{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:2UXCL6DEK3OPLEFYLXEBADP2DL","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":"645a4efb04544fee914d7f5caedbe386bd069138ab5ba06ea01432cf075a6b92","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-05-21T08:09:05Z","title_canon_sha256":"1cd1ad153398da534fe19c345a3a9639854929b33a9647a0321700e4982a3d74"},"schema_version":"1.0","source":{"id":"1905.09182","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.09182","created_at":"2026-05-17T23:45:21Z"},{"alias_kind":"arxiv_version","alias_value":"1905.09182v1","created_at":"2026-05-17T23:45:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.09182","created_at":"2026-05-17T23:45:21Z"},{"alias_kind":"pith_short_12","alias_value":"2UXCL6DEK3OP","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_16","alias_value":"2UXCL6DEK3OPLEFY","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_8","alias_value":"2UXCL6DE","created_at":"2026-05-18T12:33:07Z"}],"graph_snapshots":[{"event_id":"sha256:b118c04c0c5fbdf9028c8366d1348a0fa8077b5fc4810ea514e0f733011bf650","target":"graph","created_at":"2026-05-17T23:45:21Z","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 study the asymptotic limit, as $\\varepsilon\\searrow 0$, of solutions of the stochastic Cahn-Hilliard equation: $$\n  \\partial_t u^\\varepsilon=\\Delta \\left(-\\varepsilon\\Delta u^\\varepsilon+\\frac{1}{\\varepsilon}f(u^\\varepsilon)\\right)+\\dot{\\mathcal{W}}^\\varepsilon_t, \\\\ $$ where $\\mathcal{W}^\\varepsilon=\\varepsilon^\\sigma W$ or $\\mathcal{W}^\\varepsilon=\\varepsilon^\\sigma W^\\varepsilon$, $W$ is a $Q$-Wiener process and $W^\\varepsilon$ is smooth in time and converges to $W$ as $\\varepsilon\\searrow 0$. In the case that $\\mathcal{W}^\\varepsilon=\\varepsilon^\\sigma W$, we prove that for all $\\sigma>","authors_text":"Huanyu Yang, Rongchan Zhu","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-05-21T08:09:05Z","title":"Weak solutions to the sharp interface limit of stochastic Cahn-Hilliard equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.09182","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:b77c87feb885c7195e45038a120b825a80d63cbbeb1c01c08164cb38f380b7af","target":"record","created_at":"2026-05-17T23:45:21Z","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":"645a4efb04544fee914d7f5caedbe386bd069138ab5ba06ea01432cf075a6b92","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-05-21T08:09:05Z","title_canon_sha256":"1cd1ad153398da534fe19c345a3a9639854929b33a9647a0321700e4982a3d74"},"schema_version":"1.0","source":{"id":"1905.09182","kind":"arxiv","version":1}},"canonical_sha256":"d52e25f86456dcf590b85dc8100dfa1ae464290abd81968d012125d0b302b36f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d52e25f86456dcf590b85dc8100dfa1ae464290abd81968d012125d0b302b36f","first_computed_at":"2026-05-17T23:45:21.725749Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:45:21.725749Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"THwta0u+JMZcIgUw3oMdXRBPRFml1Wyj0bEjfeSDTTcHKDc6a3H1r8JesKZEd5vLQtD09SD6OCBy4O+qDIFtAw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:45:21.726328Z","signed_message":"canonical_sha256_bytes"},"source_id":"1905.09182","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b77c87feb885c7195e45038a120b825a80d63cbbeb1c01c08164cb38f380b7af","sha256:b118c04c0c5fbdf9028c8366d1348a0fa8077b5fc4810ea514e0f733011bf650"],"state_sha256":"5071ea9c70373eae793774975f92d1c955ca707985d8002ecb37f3640c6ad070"}