{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:BUWDSCWLDSB63CMZF4OARIKXTE","short_pith_number":"pith:BUWDSCWL","canonical_record":{"source":{"id":"1211.2877","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-11-13T02:50:36Z","cross_cats_sorted":[],"title_canon_sha256":"1e0815059d869e4a91313ddd817e728b7aabb17de6288b9e447e7bbb2932f1e9","abstract_canon_sha256":"6b7ade31850ec57a0ed6caf85751d8be6d5c74e0185b4c6d4cff64d5e1bc261d"},"schema_version":"1.0"},"canonical_sha256":"0d2c390acb1c83ed89992f1c08a1579916bfa72b89d0b9e507d42343b5730556","source":{"kind":"arxiv","id":"1211.2877","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.2877","created_at":"2026-05-18T02:46:04Z"},{"alias_kind":"arxiv_version","alias_value":"1211.2877v3","created_at":"2026-05-18T02:46:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.2877","created_at":"2026-05-18T02:46:04Z"},{"alias_kind":"pith_short_12","alias_value":"BUWDSCWLDSB6","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"BUWDSCWLDSB63CMZ","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"BUWDSCWL","created_at":"2026-05-18T12:27:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:BUWDSCWLDSB63CMZF4OARIKXTE","target":"record","payload":{"canonical_record":{"source":{"id":"1211.2877","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-11-13T02:50:36Z","cross_cats_sorted":[],"title_canon_sha256":"1e0815059d869e4a91313ddd817e728b7aabb17de6288b9e447e7bbb2932f1e9","abstract_canon_sha256":"6b7ade31850ec57a0ed6caf85751d8be6d5c74e0185b4c6d4cff64d5e1bc261d"},"schema_version":"1.0"},"canonical_sha256":"0d2c390acb1c83ed89992f1c08a1579916bfa72b89d0b9e507d42343b5730556","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:46:04.765392Z","signature_b64":"5V1H8XGYhBcY0HOmHGdksPdCZiiBiMEUOokJYWQKxZfD7qWeaZNbKDgR6eDAyywuZn7S6KeDQsHuaSbKvQpmAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0d2c390acb1c83ed89992f1c08a1579916bfa72b89d0b9e507d42343b5730556","last_reissued_at":"2026-05-18T02:46:04.764796Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:46:04.764796Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1211.2877","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:46:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rhawmWrsQztMYwhGBZu0ScAikzOVciVtjQZ5yFrTJbBeB474vKZ+T0sfFfPbTDeHOlAv5W1yE+jHynRHQcucBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T22:21:09.300954Z"},"content_sha256":"24af1241ac513a23f45f108865c4350116d23a635cb7ba5eb59509e67d794083","schema_version":"1.0","event_id":"sha256:24af1241ac513a23f45f108865c4350116d23a635cb7ba5eb59509e67d794083"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:BUWDSCWLDSB63CMZF4OARIKXTE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"How a nonconvergent recovered Hessian works in mesh adaptation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Lennard Kamenski, Weizhang Huang","submitted_at":"2012-11-13T02:50:36Z","abstract_excerpt":"Hessian recovery has been commonly used in mesh adaptation for obtaining the required magnitude and direction information of the solution error. Unfortunately, a recovered Hessian from a linear finite element approximation is nonconvergent in general as the mesh is refined. It has been observed numerically that adaptive meshes based on such a nonconvergent recovered Hessian can nevertheless lead to an optimal error in the finite element approximation. This also explains why Hessian recovery is still widely used despite its nonconvergence. In this paper we develop an error bound for the linear "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.2877","kind":"arxiv","version":3},"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":"2026-05-18T02:46:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WN8GZr4rJqEcRaVjp/ps7Ge/2+rnW6icqCUxd/oFLHII8yJA13jOAf1miWfWHgfcGuKI/sPnIKkP2nk06WuGDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T22:21:09.301293Z"},"content_sha256":"28f3c13c1a061038bd7fca0a4324a9ff0ea8b83b2528949dcbe8a761fa233fdd","schema_version":"1.0","event_id":"sha256:28f3c13c1a061038bd7fca0a4324a9ff0ea8b83b2528949dcbe8a761fa233fdd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BUWDSCWLDSB63CMZF4OARIKXTE/bundle.json","state_url":"https://pith.science/pith/