{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:QOYGAT2QXJELD3E46O5TPXH5BF","short_pith_number":"pith:QOYGAT2Q","schema_version":"1.0","canonical_sha256":"83b0604f50ba48b1ec9cf3bb37dcfd0953d7ff9ce87dfec751868f49355392d8","source":{"kind":"arxiv","id":"2502.03847","version":2},"attestation_state":"computed","paper":{"title":"Error estimates for full discretization by an almost mass conservation technique for Cahn--Hilliard systems with dynamic boundary conditions","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Nils Bullerjahn","submitted_at":"2025-02-06T07:56:31Z","abstract_excerpt":"A proof of optimal-order error estimates is given for the full discretization of the bulk--surface Cahn--Hilliard system with dynamic boundary conditions in a smooth domain. The numerical method combines a linear bulk--surface finite element discretization in space and linearly implicit backward difference formulae of order one to five in time. The error estimates are obtained by a consistency and stability analysis, based on an energy estimate and the novel approach of exploiting the almost mass conservation of the error equations to derive a Poincar\\'e-type inequality. We demonstrate how thi"},"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":"2502.03847","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.NA","submitted_at":"2025-02-06T07:56:31Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"f153ce46189db2bf766050642b0189428787e3f26b59d49b4362d8ca20a47cbb","abstract_canon_sha256":"971efef841e0963cac9c1cc00a0ffff93370b36718efb72d626a6752f5766d4d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-02T02:04:46.237786Z","signature_b64":"To13eMgG2yOT/tdV5oHAR3ASDjh7c2G7Omkoze/gUGA1xb9J5HQ/86K5KQ/NsC3zjggUjhsqTCKcmYQGVWtiCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"83b0604f50ba48b1ec9cf3bb37dcfd0953d7ff9ce87dfec751868f49355392d8","last_reissued_at":"2026-06-02T02:04:46.237141Z","signature_status":"signed_v1","first_computed_at":"2026-06-02T02:04:46.237141Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Error estimates for full discretization by an almost mass conservation technique for Cahn--Hilliard systems with dynamic boundary conditions","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Nils Bullerjahn","submitted_at":"2025-02-06T07:56:31Z","abstract_excerpt":"A proof of optimal-order error estimates is given for the full discretization of the bulk--surface Cahn--Hilliard system with dynamic boundary conditions in a smooth domain. The numerical method combines a linear bulk--surface finite element discretization in space and linearly implicit backward difference formulae of order one to five in time. The error estimates are obtained by a consistency and stability analysis, based on an energy estimate and the novel approach of exploiting the almost mass conservation of the error equations to derive a Poincar\\'e-type inequality. We demonstrate how thi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.03847","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/2502.03847/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":"2502.03847","created_at":"2026-06-02T02:04:46.237207+00:00"},{"alias_kind":"arxiv_version","alias_value":"2502.03847v2","created_at":"2026-06-02T02:04:46.237207+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.03847","created_at":"2026-06-02T02:04:46.237207+00:00"},{"alias_kind":"pith_short_12","alias_value":"QOYGAT2QXJEL","created_at":"2026-06-02T02:04:46.237207+00:00"},{"alias_kind":"pith_short_16","alias_value":"QOYGAT2QXJELD3E4","created_at":"2026-06-02T02:04:46.237207+00:00"},{"alias_kind":"pith_short_8","alias_value":"QOYGAT2Q","created_at":"2026-06-02T02:04:46.237207+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2507.01618","citing_title":"A Thermodynamically Consistent Free Boundary Model for Two-Phase Flows in an Evolving Domain with Bulk-Surface Interaction","ref_index":20,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/QOYGAT2QXJELD3E46O5TPXH5BF","json":"https://pith.science/pith/QOYGAT2QXJELD3E46O5TPXH5BF.json","graph_json":"https://pith.science/api/pith-number/QOYGAT2QXJELD3E46O5TPXH5BF/graph.json","events_json":"https://pith.science/api/pith-number/QOYGAT2QXJELD3E46O5TPXH5BF/events.json","paper":"https://pith.science/paper/QOYGAT2Q"},"agent_actions":{"view_html":"https://pith.science/pith/QOYGAT2QXJELD3E46O5TPXH5BF","download_json":"https://pith.science/pith/QOYGAT2QXJELD3E46O5TPXH5BF.json","view_paper":"https://pith.science/paper/QOYGAT2Q","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2502.03847&json=true","fetch_graph":"https://pith.science/api/pith-number/QOYGAT2QXJELD3E46O5TPXH5BF/graph.json","fetch_events":"https://pith.science/api/pith-number/QOYGAT2QXJELD3E46O5TPXH5BF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QOYGAT2QXJELD3E46O5TPXH5BF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QOYGAT2QXJELD3E46O5TPXH5BF/action/storage_attestation","attest_author":"https://pith.science/pith/QOYGAT2QXJELD3E46O5TPXH5BF/action/author_attestation","sign_citation":"https://pith.science/pith/QOYGAT2QXJELD3E46O5TPXH5BF/action/citation_signature","submit_replication":"https://pith.science/pith/QOYGAT2QXJELD3E46O5TPXH5BF/action/replication_record"}},"created_at":"2026-06-02T02:04:46.237207+00:00","updated_at":"2026-06-02T02:04:46.237207+00:00"}