{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:5RRF37NOQR3CUY5OD7HUGEL3ED","short_pith_number":"pith:5RRF37NO","canonical_record":{"source":{"id":"1809.10354","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-09-27T05:54:24Z","cross_cats_sorted":[],"title_canon_sha256":"d7edc0d7baffb2352b0cd9f90e877fc9ca7d5a79219f9aad164434c5193e4863","abstract_canon_sha256":"d37fb0106edabcb9dc668df05a4100446932d65d99dd024a8d0438a87fcd0539"},"schema_version":"1.0"},"canonical_sha256":"ec625dfdae84762a63ae1fcf43117b20c404f901669a9d275625f4a2ba40e795","source":{"kind":"arxiv","id":"1809.10354","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.10354","created_at":"2026-05-18T00:04:38Z"},{"alias_kind":"arxiv_version","alias_value":"1809.10354v1","created_at":"2026-05-18T00:04:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.10354","created_at":"2026-05-18T00:04:38Z"},{"alias_kind":"pith_short_12","alias_value":"5RRF37NOQR3C","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_16","alias_value":"5RRF37NOQR3CUY5O","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_8","alias_value":"5RRF37NO","created_at":"2026-05-18T12:32:08Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:5RRF37NOQR3CUY5OD7HUGEL3ED","target":"record","payload":{"canonical_record":{"source":{"id":"1809.10354","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-09-27T05:54:24Z","cross_cats_sorted":[],"title_canon_sha256":"d7edc0d7baffb2352b0cd9f90e877fc9ca7d5a79219f9aad164434c5193e4863","abstract_canon_sha256":"d37fb0106edabcb9dc668df05a4100446932d65d99dd024a8d0438a87fcd0539"},"schema_version":"1.0"},"canonical_sha256":"ec625dfdae84762a63ae1fcf43117b20c404f901669a9d275625f4a2ba40e795","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:04:38.526614Z","signature_b64":"t/n3hOeXhQMiVvV0ZM/eutj8Q7AXreejPy2PONjO6rsqYj3PgqUS2X7dkkPdO7z4MoPSchLQjbBTznecvVHTDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ec625dfdae84762a63ae1fcf43117b20c404f901669a9d275625f4a2ba40e795","last_reissued_at":"2026-05-18T00:04:38.526004Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:04:38.526004Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1809.10354","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":"2026-05-18T00:04:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gQ0MsWGy8YeQTzCLPQ8VegD30jZoaRcaEkoz9ffRON+fZKVDWE6Nm4NzW2lJk/nhymOL8iM6BeWyRvBcKbE/Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T04:42:23.130664Z"},"content_sha256":"468c1a6e221a6f7c6d7e29e09f6a0c77990efd816ded51253a46e76c48e1da41","schema_version":"1.0","event_id":"sha256:468c1a6e221a6f7c6d7e29e09f6a0c77990efd816ded51253a46e76c48e1da41"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:5RRF37NOQR3CUY5OD7HUGEL3ED","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Geometric Transformation of Finite Element Methods: Theory and Applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"M. Holst, M. Licht","submitted_at":"2018-09-27T05:54:24Z","abstract_excerpt":"We present a new technique to apply finite element methods to partial differential equations over curved domains. A change of variables along a coordinate transformation satisfying only low regularity assumptions can translate a Poisson problem over a curved physical domain to a Poisson problem over a polyhedral parametric domain. This greatly simplifies both the geometric setting and the practical implementation, at the cost of having globally rough non-trivial coefficients and data in the parametric Poisson problem. Our main result is that a recently developed broken Bramble-Hilbert lemma is"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.10354","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":"2026-05-18T00:04:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9PGS0Ve1hjmtIukQljdgodLUY/pOwYxIeVQ6qpF4iV5mZvsrELMAEyeRKlaf7VKU7e4ocjvl7L1A7PNtp5TfCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T04:42:23.131039Z"},"content_sha256":"152152e37cf80260af342207ebe01dc473630c3435829192d090ecec9dfec295","schema_version":"1.0","event_id":"sha256:152152e37cf80260af342207ebe01dc473630c3435829192d090ecec9dfec295"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5RRF37NOQR3CUY5OD7HUGEL3ED/bundle.json","state_url":"https://pith.science