{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:JSVNRFEYZTRHT7RYPHKSYU4UXY","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":"f4027ede7ff83323495bb3d091d08bffa609a203ed7f90b9fb65088faa6976b9","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.PR","submitted_at":"2025-09-02T16:55:18Z","title_canon_sha256":"d2d71f187fa89c4a2b8463747c9477d7730831fd379d467d49c978634bfa7c34"},"schema_version":"1.0","source":{"id":"2509.02504","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2509.02504","created_at":"2026-06-23T03:13:47Z"},{"alias_kind":"arxiv_version","alias_value":"2509.02504v2","created_at":"2026-06-23T03:13:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2509.02504","created_at":"2026-06-23T03:13:47Z"},{"alias_kind":"pith_short_12","alias_value":"JSVNRFEYZTRH","created_at":"2026-06-23T03:13:47Z"},{"alias_kind":"pith_short_16","alias_value":"JSVNRFEYZTRHT7RY","created_at":"2026-06-23T03:13:47Z"},{"alias_kind":"pith_short_8","alias_value":"JSVNRFEY","created_at":"2026-06-23T03:13:47Z"}],"graph_snapshots":[{"event_id":"sha256:cc6b7baac644b4dce88c072ccd079eeb5ca22af9f17ebfc0f81c021f53e06038","target":"graph","created_at":"2026-06-23T03:13:47Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2509.02504/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider a nonlinear stochastic heat equation on $[0,T]\\times [-L,L]$, driven by a space-time white noise $W$, with a given initial condition $u_0: \\mathbb{R} \\to \\mathbb{R}$ and three different types of (vanishing) boundary conditions: Dirichlet, Mixed and Neumann. We prove that as $L\\to\\infty$, the random field solution at any space-time position converges in the $L^p(\\Omega)$-norm ($p\\ge 1$) to the solution of the stochastic heat equation on $\\mathbb{R}$ (with the same initial condition $u_0$), and we determine the (near optimal) rate of convergence. The proof relies on estimates of diff","authors_text":"David Candil, Marta Sanz Sol\\'e, Robert C. Dalang","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.PR","submitted_at":"2025-09-02T16:55:18Z","title":"Asymptotic behavior of the stochastic heat equation over large intervals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.02504","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:c58f8da62454e9ad62d7b36fdd6b177c8c1f263d40dac0528885ebfafa0bb616","target":"record","created_at":"2026-06-23T03:13:47Z","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":"f4027ede7ff83323495bb3d091d08bffa609a203ed7f90b9fb65088faa6976b9","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.PR","submitted_at":"2025-09-02T16:55:18Z","title_canon_sha256":"d2d71f187fa89c4a2b8463747c9477d7730831fd379d467d49c978634bfa7c34"},"schema_version":"1.0","source":{"id":"2509.02504","kind":"arxiv","version":2}},"canonical_sha256":"4caad89498cce279fe3879d52c5394be122aee46a56f1fe720bd2a66b2be7920","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4caad89498cce279fe3879d52c5394be122aee46a56f1fe720bd2a66b2be7920","first_computed_at":"2026-06-23T03:13:47.209785Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-23T03:13:47.209785Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TebeHXCUQzoRhd87nBVUSj28xxuDT99lEkhvbjBUGGn7kcrwYZpIulZjh9NtiatImdKMC1VBHh4hl2wDArmLAQ==","signature_status":"signed_v1","signed_at":"2026-06-23T03:13:47.210256Z","signed_message":"canonical_sha256_bytes"},"source_id":"2509.02504","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c58f8da62454e9ad62d7b36fdd6b177c8c1f263d40dac0528885ebfafa0bb616","sha256:cc6b7baac644b4dce88c072ccd079eeb5ca22af9f17ebfc0f81c021f53e06038"],"state_sha256":"e50076f5d08578abe626128ecd29d1556c93b87de697bf4c9a9939ccae1a0ca5"}