{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:QXWYIGHYDAUXEJMMNJC37AG6AP","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":"07da6ba0a36d60338f5268da8485886969e3891a2dc6e3b7167f1d0c4fdce0a9","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-11-20T20:33:07Z","title_canon_sha256":"8a42bbe1d437ebf70e1eb2d307cefbe8d801cae6a160b3f700556c36a001219c"},"schema_version":"1.0","source":{"id":"1711.07532","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.07532","created_at":"2026-05-17T23:50:34Z"},{"alias_kind":"arxiv_version","alias_value":"1711.07532v2","created_at":"2026-05-17T23:50:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.07532","created_at":"2026-05-17T23:50:34Z"},{"alias_kind":"pith_short_12","alias_value":"QXWYIGHYDAUX","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_16","alias_value":"QXWYIGHYDAUXEJMM","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_8","alias_value":"QXWYIGHY","created_at":"2026-05-18T12:31:39Z"}],"graph_snapshots":[{"event_id":"sha256:40460f3195eca2cadb0b5e17bd21f21941d15ba5352b61ad2ecdb213b320cff9","target":"graph","created_at":"2026-05-17T23:50:34Z","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 sample path properties of the solution to the stochastic heat equation, in $\\mathbb{R}^d$ or bounded domains of $\\mathbb{R}^d$, driven by a L\\'evy space-time white noise. When viewed as a stochastic process in time with values in an infinite-dimensional space, the solution is shown to have a c\\`adl\\`ag modification in fractional Sobolev spaces of index less than $-\\frac d 2$. Concerning the partial regularity of the solution in time or space when the other variable is fixed, we determine critical values for the Blumenthal-Getoor index of the L\\'evy noise such that noises with a sma","authors_text":"Carsten Chong, Robert C. Dalang, Thomas Humeau","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-11-20T20:33:07Z","title":"Path properties of the solution to the stochastic heat equation with L\\'evy noise"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.07532","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":"sha256:8f24884d1425abf08b8e462f69781d07abf80f2ccb0d39b77908b8f27ede772d","target":"record","created_at":"2026-05-17T23:50:34Z","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":"07da6ba0a36d60338f5268da8485886969e3891a2dc6e3b7167f1d0c4fdce0a9","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-11-20T20:33:07Z","title_canon_sha256":"8a42bbe1d437ebf70e1eb2d307cefbe8d801cae6a160b3f700556c36a001219c"},"schema_version":"1.0","source":{"id":"1711.07532","kind":"arxiv","version":2}},"canonical_sha256":"85ed8418f8182972258c6a45bf80de03e8618fc58aa5e5c729f16257ef32fab2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"85ed8418f8182972258c6a45bf80de03e8618fc58aa5e5c729f16257ef32fab2","first_computed_at":"2026-05-17T23:50:34.313219Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:50:34.313219Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nxhfBjyOQEfwcjb/liwQ+Krmlqc4JEjzJ2XBmr4YYyiOBcXLgkIUeEdCWM+FDrGiStL6LOagjkNQClN1ZFICBg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:50:34.313882Z","signed_message":"canonical_sha256_bytes"},"source_id":"1711.07532","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8f24884d1425abf08b8e462f69781d07abf80f2ccb0d39b77908b8f27ede772d","sha256:40460f3195eca2cadb0b5e17bd21f21941d15ba5352b61ad2ecdb213b320cff9"],"state_sha256":"bfa96103b37244d5453e946a056035bb3bd71a6303612e76cb7dbd386fd6af26"}