{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:Z5GJW63CXEIR6SLPBYFF5HWIDS","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":"c94bdfc43b2842d236524b51984ec8d2930bb4fc817936d005810cf2dbb9cae6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-08-02T04:37:33Z","title_canon_sha256":"35388122793cd2471fb653504419d5643173281656bc389a79f95f2d858e5b5a"},"schema_version":"1.0","source":{"id":"1508.00191","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.00191","created_at":"2026-05-18T01:16:24Z"},{"alias_kind":"arxiv_version","alias_value":"1508.00191v2","created_at":"2026-05-18T01:16:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.00191","created_at":"2026-05-18T01:16:24Z"},{"alias_kind":"pith_short_12","alias_value":"Z5GJW63CXEIR","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"Z5GJW63CXEIR6SLP","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"Z5GJW63C","created_at":"2026-05-18T12:29:52Z"}],"graph_snapshots":[{"event_id":"sha256:60d979266973ec8450c5a022b91ef6b3a061cf93aa9ff68f2c390c141bfa922b","target":"graph","created_at":"2026-05-18T01:16:24Z","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 \\cite{CaZh:09}, we introduced and analyzed an improved Zienkiewicz-Zhu (ZZ) estimator for the conforming linear finite element approximation to elliptic interface problems. The estimator is based on the piecewise \"constant\" flux recovery in the $H(div;\\Omega)$ conforming finite element space. This paper extends the results of \\cite{CaZh:09} to diffusion problems with full diffusion tensor and to the flux recovery both in piecewise constant and piecewise linear $H(div)$ space.","authors_text":"Cuiyu He, Shun Zhang, Zhiqiang Cai","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-08-02T04:37:33Z","title":"Improved ZZ A Posteriori Error Estimators for Diffusion Problems: Conforming Linear Elements"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.00191","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:eeac1c68ff343c410a6f46662c0cc64a573e7e863d93b10980639cd36460a19f","target":"record","created_at":"2026-05-18T01:16:24Z","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":"c94bdfc43b2842d236524b51984ec8d2930bb4fc817936d005810cf2dbb9cae6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-08-02T04:37:33Z","title_canon_sha256":"35388122793cd2471fb653504419d5643173281656bc389a79f95f2d858e5b5a"},"schema_version":"1.0","source":{"id":"1508.00191","kind":"arxiv","version":2}},"canonical_sha256":"cf4c9b7b62b9111f496f0e0a5e9ec81cac3b25b6c60e1ca5a2909f18f6b9990d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cf4c9b7b62b9111f496f0e0a5e9ec81cac3b25b6c60e1ca5a2909f18f6b9990d","first_computed_at":"2026-05-18T01:16:24.893077Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:16:24.893077Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NrEOH16MlP6Xg6yjMv5wUsWZmhFRla/Eat3axPBjuqrUdV61KsRsS++FlncUFwPsKVLKUKTAIlnH3bg82koLAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:16:24.893810Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.00191","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:eeac1c68ff343c410a6f46662c0cc64a573e7e863d93b10980639cd36460a19f","sha256:60d979266973ec8450c5a022b91ef6b3a061cf93aa9ff68f2c390c141bfa922b"],"state_sha256":"bc85c281adf398acb6c100fbd6d38342512832e15dc27da5118f71b9ea301cc5"}