{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:O2OPLEYNSOCLLLXZW3OCQLHO2R","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":"8ea58ee6792a9e8db2c7373430c057e9f345fe2335f3d7e663b709a9456107cc","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-12-27T01:35:48Z","title_canon_sha256":"7585c2ae80653a7103040d3bba22727871c7ce23daf16d52dbeb3928d316f77f"},"schema_version":"1.0","source":{"id":"1212.6287","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.6287","created_at":"2026-05-18T03:37:40Z"},{"alias_kind":"arxiv_version","alias_value":"1212.6287v1","created_at":"2026-05-18T03:37:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.6287","created_at":"2026-05-18T03:37:40Z"},{"alias_kind":"pith_short_12","alias_value":"O2OPLEYNSOCL","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"O2OPLEYNSOCLLLXZ","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"O2OPLEYN","created_at":"2026-05-18T12:27:16Z"}],"graph_snapshots":[{"event_id":"sha256:e7255d3c11c254386cb899dc9c176ee7a24e0e725894dc949fa8a047b38dfb68","target":"graph","created_at":"2026-05-18T03:37:40Z","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":"Let $\\Omega \\subset \\RR^d$, $d \\geqslant 1$, be a bounded domain with piecewise smooth boundary $\\partial \\Omega $ and let $U$ be an open subset of a Banach space $Y$. Motivated by questions in \"Uncertainty Quantification,\" we consider a parametric family $P = (P_y)_{y \\in U}$ of uniformly strongly elliptic, second order partial differential operators $P_y$ on $\\Omega$. We allow jump discontinuities in the coefficients. We establish a regularity result for the solution $u: \\Omega \\times U \\to \\RR$ of the parametric, elliptic boundary value/transmission problem $P_y u_y = f_y$, $y \\in U$, with ","authors_text":"Hengguang Li, Victor Nistor, Yu Qiao","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-12-27T01:35:48Z","title":"Uniform shift estimates for transmission problems and optimal rates of convergence for the parametric Finite Element Method"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.6287","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:cdc6d7cd3a0d4c2920d4a5ccd79959f987d01582fceff7ad2d02e55e3634c3cd","target":"record","created_at":"2026-05-18T03:37:40Z","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":"8ea58ee6792a9e8db2c7373430c057e9f345fe2335f3d7e663b709a9456107cc","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-12-27T01:35:48Z","title_canon_sha256":"7585c2ae80653a7103040d3bba22727871c7ce23daf16d52dbeb3928d316f77f"},"schema_version":"1.0","source":{"id":"1212.6287","kind":"arxiv","version":1}},"canonical_sha256":"769cf5930d9384b5aef9b6dc282ceed44f242f55a1f5d5694af2d4b03749fdcf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"769cf5930d9384b5aef9b6dc282ceed44f242f55a1f5d5694af2d4b03749fdcf","first_computed_at":"2026-05-18T03:37:40.307122Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:37:40.307122Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"at9HSSf42cYBzBjw5xrlPzSTqw4ZaLoktx0n4D2TjRlAECe2dcKR3LbIWx0PiHi1PJFfiQqV1A++ISVrfL64Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:37:40.307914Z","signed_message":"canonical_sha256_bytes"},"source_id":"1212.6287","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cdc6d7cd3a0d4c2920d4a5ccd79959f987d01582fceff7ad2d02e55e3634c3cd","sha256:e7255d3c11c254386cb899dc9c176ee7a24e0e725894dc949fa8a047b38dfb68"],"state_sha256":"231b4266bdb66c883c2e75133d04cef189a524e219d7c78ff54bd147624caab5"}