{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:Y4M37J2QLISYDL6ZBHTP6IUYRE","short_pith_number":"pith:Y4M37J2Q","canonical_record":{"source":{"id":"1210.7076","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-10-26T09:19:01Z","cross_cats_sorted":[],"title_canon_sha256":"777d61cd42f24078c5bf34974eb66cbc8e0fd47e80feaf053ae0f6134bd882ac","abstract_canon_sha256":"e9c6144f689a7365cbd07318dbadac15f6977f009acdb2932f0056b7584381ea"},"schema_version":"1.0"},"canonical_sha256":"c719bfa7505a2581afd909e6ff229889170878d46621f08fe253c7b7c29289f9","source":{"kind":"arxiv","id":"1210.7076","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.7076","created_at":"2026-05-18T03:42:12Z"},{"alias_kind":"arxiv_version","alias_value":"1210.7076v1","created_at":"2026-05-18T03:42:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.7076","created_at":"2026-05-18T03:42:12Z"},{"alias_kind":"pith_short_12","alias_value":"Y4M37J2QLISY","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_16","alias_value":"Y4M37J2QLISYDL6Z","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_8","alias_value":"Y4M37J2Q","created_at":"2026-05-18T12:27:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:Y4M37J2QLISYDL6ZBHTP6IUYRE","target":"record","payload":{"canonical_record":{"source":{"id":"1210.7076","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-10-26T09:19:01Z","cross_cats_sorted":[],"title_canon_sha256":"777d61cd42f24078c5bf34974eb66cbc8e0fd47e80feaf053ae0f6134bd882ac","abstract_canon_sha256":"e9c6144f689a7365cbd07318dbadac15f6977f009acdb2932f0056b7584381ea"},"schema_version":"1.0"},"canonical_sha256":"c719bfa7505a2581afd909e6ff229889170878d46621f08fe253c7b7c29289f9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:42:12.836830Z","signature_b64":"taiy86lCuOOToHoPJZ2iE2bYJiRGfPSM0ciWwPJndNrPEa60k4ygSd3IlYy5SpsgSntASNawAMGaVeawET6yBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c719bfa7505a2581afd909e6ff229889170878d46621f08fe253c7b7c29289f9","last_reissued_at":"2026-05-18T03:42:12.836211Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:42:12.836211Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1210.7076","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:42:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0bPHgM0I+/jzo7QcOngaaExrETwsG7IqnQwanuxd8f3GbF4PsJdzVA/hibmBPohlMfoBEa6h8pqHWrHNx3rlAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T22:26:23.100851Z"},"content_sha256":"a2d09bc895e71f8d8582ae318be9f6efe9584d997173238111ba3e95e67cc4e3","schema_version":"1.0","event_id":"sha256:a2d09bc895e71f8d8582ae318be9f6efe9584d997173238111ba3e95e67cc4e3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:Y4M37J2QLISYDL6ZBHTP6IUYRE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Efficient implementation of finite element methods on non-matching and overlapping meshes in 3D","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Anders Logg, Andr\\'e Massing, Mats G. Larson","submitted_at":"2012-10-26T09:19:01Z","abstract_excerpt":"In recent years, a number of finite element methods have been formulated for the solution of partial differential equations on complex geometries based on non-matching or overlapping meshes. Examples of such methods include the fictitious domain method, the extended finite element method, and Nitsche's method. In all of these methods, integrals must be computed over cut cells or subsimplices which is challenging to implement, especially in three space dimensions. In this note, we address the main challenges of such an implementation and demonstrate good performance of a fully general code for "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.7076","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"2026-05-18T03:42:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"24lgbNdEKDoanSiBUidbJgjuKlxkxDHVw824V5T2chjRGRkzCGWKLV9zefx3agIRghKyPZ3z9xn6cEkhyd+YBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T22:26:23.101354Z"},"content_sha256":"402fd94703849f3f1628bdb6a8440565f8949de60d746aaf2ff78cc53f34a30f","schema_version":"1.0","event_id":"sha256:402fd94703849f3f1628bdb6a8440565f8949de60d746aaf2ff78cc53f34a30f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Y4M37J2QLISYDL6ZBHTP6IUYRE/bundle.json","state_url":"https://pith.science/pith