{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:3SSREAF5SHOKYPLOVRMZVQFHJ2","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":"730cee25eeec98415e23053813f4bde0aae62756e7575694e28c52b43e64179b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-06-30T07:01:35Z","title_canon_sha256":"334910f8e49e192a8066ecc89d23b848be4370715d221ac4190d356fee772694"},"schema_version":"1.0","source":{"id":"1106.6125","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.6125","created_at":"2026-05-18T04:19:03Z"},{"alias_kind":"arxiv_version","alias_value":"1106.6125v1","created_at":"2026-05-18T04:19:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.6125","created_at":"2026-05-18T04:19:03Z"},{"alias_kind":"pith_short_12","alias_value":"3SSREAF5SHOK","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"3SSREAF5SHOKYPLO","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"3SSREAF5","created_at":"2026-05-18T12:26:20Z"}],"graph_snapshots":[{"event_id":"sha256:a4caadc2fc15d7be5d724bf4c418ca84e8a8048f09de6b65baf7d8ddeee8c482","target":"graph","created_at":"2026-05-18T04:19:03Z","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 consider the initial boundary value problem of non-homogeneous stochastic heat equation. The derivative of the solution with respect to time receives heavy random perturbation. The space boundary is Lipschitz and we impose non-zero cylinder condition. We prove a regularity result after finding suitable spaces for the solution and the pre-assigned datum in the problem. The tools from potential theory, harmonic analysis and probability are used. Some Lemmas are as important as the main Theorem.","authors_text":"Kijung Lee, Minsuk Yang, Tongkeun Chang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-06-30T07:01:35Z","title":"On Initial-Boundary Value Problem of Stochastic Heat Equation in a Lipschitz Cylinder"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.6125","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:cc09a3349e93357f4fa69463e5700ef02a3f5dab7a17d4f7ad56472f4cb72168","target":"record","created_at":"2026-05-18T04:19:03Z","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":"730cee25eeec98415e23053813f4bde0aae62756e7575694e28c52b43e64179b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-06-30T07:01:35Z","title_canon_sha256":"334910f8e49e192a8066ecc89d23b848be4370715d221ac4190d356fee772694"},"schema_version":"1.0","source":{"id":"1106.6125","kind":"arxiv","version":1}},"canonical_sha256":"dca51200bd91dcac3d6eac599ac0a74eb60c1e82493a4091a6f726a733f1198a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dca51200bd91dcac3d6eac599ac0a74eb60c1e82493a4091a6f726a733f1198a","first_computed_at":"2026-05-18T04:19:03.934022Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:19:03.934022Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HYf2xQK6uSwr9w51D1mmClrYXnGS7KxV10mTcGQbxfsuwa+loRkrFi9SACBAKKuS210HRTkFs38RKRF1LNyWCg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:19:03.934816Z","signed_message":"canonical_sha256_bytes"},"source_id":"1106.6125","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cc09a3349e93357f4fa69463e5700ef02a3f5dab7a17d4f7ad56472f4cb72168","sha256:a4caadc2fc15d7be5d724bf4c418ca84e8a8048f09de6b65baf7d8ddeee8c482"],"state_sha256":"2ffccdeec47b4c2424ceac54ebdfa09931a4fe2f5d8f312903baca2195ae38cf"}