:24.190835Z","signature_b64":"jrL8E7Mlz3Ww+VM7xwyAbLxlAomykT9s9pq7aEryRij8J0nOvr3t7zstb8JmEH74CD7T6MkRNwpLqx/kvsB0BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3d1900844a4af5d6a7b6056ac00a30e962ad428060f92cf9838dd38cbcb6f4c2","last_reissued_at":"2026-07-05T04:21:24.188570Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:21:24.188570Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Traveling wave solution for a coupled incompressible Darcy's free boundary problem with surface tension","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Martina Magliocca, Nicolas Meunier, Thomas Alazard","submitted_at":"2022-05-09T15:05:32Z","abstract_excerpt":"We study an incompressible Darcy's free boundary problem, recently introduced in [22]. Our goal is to prove the existence of non-trivial traveling wave solutions and thus validate the interest of this model to describe cell motility. The model equations include a convection diffusion equation for the polarity marker concentration and the incompressible Darcy's equation. The mathematical novelty of this problem is the nonlinear destabilizing term in the boundary condition that describes the active character of the cell cytoskeleton. We first study the linear stability of this problem and we sho"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2205.04365","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/2205.04365/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":"2205.04365","created_at":"2026-07-05T04:21:24.190409+00:00"},{"alias_kind":"arxiv_version","alias_value":"2205.04365v1","created_at":"2026-07-05T04:21:24.190409+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2205.04365","created_at":"2026-07-05T04:21:24.190409+00:00"},{"alias_kind":"pith_short_12","alias_value":"HUMQBBCKJL25","created_at":"2026-07-05T04:21:24.190409+00:00"},{"alias_kind":"pith_short_16","alias_value":"HUMQBBCKJL25NJ5W","created_at":"2026-07-05T04:21:24.190409+00:00"},{"alias_kind":"pith_short_8","alias_value":"HUMQBBCK","created_at":"2026-07-05T04:21:24.190409+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2506.03138","citing_title":"Change of bifurcation type in 2D free boundary model of a moving cell with nonlinear diffusion","ref_index":2,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/HUMQBBCKJL25NJ5WAVVMACRQ5F","json":"https://pith.science/pith/HUMQBBCKJL25NJ5WAVVMACRQ5F.json","graph_json":"https://pith.science/api/pith-number/HUMQBBCKJL25NJ5WAVVMACRQ5F/graph.json","events_json":"https://pith.science/api/pith-number/HUMQBBCKJL25NJ5WAVVMACRQ5F/events.json","paper":"https://pith.science/paper/HUMQBBCK"},"agent_actions":{"view_html":"https://pith.science/pith/HUMQBBCKJL25NJ5WAVVMACRQ5F","download_json":"https://pith.science/pith/HUMQBBCKJL25NJ5WAVVMACRQ5F.json","view_paper":"https://pith.science/paper/HUMQBBCK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2205.04365&json=true","fetch_graph":"https://pith.science/api/pith-number/HUMQBBCKJL25NJ5WAVVMACRQ5F/graph.json","fetch_events":"https://pith.science/api/pith-number/HUMQBBCKJL25NJ5WAVVMACRQ5F/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HUMQBBCKJL25NJ5WAVVMACRQ5F/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HUMQBBCKJL25NJ5WAVVMACRQ5F/action/storage_attestation","attest_author":"https://pith.science/pith/HUMQBBCKJL25NJ5WAVVMACRQ5F/action/author_attestation","sign_citation":"https://pith.science/pith/HUMQBBCKJL25NJ5WAVVMACRQ5F/action/citation_signature","submit_replication":"https://pith.science/pith/HUMQBBCKJL25NJ5WAVVMACRQ5F/action/replication_record"}},"created_at":"2026-07-05T04:21:24.190409+00:00","updated_at":"2026-07-05T04:21:24.190409+00:00"}