/Y4M37J2QLISYDL6ZBHTP6IUYRE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Y4M37J2QLISYDL6ZBHTP6IUYRE/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":"2026-05-30T22:26:23Z","links":{"resolver":"https://pith.science/pith/Y4M37J2QLISYDL6ZBHTP6IUYRE","bundle":"https://pith.science/pith/Y4M37J2QLISYDL6ZBHTP6IUYRE/bundle.json","state":"https://pith.science/pith/Y4M37J2QLISYDL6ZBHTP6IUYRE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Y4M37J2QLISYDL6ZBHTP6IUYRE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:Y4M37J2QLISYDL6ZBHTP6IUYRE","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":"e9c6144f689a7365cbd07318dbadac15f6977f009acdb2932f0056b7584381ea","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-10-26T09:19:01Z","title_canon_sha256":"777d61cd42f24078c5bf34974eb66cbc8e0fd47e80feaf053ae0f6134bd882ac"},"schema_version":"1.0","source":{"id":"1210.7076","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.7076","created_at":"2026-05-18T03:42:12Z"},{"alias_kind":"arxiv_version","alias_value":"1210.7076v1","created_at":"2026-05-18T03:42:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.7076","created_at":"2026-05-18T03:42:12Z"},{"alias_kind":"pith_short_12","alias_value":"Y4M37J2QLISY","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_16","alias_value":"Y4M37J2QLISYDL6Z","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_8","alias_value":"Y4M37J2Q","created_at":"2026-05-18T12:27:27Z"}],"graph_snapshots":[{"event_id":"sha256:402fd94703849f3f1628bdb6a8440565f8949de60d746aaf2ff78cc53f34a30f","target":"graph","created_at":"2026-05-18T03:42:12Z","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 recent years, a number of finite element methods have been formulated for the solution of partial differential equations on complex geometries based on non-matching or overlapping meshes. Examples of such methods include the fictitious domain method, the extended finite element method, and Nitsche's method. In all of these methods, integrals must be computed over cut cells or subsimplices which is challenging to implement, especially in three space dimensions. In this note, we address the main challenges of such an implementation and demonstrate good performance of a fully general code for ","authors_text":"Anders Logg, Andr\\'e Massing, Mats G. Larson","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-10-26T09:19:01Z","title":"Efficient implementation of finite element methods on non-matching and overlapping meshes in 3D"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.7076","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:a2d09bc895e71f8d8582ae318be9f6efe9584d997173238111ba3e95e67cc4e3","target":"record","created_at":"2026-05-18T03:42:12Z","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":"e9c6144f689a7365cbd07318dbadac15f6977f009acdb2932f0056b7584381ea","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-10-26T09:19:01Z","title_canon_sha256":"777d61cd42f24078c5bf34974eb66cbc8e0fd47e80feaf053ae0f6134bd882ac"},"schema_version":"1.0","source":{"id":"1210.7076","kind":"arxiv","version":1}},"canonical_sha256":"c719bfa7505a2581afd909e6ff229889170878d46621f08fe253c7b7c29289f9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c719bfa7505a2581afd909e6ff229889170878d46621f08fe253c7b7c29289f9","first_computed_at":"2026-05-18T03:42:12.836211Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:42:12.836211Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"taiy86lCuOOToHoPJZ2iE2bYJiRGfPSM0ciWwPJndNrPEa60k4ygSd3IlYy5SpsgSntASNawAMGaVeawET6yBg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:42:12.836830Z","signed_message":"canonical_sha256_bytes"},"source_id":"1210.7076","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a2d09bc895e71f8d8582ae318be9f6efe9584d997173238111ba3e95e67cc4e3","sha256:402fd94703849f3f1628bdb6a8440565f8949de60d746aaf2ff78cc53f34a30f"],"state_sha256":"628e41903e63ed2130bb7cdd05aaa6f455c6edb9fee13550b99d06cd00520907"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qAIYgDGzkEAh9fVrY1bj57wEddcIpoHyD1iUvN9nIJbrn1TtCsXHBmHmSzFfpPMZpG/MYixDs08aYBdyeeHABw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T22:26:23.104270Z","bundle_sha256":"d2d3b73d7180535a0ccc426976514dad4abb3558b1bebf894e07ba77757ed3eb"}}