{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:XSRGGF6ITMY4AWQXC3SRGMF3DL","short_pith_number":"pith:XSRGGF6I","canonical_record":{"source":{"id":"1612.00054","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-11-30T22:07:46Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"db2118743ee8f72294811536c4e6c627bb8c0c3afc0fd598b112f473a7fc43c6","abstract_canon_sha256":"9752914ca37f77828ad560f979fa954063108d98201971ebfceba7ae076e4471"},"schema_version":"1.0"},"canonical_sha256":"bca26317c89b31c05a1716e51330bb1ad89984d5bbe62742651057b7331a9273","source":{"kind":"arxiv","id":"1612.00054","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.00054","created_at":"2026-05-18T00:40:53Z"},{"alias_kind":"arxiv_version","alias_value":"1612.00054v2","created_at":"2026-05-18T00:40:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.00054","created_at":"2026-05-18T00:40:53Z"},{"alias_kind":"pith_short_12","alias_value":"XSRGGF6ITMY4","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_16","alias_value":"XSRGGF6ITMY4AWQX","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_8","alias_value":"XSRGGF6I","created_at":"2026-05-18T12:30:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:XSRGGF6ITMY4AWQXC3SRGMF3DL","target":"record","payload":{"canonical_record":{"source":{"id":"1612.00054","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-11-30T22:07:46Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"db2118743ee8f72294811536c4e6c627bb8c0c3afc0fd598b112f473a7fc43c6","abstract_canon_sha256":"9752914ca37f77828ad560f979fa954063108d98201971ebfceba7ae076e4471"},"schema_version":"1.0"},"canonical_sha256":"bca26317c89b31c05a1716e51330bb1ad89984d5bbe62742651057b7331a9273","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:40:53.941878Z","signature_b64":"XeiP+pAR38eKpNFzL9ECD0XJMBvKziZYWaG0rXrBwr7RbLV7mEPsqpmlsdR5PpqRddVqDUheayMcYMspPxfmCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bca26317c89b31c05a1716e51330bb1ad89984d5bbe62742651057b7331a9273","last_reissued_at":"2026-05-18T00:40:53.941416Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:40:53.941416Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1612.00054","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":"2026-05-18T00:40:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iKvpqWSRidUST8VHztSSQ6eWoMJGLU0tYRjXPBM/Gs2rbOUocbLM7BnnVkwRePWeTS710tRvEcDITiFyQAunAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T15:10:05.830478Z"},"content_sha256":"fd8d7ed29d5c62580f71e440d0a0c74bb74eeb73eba02bf1c5f7b763deae3bf0","schema_version":"1.0","event_id":"sha256:fd8d7ed29d5c62580f71e440d0a0c74bb74eeb73eba02bf1c5f7b763deae3bf0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:XSRGGF6ITMY4AWQXC3SRGMF3DL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Trace Finite Element Methods for PDEs on Surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.NA","authors_text":"Arnold Reusken, Maxim A. Olshanskii","submitted_at":"2016-11-30T22:07:46Z","abstract_excerpt":"In this paper we consider a class of unfitted finite element methods for discretization of partial differential equations on surfaces. In this class of methods known as the Trace Finite Element Method (TraceFEM), restrictions or traces of background surface-independent finite element functions are used to approximate the solution of a PDE on a surface. We treat equations on steady and time-dependent (evolving) surfaces. Higher order TraceFEM is explained in detail. We review the error analysis and algebraic properties of the method. The paper navigates through the known variants of the TraceFE"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.00054","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":""},"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":"2026-05-18T00:40:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"D174u/4kA74Y95rf5agYI0ntp+A4xaspUfnu8ZuxbzNjGgNu8uyZL7Fx8ISnEvaZXnuyfi/t4YNontOFwq31Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T15:10:05.830828Z"},"content_sha256":"01107e082ae45235ef8b36b90fd68ab8b05ec0aac4619fdff4a9301231dd0b69","schema_version":"1.0","event_id":"sha256:01107e082ae45235ef8b36b90fd68ab8b05ec0aac4619fdff4a9301231dd0b69"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XSRGGF6ITMY4AWQXC3SRGMF3DL/bundle