{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:WXW37UVC23BRL5HGTZXWI7SOJD","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":"4a0cebb0aa917bbbc3488b3638f94cb3139e771467ba6f544f847a573d636ab1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-02-27T16:54:12Z","title_canon_sha256":"a8d4ff1866b09497bb06a0eaa66661ef774d4d801e48643626964497df65f91f"},"schema_version":"1.0","source":{"id":"1702.08374","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.08374","created_at":"2026-05-18T00:49:55Z"},{"alias_kind":"arxiv_version","alias_value":"1702.08374v1","created_at":"2026-05-18T00:49:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.08374","created_at":"2026-05-18T00:49:55Z"},{"alias_kind":"pith_short_12","alias_value":"WXW37UVC23BR","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_16","alias_value":"WXW37UVC23BRL5HG","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_8","alias_value":"WXW37UVC","created_at":"2026-05-18T12:31:53Z"}],"graph_snapshots":[{"event_id":"sha256:1af28461d78e9c757ca5dc91117cd264000e4e4dd5ca6b45fcadc70acd528fee","target":"graph","created_at":"2026-05-18T00:49:55Z","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":"The main result of this paper is that there are examples of stochastic partial differential equations [hereforth, SPDEs] of the type $$ \\partial_t u=\\frac12\\Delta u +\\sigma(u)\\eta \\qquad\\text{on $(0\\,,\\infty)\\times\\mathbb{R}^3$}$$ such that the solution exists and is unique as a random field in the sense of Dalang and Walsh, yet the solution has unbounded oscillations in every open neighborhood of every space-time point. We are not aware of the existence of such a construction in spatial dimensions below $3$. En route, it will be proved that there exist a large family of parabolic SPDEs whose ","authors_text":"D. Khoshnevisan, Jingyu Huang, Kunwoo Kim, Le Chen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-02-27T16:54:12Z","title":"Dense blowup for parabolic SPDEs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.08374","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":"sha256:3870c04a2e1d2ffe8f9d83bb40bd03845309a31e86496cf52a204491d78ebcf4","target":"record","created_at":"2026-05-18T00:49:55Z","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":"4a0cebb0aa917bbbc3488b3638f94cb3139e771467ba6f544f847a573d636ab1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-02-27T16:54:12Z","title_canon_sha256":"a8d4ff1866b09497bb06a0eaa66661ef774d4d801e48643626964497df65f91f"},"schema_version":"1.0","source":{"id":"1702.08374","kind":"arxiv","version":1}},"canonical_sha256":"b5edbfd2a2d6c315f4e69e6f647e4e48eb179a3105da1ceb5df571eac8163ac9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b5edbfd2a2d6c315f4e69e6f647e4e48eb179a3105da1ceb5df571eac8163ac9","first_computed_at":"2026-05-18T00:49:55.087405Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:49:55.087405Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NKpFLo1+agIHQSiV8iWGwkEetrzOAD9wYuvfeywLmCRKlBWY+mIqq/jY9U/lH63KGOwsxgzBNAjy7dyOa4kDAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:49:55.088026Z","signed_message":"canonical_sha256_bytes"},"source_id":"1702.08374","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3870c04a2e1d2ffe8f9d83bb40bd03845309a31e86496cf52a204491d78ebcf4","sha256:1af28461d78e9c757ca5dc91117cd264000e4e4dd5ca6b45fcadc70acd528fee"],"state_sha256":"1492386e57ddd54c4d7a8aee50929bf86dbb22fb1f80d908437c468dd9d8b3e6"}