{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:5R6CT4WND4UNUVO47KPUNUHVFG","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":"5ec1ac89cec1b0c84301cab6c1bae8e05c2bab12d056938b33ba5f35444eec9e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-01-08T03:10:11Z","title_canon_sha256":"efb50d048b70c5f58d32034652760913259d2ec02ae622e70eea56fd18150124"},"schema_version":"1.0","source":{"id":"1801.02297","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.02297","created_at":"2026-05-18T00:18:09Z"},{"alias_kind":"arxiv_version","alias_value":"1801.02297v1","created_at":"2026-05-18T00:18:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.02297","created_at":"2026-05-18T00:18:09Z"},{"alias_kind":"pith_short_12","alias_value":"5R6CT4WND4UN","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_16","alias_value":"5R6CT4WND4UNUVO4","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_8","alias_value":"5R6CT4WN","created_at":"2026-05-18T12:32:08Z"}],"graph_snapshots":[{"event_id":"sha256:0be61e2d6c5db421beddb8c86e702c650d61ff3d5fe007178fca04c6f61a1520","target":"graph","created_at":"2026-05-18T00:18:09Z","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":"This paper is concerned with the optimal convergence rate in homogenization of higher order parabolic systems with bounded measurable, rapidly oscillating periodic coefficients. The sharp $O(\\va)$ convergence rate in the space $L^2(0,T; H^{m-1}(\\Om))$ is obtained for both the initial-Dirichlet problem and the initial-Neumann problem. The duality argument inspired by \\cite{suslinaD2013} is used here.","authors_text":"Weisheng Niu, Yao Xu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-01-08T03:10:11Z","title":"Convergence rates in homogenization of higher order parabolic systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.02297","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:b9c2c4b085b87a455630502fbb8084c107c7cd241ada3e5c03e4f18ba67a8f75","target":"record","created_at":"2026-05-18T00:18:09Z","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":"5ec1ac89cec1b0c84301cab6c1bae8e05c2bab12d056938b33ba5f35444eec9e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-01-08T03:10:11Z","title_canon_sha256":"efb50d048b70c5f58d32034652760913259d2ec02ae622e70eea56fd18150124"},"schema_version":"1.0","source":{"id":"1801.02297","kind":"arxiv","version":1}},"canonical_sha256":"ec7c29f2cd1f28da55dcfa9f46d0f529a1ac18966243de6e3e195bea08c4e684","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ec7c29f2cd1f28da55dcfa9f46d0f529a1ac18966243de6e3e195bea08c4e684","first_computed_at":"2026-05-18T00:18:09.194226Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:18:09.194226Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Dyaw5hK5C1rQSO7soMRbMLjAwVfG2qyyCqfE84Q30Mt7G0Hic8jt/Bs6FMbxkpiE53spGGl0SQrHTePoo3XkAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:18:09.194729Z","signed_message":"canonical_sha256_bytes"},"source_id":"1801.02297","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b9c2c4b085b87a455630502fbb8084c107c7cd241ada3e5c03e4f18ba67a8f75","sha256:0be61e2d6c5db421beddb8c86e702c650d61ff3d5fe007178fca04c6f61a1520"],"state_sha256":"b0f377cefc8ca110a31ada27e9c88dca09a22704c5ecbc5b700bedd5495ccebc"}