{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:26S36F7S7R647WBJUZVFVHBIJ4","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":"1126c194eb937f0bef27ff9efe6369a7e805b2d780831742eb59ce048f3056f6","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-03-02T15:38:24Z","title_canon_sha256":"eb05b888a554db84f165b6efcee14a4b44bac8d8bb034303a4089ede20f7d785"},"schema_version":"1.0","source":{"id":"1503.00578","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.00578","created_at":"2026-05-18T01:25:24Z"},{"alias_kind":"arxiv_version","alias_value":"1503.00578v2","created_at":"2026-05-18T01:25:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.00578","created_at":"2026-05-18T01:25:24Z"},{"alias_kind":"pith_short_12","alias_value":"26S36F7S7R64","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_16","alias_value":"26S36F7S7R647WBJ","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_8","alias_value":"26S36F7S","created_at":"2026-05-18T12:28:59Z"}],"graph_snapshots":[{"event_id":"sha256:d82482dd01ddc8429b42ec2edf64796ce37b8d49249ae2c8abd02fa7d2869c00","target":"graph","created_at":"2026-05-18T01:25:24Z","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 investigate the global fluctuations of solutions to elliptic equations with random coefficients in the discrete setting. In dimension $d\\geq 3$ and for i.i.d.\\ coefficients, we show that after a suitable scaling, these fluctuations converge to a Gaussian field that locally resembles a (generalized) Gaussian free field. The paper begins with a heuristic derivation of the result, which can be read independently and was obtained jointly with Scott Armstrong.","authors_text":"Jean-Christophe Mourrat, Yu Gu","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-03-02T15:38:24Z","title":"Scaling limit of fluctuations in stochastic homogenization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.00578","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":"sha256:83d4c4aa259e69a4248c0caafa07d4cbac44ab632b4d6e66cce42ab7eb8b51fd","target":"record","created_at":"2026-05-18T01:25:24Z","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":"1126c194eb937f0bef27ff9efe6369a7e805b2d780831742eb59ce048f3056f6","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-03-02T15:38:24Z","title_canon_sha256":"eb05b888a554db84f165b6efcee14a4b44bac8d8bb034303a4089ede20f7d785"},"schema_version":"1.0","source":{"id":"1503.00578","kind":"arxiv","version":2}},"canonical_sha256":"d7a5bf17f2fc7dcfd829a66a5a9c284f16bfedef32fc07b43ba39eb303981123","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d7a5bf17f2fc7dcfd829a66a5a9c284f16bfedef32fc07b43ba39eb303981123","first_computed_at":"2026-05-18T01:25:24.637575Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:25:24.637575Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XGi8Ug87FhVKwodCu8/8OdwZNwHqGJGi7oKgXMhlOYqMyRtY9hOuvI5g6BWikOu3rxylqRJIAtRvZAPlZn/tBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:25:24.637985Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.00578","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:83d4c4aa259e69a4248c0caafa07d4cbac44ab632b4d6e66cce42ab7eb8b51fd","sha256:d82482dd01ddc8429b42ec2edf64796ce37b8d49249ae2c8abd02fa7d2869c00"],"state_sha256":"dc52c2f6ab4da87b309149f5868cead65193d456f7cfcffa4c042c848abefefb"}