{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:3OFURQHKAJZ273EJWGXKL63GUU","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":"f7b1b0e898c0fe6907be260c6e6fe2c62e30c30a967f0bb97ff981de9de41e73","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-09-28T19:57:24Z","title_canon_sha256":"e17c2015acbbc50188a25dfb39afb161df289437ca10e989ee3a7d932656ec9f"},"schema_version":"1.0","source":{"id":"1810.00066","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.00066","created_at":"2026-05-18T00:04:28Z"},{"alias_kind":"arxiv_version","alias_value":"1810.00066v1","created_at":"2026-05-18T00:04:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.00066","created_at":"2026-05-18T00:04:28Z"},{"alias_kind":"pith_short_12","alias_value":"3OFURQHKAJZ2","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_16","alias_value":"3OFURQHKAJZ273EJ","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_8","alias_value":"3OFURQHK","created_at":"2026-05-18T12:32:02Z"}],"graph_snapshots":[{"event_id":"sha256:064bce5fea66e1b3119f023f22d6ea59b0a77ea46805d70191d028dadd12724f","target":"graph","created_at":"2026-05-18T00:04:28Z","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":"In this paper, we study the following stochastic heat equation \\[\n  \\partial_tu=\\mathcal{L} u(t,x)+\\dot{B},\\quad\n  u(0,x)=0,\\quad 0\\le t\\le T,\\quad x\\in\\mathbb{R}d, \\] where $\\mathcal{L}$ is the generator of a L\\'evy process $X$ taking value in $\\mathbb{R}^d$, $B$ is a fractional-colored Gaussian noise with Hurst index $H\\in\\left(\\frac12,\\,1\\right)$ for the time variable and spatial covariance function $f$ which is the Fourier transform of a tempered measure $\\mu.$\n  After establishing the existence of solution for the stochastic heat equation, we study the regularity of the solution $\\{u(t,x)","authors_text":"Dongsheng Wu, Randall Herrell, Renming Song, Yimin Xiao","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-09-28T19:57:24Z","title":"Sharp Space-Time Regularity of the Solution to Stochastic Heat Equation Driven by Fractional-Colored Noise"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.00066","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":"sha256:9c93feb93fc72cb5eedb8735ad6e812099275fa4ccc0373f50d09a1d5fd70532","target":"record","created_at":"2026-05-18T00:04:28Z","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":"f7b1b0e898c0fe6907be260c6e6fe2c62e30c30a967f0bb97ff981de9de41e73","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-09-28T19:57:24Z","title_canon_sha256":"e17c2015acbbc50188a25dfb39afb161df289437ca10e989ee3a7d932656ec9f"},"schema_version":"1.0","source":{"id":"1810.00066","kind":"arxiv","version":1}},"canonical_sha256":"db8b48c0ea0273afec89b1aea5fb66a512123d057aa036956271b0838c0759b6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"db8b48c0ea0273afec89b1aea5fb66a512123d057aa036956271b0838c0759b6","first_computed_at":"2026-05-18T00:04:28.940750Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:04:28.940750Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"U7sVylAart5J6h+kTl5fVssDZs+DkNCg38eSLuIMXn6ud4rMY7hyjS6Cg1Z+oyg3Ck16V8gTUcrjwrKXDqFkBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:04:28.941473Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.00066","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9c93feb93fc72cb5eedb8735ad6e812099275fa4ccc0373f50d09a1d5fd70532","sha256:064bce5fea66e1b3119f023f22d6ea59b0a77ea46805d70191d028dadd12724f"],"state_sha256":"3b44d928401db83e6b199f7800c68e02a13bd9f371e705f00af81d5f40eff8ee"}