{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:NS2WZS5HYK7IEMROGS72HFGVXE","short_pith_number":"pith:NS2WZS5H","canonical_record":{"source":{"id":"1801.04122","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-01-12T10:20:40Z","cross_cats_sorted":[],"title_canon_sha256":"8fcd6e0aef49f3817b32f872e476e1fd83d417e8586df4fd3358438ee8be88a8","abstract_canon_sha256":"6ff2010633d9f3ca4bbbeb04d32cee74e6accec3ed8d95d4d0bc3822d3e9258d"},"schema_version":"1.0"},"canonical_sha256":"6cb56ccba7c2be82322e34bfa394d5b92b5e7829edbb98c463d59b070b37f59f","source":{"kind":"arxiv","id":"1801.04122","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.04122","created_at":"2026-05-18T00:26:11Z"},{"alias_kind":"arxiv_version","alias_value":"1801.04122v1","created_at":"2026-05-18T00:26:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.04122","created_at":"2026-05-18T00:26:11Z"},{"alias_kind":"pith_short_12","alias_value":"NS2WZS5HYK7I","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_16","alias_value":"NS2WZS5HYK7IEMRO","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_8","alias_value":"NS2WZS5H","created_at":"2026-05-18T12:32:40Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:NS2WZS5HYK7IEMROGS72HFGVXE","target":"record","payload":{"canonical_record":{"source":{"id":"1801.04122","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-01-12T10:20:40Z","cross_cats_sorted":[],"title_canon_sha256":"8fcd6e0aef49f3817b32f872e476e1fd83d417e8586df4fd3358438ee8be88a8","abstract_canon_sha256":"6ff2010633d9f3ca4bbbeb04d32cee74e6accec3ed8d95d4d0bc3822d3e9258d"},"schema_version":"1.0"},"canonical_sha256":"6cb56ccba7c2be82322e34bfa394d5b92b5e7829edbb98c463d59b070b37f59f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:26:11.800404Z","signature_b64":"fLCeqaVdKjw2EOBSPg4pRe+5QWD0bkLxFJ7kFQw01MpYNGnMwJbryVdJ/9LG02FoM7tRP9MUIz9+rbCvjRVpDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6cb56ccba7c2be82322e34bfa394d5b92b5e7829edbb98c463d59b070b37f59f","last_reissued_at":"2026-05-18T00:26:11.799903Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:26:11.799903Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1801.04122","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":"2026-05-18T00:26:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hYyrjaiBgSEB3pvnn9WlonGOdjprhx212O9OuW0FShFBJP8t64Ie0IBFZRG+EwJz8cn0TsOwTxtt4YwirbSDCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T07:50:08.859221Z"},"content_sha256":"61d7f485b40e0c86207c64684f378ab91a4156d8fd9a1905662f3143509a9fd5","schema_version":"1.0","event_id":"sha256:61d7f485b40e0c86207c64684f378ab91a4156d8fd9a1905662f3143509a9fd5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:NS2WZS5HYK7IEMROGS72HFGVXE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Robust error estimation for lowest-order approximation of nearly incompressible elasticity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Arbaz Khan, Catherine E. Powell, David J. Silvester","submitted_at":"2018-01-12T10:20:40Z","abstract_excerpt":"We consider so-called Herrmann and Hydrostatic mixed formulations of classical linear elasticity and analyse the error associated with locally stabilised $P_1-P_0$ finite element approximation. First, we prove a stability estimate for the discrete problem and establish an a priori estimate for the associated energy error. Second, we consider a residual-based a posteriori error estimator as well as a local Poisson problem estimator. We establish bounds for the energy error that are independent of the Lam\\'{e} coefficients and prove that the estimators are robust in the incompressible limit. A k"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.04122","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":"2026-05-18T00:26:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"roFTlNibNrpEpMxH29sXGm+8xifzH154Eyyh1bDn+GgRzWITKW3UmbmEKqhlB/o0xnhcQ1W2PpelcKNLYv+bAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T07:50:08.859593Z"},"content_sha256":"21953cb7221432acd471d53b8fa6074dc9d3de832353b1cf117ed4c260635c5e","schema_version":"1.0","event_id":"sha256:21953cb7221432acd471d53b8fa6074dc9d3de832353b1cf117ed4c260635c5e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NS2WZS5HYK7IEMROGS72HFGVXE/bundle.json","state_url":"https://pith.science