{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:TZ5R566E72TUSYOVDC7ALQTCF6","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"145e8851270ca0811c2a4bfda363d1babd3a119e930e5685508f9c3476e45905","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-08-14T01:32:51Z","title_canon_sha256":"5168ead8ec121d0d0f742ef7f579a78aaacf23cfe8e43b615416ad7269aa2ee4"},"schema_version":"1.0","source":{"id":"1908.04910","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.04910","created_at":"2026-07-05T02:19:53Z"},{"alias_kind":"arxiv_version","alias_value":"1908.04910v2","created_at":"2026-07-05T02:19:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.04910","created_at":"2026-07-05T02:19:53Z"},{"alias_kind":"pith_short_12","alias_value":"TZ5R566E72TU","created_at":"2026-07-05T02:19:53Z"},{"alias_kind":"pith_short_16","alias_value":"TZ5R566E72TUSYOV","created_at":"2026-07-05T02:19:53Z"},{"alias_kind":"pith_short_8","alias_value":"TZ5R566E","created_at":"2026-07-05T02:19:53Z"}],"graph_snapshots":[{"event_id":"sha256:391cfdd14640fb380fa8362d50e26e84fbd0e13957e29bcf357c9f742dc1abac","target":"graph","created_at":"2026-07-05T02:19:53Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1908.04910/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The Cahn--Hilliard equation is a widely used model that describes amongst others phase separation processes of binary mixtures or two-phase flows. In the recent years, different types of boundary conditions for the Cahn--Hilliard equation were proposed and analyzed. In this publication, we are concerned with the numerical treatment of a recent model which introduces an additional Cahn--Hilliard type equation on the boundary as closure for the Cahn--Hilliard equation in the domain [C. Liu, H. Wu, Arch. Ration. Mech. An., 2019]. By identifying a mapping between the phase-field parameter and the ","authors_text":"Stefan Metzger","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-08-14T01:32:51Z","title":"An efficient and convergent finite element scheme for Cahn--Hilliard equations with dynamic boundary conditions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.04910","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:1f50a54829efe7be7b3fef9d8cf4649de7cad49e6caaccccbc7de58283cd6ae7","target":"record","created_at":"2026-07-05T02:19:53Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"145e8851270ca0811c2a4bfda363d1babd3a119e930e5685508f9c3476e45905","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-08-14T01:32:51Z","title_canon_sha256":"5168ead8ec121d0d0f742ef7f579a78aaacf23cfe8e43b615416ad7269aa2ee4"},"schema_version":"1.0","source":{"id":"1908.04910","kind":"arxiv","version":2}},"canonical_sha256":"9e7b1efbc4fea74961d518be05c2622f83f6b3c9c495cca8edcdaf40c36d7cda","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9e7b1efbc4fea74961d518be05c2622f83f6b3c9c495cca8edcdaf40c36d7cda","first_computed_at":"2026-07-05T02:19:53.206289Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:19:53.206289Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AssVJxcqHXT1TMq3ooUhLLxfPwsIr8MjdUChNMxDQmcP7k5Mu2JgeBSeJIl3posF7ForML5kcL4g0dMIPuigBw==","signature_status":"signed_v1","signed_at":"2026-07-05T02:19:53.206682Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.04910","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1f50a54829efe7be7b3fef9d8cf4649de7cad49e6caaccccbc7de58283cd6ae7","sha256:391cfdd14640fb380fa8362d50e26e84fbd0e13957e29bcf357c9f742dc1abac"],"state_sha256":"4d075691619ed137d2b089a0ef6226da6468dc0b859b7ba74dc9dad88649d814"}