{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:KRHKPCJEO7PVSNVR5X3ONOOX2V","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":"eed0765958f3c8544b50217e63f3e4efab69e3653757823909e1617751e319eb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-08-18T03:21:54Z","title_canon_sha256":"fe480024568f8dfd1b04ba37d8b28e32c7fd7873a8603f3e5720bbc42fa0fae8"},"schema_version":"1.0","source":{"id":"1508.04203","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.04203","created_at":"2026-05-18T01:30:34Z"},{"alias_kind":"arxiv_version","alias_value":"1508.04203v2","created_at":"2026-05-18T01:30:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.04203","created_at":"2026-05-18T01:30:34Z"},{"alias_kind":"pith_short_12","alias_value":"KRHKPCJEO7PV","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_16","alias_value":"KRHKPCJEO7PVSNVR","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_8","alias_value":"KRHKPCJE","created_at":"2026-05-18T12:29:29Z"}],"graph_snapshots":[{"event_id":"sha256:52afc33e93a27868c04ec3f802e21eee4ae82c4dfdc9c3934ac8884d220502fc","target":"graph","created_at":"2026-05-18T01:30:34Z","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 studies the convergence rates in $L^2$ and $H^1$ of Dirichelt problems for Stokes systems with rapidly oscillating periodic coefficients, without any regularity assumptions on the coefficients.","authors_text":"Shu Gu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-08-18T03:21:54Z","title":"Convergence Rates in Homogenization of Stokes Systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.04203","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":"sha256:581f46ce92da49654f0c1d8f0a8d028a28518eb6b6f37b7be34ac1b3a24fe210","target":"record","created_at":"2026-05-18T01:30:34Z","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":"eed0765958f3c8544b50217e63f3e4efab69e3653757823909e1617751e319eb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-08-18T03:21:54Z","title_canon_sha256":"fe480024568f8dfd1b04ba37d8b28e32c7fd7873a8603f3e5720bbc42fa0fae8"},"schema_version":"1.0","source":{"id":"1508.04203","kind":"arxiv","version":2}},"canonical_sha256":"544ea7892477df5936b1edf6e6b9d7d574b1c5219617eb02b4255efe96d78808","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"544ea7892477df5936b1edf6e6b9d7d574b1c5219617eb02b4255efe96d78808","first_computed_at":"2026-05-18T01:30:34.116399Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:30:34.116399Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6UgaswVgMVLMF/QaCvdLAcjpy+YeEyb4pjVGDpkWqvxEKeik0q4Qe2VQLkLDdU8RTson4RhflaVnuoRqy8HMCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:30:34.117171Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.04203","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:581f46ce92da49654f0c1d8f0a8d028a28518eb6b6f37b7be34ac1b3a24fe210","sha256:52afc33e93a27868c04ec3f802e21eee4ae82c4dfdc9c3934ac8884d220502fc"],"state_sha256":"216e6c19b65be27ce98ff3d13aef5014e5198543945f13a71f48ad90c279cb13"}