{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:ZZB6PLXWZ2POT5PY6TYRPALGS4","short_pith_number":"pith:ZZB6PLXW","schema_version":"1.0","canonical_sha256":"ce43e7aef6ce9ee9f5f8f4f11781669720c44a865a7291567181b35a3a5b6f9a","source":{"kind":"arxiv","id":"1812.03804","version":3},"attestation_state":"computed","paper":{"title":"Generation of fine transition layers and their dynamics for the stochastic Allen--Cahn equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Dimitra Antonopoulou, Georgia Karali, Hiroshi Matano, Matthieu Alfaro","submitted_at":"2018-12-10T14:16:08Z","abstract_excerpt":"We study an $\\ep$-dependent stochastic Allen--Cahn equation with a mild random noise on a bounded domain in $\\mathbb{R}^n$, $n\\geq 2$. Here $\\ep$ is a small positive parameter that represents formally the thickness of the solution interface, while the mild noise $\\xi^\\ep(t)$ is a smooth random function of $t$ of order $\\mathcal O(\\ep^{-\\gamma})$ with $0<\\gamma<1/3$ that converges to white noise as $\\ep\\rightarrow 0^+$. We consider initial data that are independent of $\\ep$ satisfying some non-degeneracy conditions, and prove that steep transition layers---or interfaces---develop within a very "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1812.03804","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-12-10T14:16:08Z","cross_cats_sorted":[],"title_canon_sha256":"0b15fe23c10b273b41061a155fa198d2da1b3056f103fd23acf91114f2ec9528","abstract_canon_sha256":"d006f84814a09939dc821085da0f19f216f071f50a10a2fcf8e9ce188215d653"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:57:56.781133Z","signature_b64":"Rc5YMRV1dkFQ05cEWwz8W8V2x7TwschY6oQu+tHx2LvqFlZ8XMWtqTUFmNpddq7Tmw3sFAhYX9SYvSlOFaVOCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ce43e7aef6ce9ee9f5f8f4f11781669720c44a865a7291567181b35a3a5b6f9a","last_reissued_at":"2026-05-17T23:57:56.780486Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:57:56.780486Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Generation of fine transition layers and their dynamics for the stochastic Allen--Cahn equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Dimitra Antonopoulou, Georgia Karali, Hiroshi Matano, Matthieu Alfaro","submitted_at":"2018-12-10T14:16:08Z","abstract_excerpt":"We study an $\\ep$-dependent stochastic Allen--Cahn equation with a mild random noise on a bounded domain in $\\mathbb{R}^n$, $n\\geq 2$. Here $\\ep$ is a small positive parameter that represents formally the thickness of the solution interface, while the mild noise $\\xi^\\ep(t)$ is a smooth random function of $t$ of order $\\mathcal O(\\ep^{-\\gamma})$ with $0<\\gamma<1/3$ that converges to white noise as $\\ep\\rightarrow 0^+$. We consider initial data that are independent of $\\ep$ satisfying some non-degeneracy conditions, and prove that steep transition layers---or interfaces---develop within a very "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.03804","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1812.03804","created_at":"2026-05-17T23:57:56.780578+00:00"},{"alias_kind":"arxiv_version","alias_value":"1812.03804v3","created_at":"2026-05-17T23:57:56.780578+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.03804","created_at":"2026-05-17T23:57:56.780578+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZZB6PLXWZ2PO","created_at":"2026-05-18T12:33:07.085635+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZZB6PLXWZ2POT5PY","created_at":"2026-05-18T12:33:07.085635+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZZB6PLXW","created_at":"2026-05-18T12:33:07.085635+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/ZZB6PLXWZ2POT5PY6TYRPALGS4","json":"https://pith.science/pith/ZZB6PLXWZ2POT5PY6TYRPALGS4.json","graph_json":"https://pith.science/api/pith-number/ZZB6PLXWZ2POT5PY6TYRPALGS4/graph.json","events_json":"https://pith.science/api/pith-number/ZZB6PLXWZ2POT5PY6TYRPALGS4/events.json","paper":"https://pith.science/paper/ZZB6PLXW"},"agent_actions":{"view_html":"https://pith.science/pith/ZZB6PLXWZ2POT5PY6TYRPALGS4","download_json":"https://pith.science/pith/ZZB6PLXWZ2POT5PY6TYRPALGS4.json","view_paper":"https://pith.science/paper/ZZB6PLXW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1812.03804&json=true","fetch_graph":"https://pith.science/api/pith-number/ZZB6PLXWZ2POT5PY6TYRPALGS4/graph.json","fetch_events":"https://pith.science/api/pith-number/ZZB6PLXWZ2POT5PY6TYRPALGS4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZZB6PLXWZ2POT5PY6TYRPALGS4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZZB6PLXWZ2POT5PY6TYRPALGS4/action/storage_attestation","attest_author":"https://pith.science/pith/ZZB6PLXWZ2POT5PY6TYRPALGS4/action/author_attestation","sign_citation":"https://pith.science/pith/ZZB6PLXWZ2POT5PY6TYRPALGS4/action/citation_signature","submit_replication":"https://pith.science/pith/ZZB6PLXWZ2POT5PY6TYRPALGS4/action/replication_record"}},"created_at":"2026-05-17T23:57:56.780578+00:00","updated_at":"2026-05-17T23:57:56.780578+00:00"}