{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:JXSMUNUQV7N7TNRV3ZT4BXNAMT","short_pith_number":"pith:JXSMUNUQ","canonical_record":{"source":{"id":"1402.2117","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-02-10T11:39:18Z","cross_cats_sorted":[],"title_canon_sha256":"3d5c8e49f38e0e6fe9687b02f3d88527f76602b0cb2fde93ebefffb3eb53da00","abstract_canon_sha256":"bd872f1a640d95902f1b22708a3bccc2eca70a92732c8fa2b7c690421b2876da"},"schema_version":"1.0"},"canonical_sha256":"4de4ca3690afdbf9b635de67c0dda064ccd617f8a7fa2712c461f972b369179e","source":{"kind":"arxiv","id":"1402.2117","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.2117","created_at":"2026-05-18T02:59:32Z"},{"alias_kind":"arxiv_version","alias_value":"1402.2117v1","created_at":"2026-05-18T02:59:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.2117","created_at":"2026-05-18T02:59:32Z"},{"alias_kind":"pith_short_12","alias_value":"JXSMUNUQV7N7","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_16","alias_value":"JXSMUNUQV7N7TNRV","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_8","alias_value":"JXSMUNUQ","created_at":"2026-05-18T12:28:35Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:JXSMUNUQV7N7TNRV3ZT4BXNAMT","target":"record","payload":{"canonical_record":{"source":{"id":"1402.2117","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-02-10T11:39:18Z","cross_cats_sorted":[],"title_canon_sha256":"3d5c8e49f38e0e6fe9687b02f3d88527f76602b0cb2fde93ebefffb3eb53da00","abstract_canon_sha256":"bd872f1a640d95902f1b22708a3bccc2eca70a92732c8fa2b7c690421b2876da"},"schema_version":"1.0"},"canonical_sha256":"4de4ca3690afdbf9b635de67c0dda064ccd617f8a7fa2712c461f972b369179e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:59:32.261527Z","signature_b64":"j6ifYt6n87bco0E+X3GihI/D1n/PsNyKvHfvSmZ9gUalSPMWw2SGyjp+WdQEdREMkvRS0lU+QvSzi47E9+5aCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4de4ca3690afdbf9b635de67c0dda064ccd617f8a7fa2712c461f972b369179e","last_reissued_at":"2026-05-18T02:59:32.260797Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:59:32.260797Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1402.2117","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":"2026-05-18T02:59:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AF0T8RzOEUxBx1cWS03qdo9RKaPKyq+L/o3QW/QTGxFeFpTdtRLvXxHvEAyrjIIxbJqY+HPsHZp2e8UkkC/SCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T04:30:51.458061Z"},"content_sha256":"c892c48817e08f09eaf80872fbdee7379794789a856c06fdf7bfb9789b9e0cb4","schema_version":"1.0","event_id":"sha256:c892c48817e08f09eaf80872fbdee7379794789a856c06fdf7bfb9789b9e0cb4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:JXSMUNUQV7N7TNRV3ZT4BXNAMT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Adaptive discontinuous Galerkin methods on surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Andreas Dedner, Pravin Madhavan","submitted_at":"2014-02-10T11:39:18Z","abstract_excerpt":"We present a dual weighted residual-based a posteriori error estimate for a discontinuous Galerkin (DG) approximation of a linear second-order elliptic problem on compact smooth connected and oriented surfaces in $\\mathbb{R}^{3}$ which are implicitly represented as level sets of a smooth function. We show that the error in the energy norm may be split into a \"residual part\" and a higher order \"geometric part\". Upper and lower bounds for the resulting a posteriori error estimator are proven and we consider a number of challenging test problems to demonstrate the reliability and efficiency of th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.2117","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":"2026-05-18T02:59:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3YIc6cdn9YwV3p8786/gizpLOQUvX++thoZlhgmQuErN9JcUX+gXnGmcaeDEkt8ImC3CW364sJYVuQeTkR2XBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T04:30:51.458438Z"},"content_sha256":"73826e0060f9d68d86226e277eec993e0663b429b6797f1833e60b641b9811e9","schema_version":"1.0","event_id":"sha256:73826e0060f9d68d86226e277eec993e0663b429b6797f1833e60b641b9811e9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JXSMUNUQV7N7TNRV3ZT4BXNAMT/bundle.json","state_url":"https://pith.