/pith/5RRF37NOQR3CUY5OD7HUGEL3ED/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5RRF37NOQR3CUY5OD7HUGEL3ED/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":"2026-06-29T04:42:23Z","links":{"resolver":"https://pith.science/pith/5RRF37NOQR3CUY5OD7HUGEL3ED","bundle":"https://pith.science/pith/5RRF37NOQR3CUY5OD7HUGEL3ED/bundle.json","state":"https://pith.science/pith/5RRF37NOQR3CUY5OD7HUGEL3ED/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5RRF37NOQR3CUY5OD7HUGEL3ED/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:5RRF37NOQR3CUY5OD7HUGEL3ED","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":"d37fb0106edabcb9dc668df05a4100446932d65d99dd024a8d0438a87fcd0539","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-09-27T05:54:24Z","title_canon_sha256":"d7edc0d7baffb2352b0cd9f90e877fc9ca7d5a79219f9aad164434c5193e4863"},"schema_version":"1.0","source":{"id":"1809.10354","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.10354","created_at":"2026-05-18T00:04:38Z"},{"alias_kind":"arxiv_version","alias_value":"1809.10354v1","created_at":"2026-05-18T00:04:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.10354","created_at":"2026-05-18T00:04:38Z"},{"alias_kind":"pith_short_12","alias_value":"5RRF37NOQR3C","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_16","alias_value":"5RRF37NOQR3CUY5O","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_8","alias_value":"5RRF37NO","created_at":"2026-05-18T12:32:08Z"}],"graph_snapshots":[{"event_id":"sha256:152152e37cf80260af342207ebe01dc473630c3435829192d090ecec9dfec295","target":"graph","created_at":"2026-05-18T00:04:38Z","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 present a new technique to apply finite element methods to partial differential equations over curved domains. A change of variables along a coordinate transformation satisfying only low regularity assumptions can translate a Poisson problem over a curved physical domain to a Poisson problem over a polyhedral parametric domain. This greatly simplifies both the geometric setting and the practical implementation, at the cost of having globally rough non-trivial coefficients and data in the parametric Poisson problem. Our main result is that a recently developed broken Bramble-Hilbert lemma is","authors_text":"M. Holst, M. Licht","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-09-27T05:54:24Z","title":"Geometric Transformation of Finite Element Methods: Theory and Applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.10354","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":"sha256:468c1a6e221a6f7c6d7e29e09f6a0c77990efd816ded51253a46e76c48e1da41","target":"record","created_at":"2026-05-18T00:04:38Z","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":"d37fb0106edabcb9dc668df05a4100446932d65d99dd024a8d0438a87fcd0539","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-09-27T05:54:24Z","title_canon_sha256":"d7edc0d7baffb2352b0cd9f90e877fc9ca7d5a79219f9aad164434c5193e4863"},"schema_version":"1.0","source":{"id":"1809.10354","kind":"arxiv","version":1}},"canonical_sha256":"ec625dfdae84762a63ae1fcf43117b20c404f901669a9d275625f4a2ba40e795","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ec625dfdae84762a63ae1fcf43117b20c404f901669a9d275625f4a2ba40e795","first_computed_at":"2026-05-18T00:04:38.526004Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:04:38.526004Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"t/n3hOeXhQMiVvV0ZM/eutj8Q7AXreejPy2PONjO6rsqYj3PgqUS2X7dkkPdO7z4MoPSchLQjbBTznecvVHTDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:04:38.526614Z","signed_message":"canonical_sha256_bytes"},"source_id":"1809.10354","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:468c1a6e221a6f7c6d7e29e09f6a0c77990efd816ded51253a46e76c48e1da41","sha256:152152e37cf80260af342207ebe01dc473630c3435829192d090ecec9dfec295"],"state_sha256":"03a3aabdc5667f7f14728683fab41a3f0759729a1c9a35bc61337eef475d33fc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7vavVroI5uMl/hj5UqIvRGmYVfDTCFAOjiH0qFj5rEdLUYHAkcINcEghaWHV2ey4Cogi/RrKfk9nu6kM2gQhAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-29T04:42:23.133023Z","bundle_sha256":"a4622b9dbe9d155b46383923cfa28e96f5924494a8828efa3393a09230abfd3f"}}