{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:GE76AYAJ5L4IOGCHKAYJSCPYRJ","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":"3be3008aad62da90305c3198923126fc8d82bd8132a4f4f3b76558b746401cbc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-04-07T22:07:56Z","title_canon_sha256":"4ef7e5cdde3b8d2f9d0f23b9d060b6a5e3d33bffc9487f58635f4fbb86f2bf9f"},"schema_version":"1.0","source":{"id":"1604.02187","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.02187","created_at":"2026-05-18T00:45:49Z"},{"alias_kind":"arxiv_version","alias_value":"1604.02187v2","created_at":"2026-05-18T00:45:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.02187","created_at":"2026-05-18T00:45:49Z"},{"alias_kind":"pith_short_12","alias_value":"GE76AYAJ5L4I","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"GE76AYAJ5L4IOGCH","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"GE76AYAJ","created_at":"2026-05-18T12:30:19Z"}],"graph_snapshots":[{"event_id":"sha256:d58c3484e67db85ba92595c6e8917f5d3d3583ffb41278a99971442819c2106c","target":"graph","created_at":"2026-05-18T00:45:49Z","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 propose two nonconforming finite elements to approximate a boundary value problem arising from strain gradient elasticity, which is a higher-order perturbation of the linearized elastic system. Our elements are H$^2-$nonconforming while H$^1-$conforming. We show both elements converges in the energy norm uniformly with respect to the perturbation parameter.","authors_text":"Hongliang Li, Pingbing Ming, Zhong-ci Shi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-04-07T22:07:56Z","title":"Two robust nonconforming H$^2-$elements for linear strain gradient elasticity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.02187","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":"sha256:0d40b3547ee55d15f7bb1378ed02099836304bc400a40e5db7f7f9e6fcbe5e2f","target":"record","created_at":"2026-05-18T00:45:49Z","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":"3be3008aad62da90305c3198923126fc8d82bd8132a4f4f3b76558b746401cbc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-04-07T22:07:56Z","title_canon_sha256":"4ef7e5cdde3b8d2f9d0f23b9d060b6a5e3d33bffc9487f58635f4fbb86f2bf9f"},"schema_version":"1.0","source":{"id":"1604.02187","kind":"arxiv","version":2}},"canonical_sha256":"313fe06009eaf887184750309909f88a5c32717742be15914666095bded9db55","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"313fe06009eaf887184750309909f88a5c32717742be15914666095bded9db55","first_computed_at":"2026-05-18T00:45:49.657331Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:45:49.657331Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kn350ZBbjxVNC3rdC8E/m3G67zDD3lODqOAbTE2nkbZmiWgMzASIN5vovVpXpU7g+w3mzdxppcNeksPI534VBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:45:49.658023Z","signed_message":"canonical_sha256_bytes"},"source_id":"1604.02187","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0d40b3547ee55d15f7bb1378ed02099836304bc400a40e5db7f7f9e6fcbe5e2f","sha256:d58c3484e67db85ba92595c6e8917f5d3d3583ffb41278a99971442819c2106c"],"state_sha256":"b8a562d1e2d68169e128c846a186580fb9295f02d4e3c08e8e8546cacd86c120"}