science/pith/JXSMUNUQV7N7TNRV3ZT4BXNAMT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JXSMUNUQV7N7TNRV3ZT4BXNAMT/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":"2026-06-21T04:30:51Z","links":{"resolver":"https://pith.science/pith/JXSMUNUQV7N7TNRV3ZT4BXNAMT","bundle":"https://pith.science/pith/JXSMUNUQV7N7TNRV3ZT4BXNAMT/bundle.json","state":"https://pith.science/pith/JXSMUNUQV7N7TNRV3ZT4BXNAMT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JXSMUNUQV7N7TNRV3ZT4BXNAMT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:JXSMUNUQV7N7TNRV3ZT4BXNAMT","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":"bd872f1a640d95902f1b22708a3bccc2eca70a92732c8fa2b7c690421b2876da","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-02-10T11:39:18Z","title_canon_sha256":"3d5c8e49f38e0e6fe9687b02f3d88527f76602b0cb2fde93ebefffb3eb53da00"},"schema_version":"1.0","source":{"id":"1402.2117","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.2117","created_at":"2026-05-18T02:59:32Z"},{"alias_kind":"arxiv_version","alias_value":"1402.2117v1","created_at":"2026-05-18T02:59:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.2117","created_at":"2026-05-18T02:59:32Z"},{"alias_kind":"pith_short_12","alias_value":"JXSMUNUQV7N7","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_16","alias_value":"JXSMUNUQV7N7TNRV","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_8","alias_value":"JXSMUNUQ","created_at":"2026-05-18T12:28:35Z"}],"graph_snapshots":[{"event_id":"sha256:73826e0060f9d68d86226e277eec993e0663b429b6797f1833e60b641b9811e9","target":"graph","created_at":"2026-05-18T02:59:32Z","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 present a dual weighted residual-based a posteriori error estimate for a discontinuous Galerkin (DG) approximation of a linear second-order elliptic problem on compact smooth connected and oriented surfaces in $\\mathbb{R}^{3}$ which are implicitly represented as level sets of a smooth function. We show that the error in the energy norm may be split into a \"residual part\" and a higher order \"geometric part\". Upper and lower bounds for the resulting a posteriori error estimator are proven and we consider a number of challenging test problems to demonstrate the reliability and efficiency of th","authors_text":"Andreas Dedner, Pravin Madhavan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-02-10T11:39:18Z","title":"Adaptive discontinuous Galerkin methods on surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.2117","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:c892c48817e08f09eaf80872fbdee7379794789a856c06fdf7bfb9789b9e0cb4","target":"record","created_at":"2026-05-18T02:59:32Z","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":"bd872f1a640d95902f1b22708a3bccc2eca70a92732c8fa2b7c690421b2876da","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-02-10T11:39:18Z","title_canon_sha256":"3d5c8e49f38e0e6fe9687b02f3d88527f76602b0cb2fde93ebefffb3eb53da00"},"schema_version":"1.0","source":{"id":"1402.2117","kind":"arxiv","version":1}},"canonical_sha256":"4de4ca3690afdbf9b635de67c0dda064ccd617f8a7fa2712c461f972b369179e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4de4ca3690afdbf9b635de67c0dda064ccd617f8a7fa2712c461f972b369179e","first_computed_at":"2026-05-18T02:59:32.260797Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:59:32.260797Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"j6ifYt6n87bco0E+X3GihI/D1n/PsNyKvHfvSmZ9gUalSPMWw2SGyjp+WdQEdREMkvRS0lU+QvSzi47E9+5aCg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:59:32.261527Z","signed_message":"canonical_sha256_bytes"},"source_id":"1402.2117","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c892c48817e08f09eaf80872fbdee7379794789a856c06fdf7bfb9789b9e0cb4","sha256:73826e0060f9d68d86226e277eec993e0663b429b6797f1833e60b641b9811e9"],"state_sha256":"cec6fdd6247cc264256519e3b73f91ab4daa400c735c92bb201bd58c953bbf6e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qftoEyxD1OZNaC6eij3pMk1OOZlutG2tDVtZ6glz3QaC78C2fEo6H04QDcaiVPj8phBa3PONjBObpgoP6lrjAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T04:30:51.460343Z","bundle_sha256":"5de9e34eb96bc708f36cb5a4c95a5045c62ae2a61c5be4f234fc5a81785af8af"}}