{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:6BHQAYYJBQTT5QU374VPXDX6IN","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":"4a0d02faee958cb7f03ce3de26da6507e54f657f8089c53a6560e1e8cb1fbc8e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-04-22T16:32:05Z","title_canon_sha256":"cfa625d230c693b566fa56a9f306e82b1510bd432d1812aedd0507758bfb45ad"},"schema_version":"1.0","source":{"id":"1604.06735","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.06735","created_at":"2026-05-18T01:16:28Z"},{"alias_kind":"arxiv_version","alias_value":"1604.06735v1","created_at":"2026-05-18T01:16:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.06735","created_at":"2026-05-18T01:16:28Z"},{"alias_kind":"pith_short_12","alias_value":"6BHQAYYJBQTT","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"6BHQAYYJBQTT5QU3","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"6BHQAYYJ","created_at":"2026-05-18T12:30:01Z"}],"graph_snapshots":[{"event_id":"sha256:bfe47fc2d8bdfd893f364492898280e16be8ce401f173b213a053c9718cd48aa","target":"graph","created_at":"2026-05-18T01:16:28Z","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":"For a family of second-order parabolic systems with bounded measurable, rapidly oscillating and time-dependent periodic coefficients, we investigate the sharp convergence rates of weak solutions in $L^2$. Both initial-Dirichlet and initial-Neumann problems are studied.","authors_text":"Jun Geng, Zhongwei Shen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-04-22T16:32:05Z","title":"Convergence Rates in Parabolic Homogenization with Time-Dependent Periodic Coefficients"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.06735","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":"sha256:3fe3e5f134859a8567050e6f57798b37504de80d944131b2327f5e4a20b5f16a","target":"record","created_at":"2026-05-18T01:16:28Z","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":"4a0d02faee958cb7f03ce3de26da6507e54f657f8089c53a6560e1e8cb1fbc8e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-04-22T16:32:05Z","title_canon_sha256":"cfa625d230c693b566fa56a9f306e82b1510bd432d1812aedd0507758bfb45ad"},"schema_version":"1.0","source":{"id":"1604.06735","kind":"arxiv","version":1}},"canonical_sha256":"f04f0063090c273ec29bff2afb8efe43591309898633f958fcfc4a66c15b30b0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f04f0063090c273ec29bff2afb8efe43591309898633f958fcfc4a66c15b30b0","first_computed_at":"2026-05-18T01:16:28.296488Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:16:28.296488Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"D15ehEhISBaxaZDNO0EZUL2SZvQKA5ZoXz8B3op7xcUkwjnCDPzK84QtuhpnSFjsK2g2UqSaSZkUr66e9sJlDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:16:28.297025Z","signed_message":"canonical_sha256_bytes"},"source_id":"1604.06735","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3fe3e5f134859a8567050e6f57798b37504de80d944131b2327f5e4a20b5f16a","sha256:bfe47fc2d8bdfd893f364492898280e16be8ce401f173b213a053c9718cd48aa"],"state_sha256":"045fde2a0b8b467d174502200e046fc1aa4b6798a7074cc11ed674d59177d12b"}