{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:5TMWMSCYXV4JFSE7XRPDAWOUEO","short_pith_number":"pith:5TMWMSCY","schema_version":"1.0","canonical_sha256":"ecd9664858bd7892c89fbc5e3059d423b5b59e0aa093d94010e73b31cf5a95d1","source":{"kind":"arxiv","id":"2205.09822","version":2},"attestation_state":"computed","paper":{"title":"Regularisation and separation for evolving surface Cahn-Hilliard equations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Andrea Poiatti, Charles M. Elliott, Diogo Caetano, Maurizio Grasselli","submitted_at":"2022-05-19T19:50:03Z","abstract_excerpt":"We consider the Cahn-Hilliard equation with constant mobility and logarithmic potential on a two-dimensional evolving closed surface embedded in $\\mathbb R^3$, as well as a related weighted model. The well-posedness of weak solutions for the corresponding initial value problems on a given time interval $[0,T]$ have already been established by the first two authors. Here we first prove some regularisation properties of weak solutions in finite time. Then, we show the validity of the strict separation property for both the problems. This means that the solutions stay uniformly away from the pure"},"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":"2205.09822","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2022-05-19T19:50:03Z","cross_cats_sorted":[],"title_canon_sha256":"fa24c4a6064f65f0261deb3ee69b48d5db6492f8f340c8c80495b6e696a69e01","abstract_canon_sha256":"acdd6b9385183d9e94cdde57ba7e5d4456c59fb40801d0f78d9ea49825bd4d60"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:38:42.610085Z","signature_b64":"WA4+GFbmyLJhzCGQRtb+Z+prdLVJ64xiiaTiZPChjYQ0zmPLQq3jMXGMQ1g3b/xf6Zrd/Qs5pjV6nj8msBB1AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ecd9664858bd7892c89fbc5e3059d423b5b59e0aa093d94010e73b31cf5a95d1","last_reissued_at":"2026-07-05T05:38:42.609655Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:38:42.609655Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Regularisation and separation for evolving surface Cahn-Hilliard equations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Andrea Poiatti, Charles M. Elliott, Diogo Caetano, Maurizio Grasselli","submitted_at":"2022-05-19T19:50:03Z","abstract_excerpt":"We consider the Cahn-Hilliard equation with constant mobility and logarithmic potential on a two-dimensional evolving closed surface embedded in $\\mathbb R^3$, as well as a related weighted model. The well-posedness of weak solutions for the corresponding initial value problems on a given time interval $[0,T]$ have already been established by the first two authors. Here we first prove some regularisation properties of weak solutions in finite time. Then, we show the validity of the strict separation property for both the problems. This means that the solutions stay uniformly away from the pure"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2205.09822","kind":"arxiv","version":2},"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/2205.09822/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":"2205.09822","created_at":"2026-07-05T05:38:42.609718+00:00"},{"alias_kind":"arxiv_version","alias_value":"2205.09822v2","created_at":"2026-07-05T05:38:42.609718+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2205.09822","created_at":"2026-07-05T05:38:42.609718+00:00"},{"alias_kind":"pith_short_12","alias_value":"5TMWMSCYXV4J","created_at":"2026-07-05T05:38:42.609718+00:00"},{"alias_kind":"pith_short_16","alias_value":"5TMWMSCYXV4JFSE7","created_at":"2026-07-05T05:38:42.609718+00:00"},{"alias_kind":"pith_short_8","alias_value":"5TMWMSCY","created_at":"2026-07-05T05:38:42.609718+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/5TMWMSCYXV4JFSE7XRPDAWOUEO","json":"https://pith.science/pith/5TMWMSCYXV4JFSE7XRPDAWOUEO.json","graph_json":"https://pith.science/api/pith-number/5TMWMSCYXV4JFSE7XRPDAWOUEO/graph.json","events_json":"https://pith.science/api/pith-number/5TMWMSCYXV4JFSE7XRPDAWOUEO/events.json","paper":"https://pith.science/paper/5TMWMSCY"},"agent_actions":{"view_html":"https://pith.science/pith/5TMWMSCYXV4JFSE7XRPDAWOUEO","download_json":"https://pith.science/pith/5TMWMSCYXV4JFSE7XRPDAWOUEO.json","view_paper":"https://pith.science/paper/5TMWMSCY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2205.09822&json=true","fetch_graph":"https://pith.science/api/pith-number/5TMWMSCYXV4JFSE7XRPDAWOUEO/graph.json","fetch_events":"https://pith.science/api/pith-number/5TMWMSCYXV4JFSE7XRPDAWOUEO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5TMWMSCYXV4JFSE7XRPDAWOUEO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5TMWMSCYXV4JFSE7XRPDAWOUEO/action/storage_attestation","attest_author":"https://pith.science/pith/5TMWMSCYXV4JFSE7XRPDAWOUEO/action/author_attestation","sign_citation":"https://pith.science/pith/5TMWMSCYXV4JFSE7XRPDAWOUEO/action/citation_signature","submit_replication":"https://pith.science/pith/5TMWMSCYXV4JFSE7XRPDAWOUEO/action/replication_record"}},"created_at":"2026-07-05T05:38:42.609718+00:00","updated_at":"2026-07-05T05:38:42.609718+00:00"}