{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:67DYXT3BQYNT5RJMLTGK2XG7TM","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":"f85d8ef713e87b26b4af131559104117d1c193018ab184c05458ca1f36db5745","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-04-23T03:02:27Z","title_canon_sha256":"012f58624e14271291230ad1edf1b43cdc07621ac932c8149d693d7fb8f50249"},"schema_version":"1.0","source":{"id":"1304.6155","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.6155","created_at":"2026-05-18T02:54:39Z"},{"alias_kind":"arxiv_version","alias_value":"1304.6155v3","created_at":"2026-05-18T02:54:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.6155","created_at":"2026-05-18T02:54:39Z"},{"alias_kind":"pith_short_12","alias_value":"67DYXT3BQYNT","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_16","alias_value":"67DYXT3BQYNT5RJM","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_8","alias_value":"67DYXT3B","created_at":"2026-05-18T12:27:36Z"}],"graph_snapshots":[{"event_id":"sha256:2692fcae3bd1b73bc00731344728a67d7864ae39eae2607195ea9b0813b9391e","target":"graph","created_at":"2026-05-18T02:54:39Z","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"},"paper":{"abstract_excerpt":"In this paper, we study numerical methods for the solution of partial differential equations on evolving surfaces. The evolving hypersurface in $\\Bbb{R}^d$ defines a $d$-dimensional space-time manifold in the space-time continuum $\\Bbb{R}^{d+1}$. We derive and analyze a variational formulation for a class of diffusion problems on the space-time manifold. For this variational formulation new well-posedness and stability results are derived. The analysis is based on an inf-sup condition and involves some natural, but non-standard, (anisotropic) function spaces. Based on this formulation a discre","authors_text":"Arnold Reusken, Maxim A. Olshanskii, Xianmin Xu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-04-23T03:02:27Z","title":"An Eulerian space-time finite element method for diffusion problems on evolving surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.6155","kind":"arxiv","version":3},"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:ee5f0a6d4017234d4f9bbe6d58d0b96b84308a0eab90fd27f4e4b55a81f813b6","target":"record","created_at":"2026-05-18T02:54:39Z","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":"f85d8ef713e87b26b4af131559104117d1c193018ab184c05458ca1f36db5745","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-04-23T03:02:27Z","title_canon_sha256":"012f58624e14271291230ad1edf1b43cdc07621ac932c8149d693d7fb8f50249"},"schema_version":"1.0","source":{"id":"1304.6155","kind":"arxiv","version":3}},"canonical_sha256":"f7c78bcf61861b3ec52c5cccad5cdf9b1c73b1055f3d55124de26998e55e981a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f7c78bcf61861b3ec52c5cccad5cdf9b1c73b1055f3d55124de26998e55e981a","first_computed_at":"2026-05-18T02:54:39.634731Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:54:39.634731Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Uxmk3b3BA+zBXiBsvyKikJZ738yKc/yr08boJS17H7ZInSb9vyEGUsSIoF+5D1WBd2FF2fm290mprbE5MSmXBw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:54:39.635158Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.6155","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ee5f0a6d4017234d4f9bbe6d58d0b96b84308a0eab90fd27f4e4b55a81f813b6","sha256:2692fcae3bd1b73bc00731344728a67d7864ae39eae2607195ea9b0813b9391e"],"state_sha256":"4bc045417d7963307812e0ce2a4caa124041c20ab5e2706c5938d4b9d1254f80"}