.json","state_url":"https://pith.science/pith/XSRGGF6ITMY4AWQXC3SRGMF3DL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XSRGGF6ITMY4AWQXC3SRGMF3DL/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":"2026-06-09T15:10:05Z","links":{"resolver":"https://pith.science/pith/XSRGGF6ITMY4AWQXC3SRGMF3DL","bundle":"https://pith.science/pith/XSRGGF6ITMY4AWQXC3SRGMF3DL/bundle.json","state":"https://pith.science/pith/XSRGGF6ITMY4AWQXC3SRGMF3DL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XSRGGF6ITMY4AWQXC3SRGMF3DL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:XSRGGF6ITMY4AWQXC3SRGMF3DL","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":"9752914ca37f77828ad560f979fa954063108d98201971ebfceba7ae076e4471","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-11-30T22:07:46Z","title_canon_sha256":"db2118743ee8f72294811536c4e6c627bb8c0c3afc0fd598b112f473a7fc43c6"},"schema_version":"1.0","source":{"id":"1612.00054","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.00054","created_at":"2026-05-18T00:40:53Z"},{"alias_kind":"arxiv_version","alias_value":"1612.00054v2","created_at":"2026-05-18T00:40:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.00054","created_at":"2026-05-18T00:40:53Z"},{"alias_kind":"pith_short_12","alias_value":"XSRGGF6ITMY4","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_16","alias_value":"XSRGGF6ITMY4AWQX","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_8","alias_value":"XSRGGF6I","created_at":"2026-05-18T12:30:51Z"}],"graph_snapshots":[{"event_id":"sha256:01107e082ae45235ef8b36b90fd68ab8b05ec0aac4619fdff4a9301231dd0b69","target":"graph","created_at":"2026-05-18T00:40:53Z","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"},"paper":{"abstract_excerpt":"In this paper we consider a class of unfitted finite element methods for discretization of partial differential equations on surfaces. In this class of methods known as the Trace Finite Element Method (TraceFEM), restrictions or traces of background surface-independent finite element functions are used to approximate the solution of a PDE on a surface. We treat equations on steady and time-dependent (evolving) surfaces. Higher order TraceFEM is explained in detail. We review the error analysis and algebraic properties of the method. The paper navigates through the known variants of the TraceFE","authors_text":"Arnold Reusken, Maxim A. Olshanskii","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-11-30T22:07:46Z","title":"Trace Finite Element Methods for PDEs on Surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.00054","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:fd8d7ed29d5c62580f71e440d0a0c74bb74eeb73eba02bf1c5f7b763deae3bf0","target":"record","created_at":"2026-05-18T00:40:53Z","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":"9752914ca37f77828ad560f979fa954063108d98201971ebfceba7ae076e4471","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-11-30T22:07:46Z","title_canon_sha256":"db2118743ee8f72294811536c4e6c627bb8c0c3afc0fd598b112f473a7fc43c6"},"schema_version":"1.0","source":{"id":"1612.00054","kind":"arxiv","version":2}},"canonical_sha256":"bca26317c89b31c05a1716e51330bb1ad89984d5bbe62742651057b7331a9273","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bca26317c89b31c05a1716e51330bb1ad89984d5bbe62742651057b7331a9273","first_computed_at":"2026-05-18T00:40:53.941416Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:40:53.941416Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XeiP+pAR38eKpNFzL9ECD0XJMBvKziZYWaG0rXrBwr7RbLV7mEPsqpmlsdR5PpqRddVqDUheayMcYMspPxfmCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:40:53.941878Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.00054","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fd8d7ed29d5c62580f71e440d0a0c74bb74eeb73eba02bf1c5f7b763deae3bf0","sha256:01107e082ae45235ef8b36b90fd68ab8b05ec0aac4619fdff4a9301231dd0b69"],"state_sha256":"61611fa21db032b1543f95e6fd974a952e9da6a21eafaae61af9e28ecbbc5d97"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EPcN6vrC/sHEC2u8mvz4ys7mCSxOEDgW7dT1UrpP3OZ4yuK9KxLOwoCp5ONB4E1ttPiUZkHz3G2lS7aE0snkAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T15:10:05.832829Z","bundle_sha256":"5fc3c7d051ee00ecdf19dd89b0244d30f3ca8984a5b21ddaadd0eb37cde00d3d"}}