{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:TZ5R566E72TUSYOVDC7ALQTCF6","short_pith_number":"pith:TZ5R566E","canonical_record":{"source":{"id":"1908.04910","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-08-14T01:32:51Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"5168ead8ec121d0d0f742ef7f579a78aaacf23cfe8e43b615416ad7269aa2ee4","abstract_canon_sha256":"145e8851270ca0811c2a4bfda363d1babd3a119e930e5685508f9c3476e45905"},"schema_version":"1.0"},"canonical_sha256":"9e7b1efbc4fea74961d518be05c2622f83f6b3c9c495cca8edcdaf40c36d7cda","source":{"kind":"arxiv","id":"1908.04910","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:TZ5R566E72TUSYOVDC7ALQTCF6","target":"record","payload":{"canonical_record":{"source":{"id":"1908.04910","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-08-14T01:32:51Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"5168ead8ec121d0d0f742ef7f579a78aaacf23cfe8e43b615416ad7269aa2ee4","abstract_canon_sha256":"145e8851270ca0811c2a4bfda363d1babd3a119e930e5685508f9c3476e45905"},"schema_version":"1.0"},"canonical_sha256":"9e7b1efbc4fea74961d518be05c2622f83f6b3c9c495cca8edcdaf40c36d7cda","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:19:53.206682Z","signature_b64":"AssVJxcqHXT1TMq3ooUhLLxfPwsIr8MjdUChNMxDQmcP7k5Mu2JgeBSeJIl3posF7ForML5kcL4g0dMIPuigBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9e7b1efbc4fea74961d518be05c2622f83f6b3c9c495cca8edcdaf40c36d7cda","last_reissued_at":"2026-07-05T02:19:53.206289Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:19:53.206289Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1908.04910","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T02:19:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PD9lxZDkZ0ubbABTmpPyQJicaSpXWIFEdJhHnrJK1T+AsXSFPGw+Ewa7kMeA2eEsg7PqNwRelWQU/xObcws/Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T03:40:28.677935Z"},"content_sha256":"1f50a54829efe7be7b3fef9d8cf4649de7cad49e6caaccccbc7de58283cd6ae7","schema_version":"1.0","event_id":"sha256:1f50a54829efe7be7b3fef9d8cf4649de7cad49e6caaccccbc7de58283cd6ae7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:TZ5R566E72TUSYOVDC7ALQTCF6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An efficient and convergent finite element scheme for Cahn--Hilliard equations with dynamic boundary conditions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Stefan Metzger","submitted_at":"2019-08-14T01:32:51Z","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 "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.04910","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/1908.04910/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T02:19:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pIzIbGSPnWNWkCkaHJR3bsK0CbjYv0fhKcaieaSPhi6rp/O3Z7To2Xt6HxbhMr28HceA+uFJFrWFcRJUQKxhAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T03:40:28.678442Z"},"content_sha256":"391cfdd14640fb380fa8362d50e26e84fbd0e13957e29bcf357c9f742dc1abac","schema_version":"1.0","event_id":"sha256:391cfdd14640fb380fa8362d50e26e84fbd0e13957e29bcf357c9f742dc1abac"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TZ5R566E72TUSYOVDC7ALQTCF6/bundle.json","state_url":"https://pith.science/pith/TZ5R566E72TUSYOVDC7ALQTCF6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TZ5R566E72TUSYOVDC7ALQTCF6/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-16T03:40:28Z","links":{"resolver":"https://pith.science/pith/TZ5R566E72TUSYOVDC7ALQTCF6","bundle":"https://pith.science/pith/TZ5R566E72TUSYOVDC7ALQTCF6/bundle.json","state":"https://pith.science/pith/TZ5R566E72TUSYOVDC7ALQTCF6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TZ5R566E72TUSYOVDC7ALQTCF6/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"x5i6RTCncv0ZO3umLfRYSUoG6v6P3jYuqPBAnB/5QfyfWsde+PCpLa1r4Is4dUoyhA09Odi68p6cNDG7fa6eAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T03:40:28.683978Z","bundle_sha256":"c6c04958a8ab8b55156341c2d164333229722e02e05daf15e07cc59125becb3c"}}