BUWDSCWLDSB63CMZF4OARIKXTE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BUWDSCWLDSB63CMZF4OARIKXTE/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":"2026-06-01T22:21:09Z","links":{"resolver":"https://pith.science/pith/BUWDSCWLDSB63CMZF4OARIKXTE","bundle":"https://pith.science/pith/BUWDSCWLDSB63CMZF4OARIKXTE/bundle.json","state":"https://pith.science/pith/BUWDSCWLDSB63CMZF4OARIKXTE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BUWDSCWLDSB63CMZF4OARIKXTE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:BUWDSCWLDSB63CMZF4OARIKXTE","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":"6b7ade31850ec57a0ed6caf85751d8be6d5c74e0185b4c6d4cff64d5e1bc261d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-11-13T02:50:36Z","title_canon_sha256":"1e0815059d869e4a91313ddd817e728b7aabb17de6288b9e447e7bbb2932f1e9"},"schema_version":"1.0","source":{"id":"1211.2877","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.2877","created_at":"2026-05-18T02:46:04Z"},{"alias_kind":"arxiv_version","alias_value":"1211.2877v3","created_at":"2026-05-18T02:46:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.2877","created_at":"2026-05-18T02:46:04Z"},{"alias_kind":"pith_short_12","alias_value":"BUWDSCWLDSB6","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"BUWDSCWLDSB63CMZ","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"BUWDSCWL","created_at":"2026-05-18T12:27:01Z"}],"graph_snapshots":[{"event_id":"sha256:28f3c13c1a061038bd7fca0a4324a9ff0ea8b83b2528949dcbe8a761fa233fdd","target":"graph","created_at":"2026-05-18T02:46:04Z","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":"Hessian recovery has been commonly used in mesh adaptation for obtaining the required magnitude and direction information of the solution error. Unfortunately, a recovered Hessian from a linear finite element approximation is nonconvergent in general as the mesh is refined. It has been observed numerically that adaptive meshes based on such a nonconvergent recovered Hessian can nevertheless lead to an optimal error in the finite element approximation. This also explains why Hessian recovery is still widely used despite its nonconvergence. In this paper we develop an error bound for the linear ","authors_text":"Lennard Kamenski, Weizhang Huang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-11-13T02:50:36Z","title":"How a nonconvergent recovered Hessian works in mesh adaptation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.2877","kind":"arxiv","version":3},"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":"sha256:24af1241ac513a23f45f108865c4350116d23a635cb7ba5eb59509e67d794083","target":"record","created_at":"2026-05-18T02:46:04Z","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":"6b7ade31850ec57a0ed6caf85751d8be6d5c74e0185b4c6d4cff64d5e1bc261d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-11-13T02:50:36Z","title_canon_sha256":"1e0815059d869e4a91313ddd817e728b7aabb17de6288b9e447e7bbb2932f1e9"},"schema_version":"1.0","source":{"id":"1211.2877","kind":"arxiv","version":3}},"canonical_sha256":"0d2c390acb1c83ed89992f1c08a1579916bfa72b89d0b9e507d42343b5730556","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0d2c390acb1c83ed89992f1c08a1579916bfa72b89d0b9e507d42343b5730556","first_computed_at":"2026-05-18T02:46:04.764796Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:46:04.764796Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5V1H8XGYhBcY0HOmHGdksPdCZiiBiMEUOokJYWQKxZfD7qWeaZNbKDgR6eDAyywuZn7S6KeDQsHuaSbKvQpmAw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:46:04.765392Z","signed_message":"canonical_sha256_bytes"},"source_id":"1211.2877","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:24af1241ac513a23f45f108865c4350116d23a635cb7ba5eb59509e67d794083","sha256:28f3c13c1a061038bd7fca0a4324a9ff0ea8b83b2528949dcbe8a761fa233fdd"],"state_sha256":"a1a6a6746e5e06f885d32b352a17139318dc485c0125d44b8c0011f5d0164503"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nidZwS/m/31ClcsF/90/OA8pXL2PoWXqy5cM6ZhIsS4pGdELO1tevgglgCJbEZXgr2uY+bM+SW4B58CdilQdBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T22:21:09.303193Z","bundle_sha256":"1119fe9a0873fe9a845f735e9e9c9aa150e3a22451efdfa9ccfba5ff14e48804"}}