/pith/NS2WZS5HYK7IEMROGS72HFGVXE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NS2WZS5HYK7IEMROGS72HFGVXE/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":"2026-05-30T07:50:08Z","links":{"resolver":"https://pith.science/pith/NS2WZS5HYK7IEMROGS72HFGVXE","bundle":"https://pith.science/pith/NS2WZS5HYK7IEMROGS72HFGVXE/bundle.json","state":"https://pith.science/pith/NS2WZS5HYK7IEMROGS72HFGVXE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NS2WZS5HYK7IEMROGS72HFGVXE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:NS2WZS5HYK7IEMROGS72HFGVXE","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":"6ff2010633d9f3ca4bbbeb04d32cee74e6accec3ed8d95d4d0bc3822d3e9258d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-01-12T10:20:40Z","title_canon_sha256":"8fcd6e0aef49f3817b32f872e476e1fd83d417e8586df4fd3358438ee8be88a8"},"schema_version":"1.0","source":{"id":"1801.04122","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.04122","created_at":"2026-05-18T00:26:11Z"},{"alias_kind":"arxiv_version","alias_value":"1801.04122v1","created_at":"2026-05-18T00:26:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.04122","created_at":"2026-05-18T00:26:11Z"},{"alias_kind":"pith_short_12","alias_value":"NS2WZS5HYK7I","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_16","alias_value":"NS2WZS5HYK7IEMRO","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_8","alias_value":"NS2WZS5H","created_at":"2026-05-18T12:32:40Z"}],"graph_snapshots":[{"event_id":"sha256:21953cb7221432acd471d53b8fa6074dc9d3de832353b1cf117ed4c260635c5e","target":"graph","created_at":"2026-05-18T00:26:11Z","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 consider so-called Herrmann and Hydrostatic mixed formulations of classical linear elasticity and analyse the error associated with locally stabilised $P_1-P_0$ finite element approximation. First, we prove a stability estimate for the discrete problem and establish an a priori estimate for the associated energy error. Second, we consider a residual-based a posteriori error estimator as well as a local Poisson problem estimator. We establish bounds for the energy error that are independent of the Lam\\'{e} coefficients and prove that the estimators are robust in the incompressible limit. A k","authors_text":"Arbaz Khan, Catherine E. Powell, David J. Silvester","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-01-12T10:20:40Z","title":"Robust error estimation for lowest-order approximation of nearly incompressible elasticity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.04122","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":"sha256:61d7f485b40e0c86207c64684f378ab91a4156d8fd9a1905662f3143509a9fd5","target":"record","created_at":"2026-05-18T00:26:11Z","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":"6ff2010633d9f3ca4bbbeb04d32cee74e6accec3ed8d95d4d0bc3822d3e9258d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-01-12T10:20:40Z","title_canon_sha256":"8fcd6e0aef49f3817b32f872e476e1fd83d417e8586df4fd3358438ee8be88a8"},"schema_version":"1.0","source":{"id":"1801.04122","kind":"arxiv","version":1}},"canonical_sha256":"6cb56ccba7c2be82322e34bfa394d5b92b5e7829edbb98c463d59b070b37f59f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6cb56ccba7c2be82322e34bfa394d5b92b5e7829edbb98c463d59b070b37f59f","first_computed_at":"2026-05-18T00:26:11.799903Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:26:11.799903Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fLCeqaVdKjw2EOBSPg4pRe+5QWD0bkLxFJ7kFQw01MpYNGnMwJbryVdJ/9LG02FoM7tRP9MUIz9+rbCvjRVpDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:26:11.800404Z","signed_message":"canonical_sha256_bytes"},"source_id":"1801.04122","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:61d7f485b40e0c86207c64684f378ab91a4156d8fd9a1905662f3143509a9fd5","sha256:21953cb7221432acd471d53b8fa6074dc9d3de832353b1cf117ed4c260635c5e"],"state_sha256":"d4819ec0534754e66c487169c9a532ac5344927503570bfc7ba2280ee0024ab1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3Rhb0T3QVcLqpRD6aPIuQzXzIjTpp3CaiviLilCInhRc2L5esAxJXD+C61fBFsLcGE6TnVk4ftLW/s/ICdS4CA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T07:50:08.861819Z","bundle_sha256":"3e7ec092c17ccc348cf268e8be63b26c6257e383063d15c5381635e8de5d7c14"}}