{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:IIUTKYE5SPPVGKMSZIDKLMNHS5","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":"ad3193cbbcfa7de0a95c66a4e19547ea93cb06881fb25045af286beed3e577bb","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-06-04T10:28:17Z","title_canon_sha256":"e0c7f5a1bddf18292c2c18df7b2cd17870b70b0c47afd257848e4d6a0c195ea4"},"schema_version":"1.0","source":{"id":"1406.0996","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.0996","created_at":"2026-05-18T02:28:40Z"},{"alias_kind":"arxiv_version","alias_value":"1406.0996v3","created_at":"2026-05-18T02:28:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.0996","created_at":"2026-05-18T02:28:40Z"},{"alias_kind":"pith_short_12","alias_value":"IIUTKYE5SPPV","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"IIUTKYE5SPPVGKMS","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"IIUTKYE5","created_at":"2026-05-18T12:28:33Z"}],"graph_snapshots":[{"event_id":"sha256:94f3b664c89fa5551bfff86fd4d7b0be295c451737268fbcacf163e6d1a065d3","target":"graph","created_at":"2026-05-18T02:28:40Z","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":"We present quantitative results for the homogenization of uniformly convex integral functionals with random coefficients under independence assumptions. The main result is an error estimate for the Dirichlet problem which is algebraic (but sub-optimal) in the size of the error, but optimal in stochastic integrability. As an application, we obtain quenched $C^{0,1}$ estimates for local minimizers of such energy functionals.","authors_text":"Charles K. Smart, Scott N. Armstrong","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-06-04T10:28:17Z","title":"Quantitative stochastic homogenization of convex integral functionals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.0996","kind":"arxiv","version":3},"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":"sha256:9d01c80aa39cb1031cb78fe41f3d112bc81859bde77255d13c0421c7e4193718","target":"record","created_at":"2026-05-18T02:28:40Z","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":"ad3193cbbcfa7de0a95c66a4e19547ea93cb06881fb25045af286beed3e577bb","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-06-04T10:28:17Z","title_canon_sha256":"e0c7f5a1bddf18292c2c18df7b2cd17870b70b0c47afd257848e4d6a0c195ea4"},"schema_version":"1.0","source":{"id":"1406.0996","kind":"arxiv","version":3}},"canonical_sha256":"422935609d93df532992ca06a5b1a79743be0b065284372dbcae44edb05825e6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"422935609d93df532992ca06a5b1a79743be0b065284372dbcae44edb05825e6","first_computed_at":"2026-05-18T02:28:40.594344Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:28:40.594344Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BWKDmAdr+0TCYzxPQbNPr1cLw3CDRmME1vbGLK2mgKq/92eQdw8qIAHS8xvOr/AwtYb5EoD6tO/3hf+UtIutBw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:28:40.594798Z","signed_message":"canonical_sha256_bytes"},"source_id":"1406.0996","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9d01c80aa39cb1031cb78fe41f3d112bc81859bde77255d13c0421c7e4193718","sha256:94f3b664c89fa5551bfff86fd4d7b0be295c451737268fbcacf163e6d1a065d3"],"state_sha256":"a08d926beb7ef869cbc67d1b676e56c00090fbb02cd6aba598b138fc5b09a7ee"}