{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:DJA3RFFVFQN3SUPIOHF7ZS4EWD","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":"e6857ac36077a68351eac79d1663140a5789234f9619a82fbea01bdd122d367d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-07-21T13:57:30Z","title_canon_sha256":"8cfff0c332b9677cd5a7441bb40742887ed5760f95e1eb42a34fccc21ea7acd8"},"schema_version":"1.0","source":{"id":"1507.05835","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.05835","created_at":"2026-05-18T01:36:32Z"},{"alias_kind":"arxiv_version","alias_value":"1507.05835v1","created_at":"2026-05-18T01:36:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.05835","created_at":"2026-05-18T01:36:32Z"},{"alias_kind":"pith_short_12","alias_value":"DJA3RFFVFQN3","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_16","alias_value":"DJA3RFFVFQN3SUPI","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_8","alias_value":"DJA3RFFV","created_at":"2026-05-18T12:29:17Z"}],"graph_snapshots":[{"event_id":"sha256:264814ef7db9f5adeed29341bd39812ac053b304a9c8d3c86c7164790ba1ccce","target":"graph","created_at":"2026-05-18T01:36:32Z","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":"We develop a discontinuous cut finite element method (CutFEM) for the Laplace-Beltrami operator on a hypersurface embedded in $\\mathbb{R}^d$. The method is constructed by using a discontinuous piecewise linear finite element space defined on a background mesh in $\\mathbb{R}^d$. The surface is approximated by a continuous piecewise linear surface that cuts through the background mesh in an arbitrary fashion. Then a discontinuous Galerkin method is formulated on the discrete surface and in order to obtain coercivity, certain stabilization terms are added on the faces between neighboring elements","authors_text":"Andre Massing, Erik Burman, Mats G. Larson, Peter Hansbo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-07-21T13:57:30Z","title":"A Cut Discontinuous Galerkin Method for the Laplace-Beltrami Operator"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.05835","kind":"arxiv","version":1},"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:d943231d669164e82212673c4994dd4f2c88ab537db7df4e003d698df30016e5","target":"record","created_at":"2026-05-18T01:36:32Z","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":"e6857ac36077a68351eac79d1663140a5789234f9619a82fbea01bdd122d367d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-07-21T13:57:30Z","title_canon_sha256":"8cfff0c332b9677cd5a7441bb40742887ed5760f95e1eb42a34fccc21ea7acd8"},"schema_version":"1.0","source":{"id":"1507.05835","kind":"arxiv","version":1}},"canonical_sha256":"1a41b894b52c1bb951e871cbfccb84b0efa937852bb02e1325c401f02e7f3f92","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1a41b894b52c1bb951e871cbfccb84b0efa937852bb02e1325c401f02e7f3f92","first_computed_at":"2026-05-18T01:36:32.309029Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:36:32.309029Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bdpQwqoHbDMLR4wo70gYlQjUiv6Ed1R02r4vvj1fb5O2PcNLNpNO+nmvEqJk33KNMC6J5WJ0z5GW1fUQAJeJBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:36:32.309495Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.05835","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d943231d669164e82212673c4994dd4f2c88ab537db7df4e003d698df30016e5","sha256:264814ef7db9f5adeed29341bd39812ac053b304a9c8d3c86c7164790ba1ccce"],"state_sha256":"fad3d9e9778d9686104b1321e62e8cc8058c53664d41c682ffdbc372447579d5"}