{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:RT57NTTPRTBX2G337BO6ZGRERU","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":"9a24dc8cdda9cf8470ec0b2a2ccd88d2ad0ba507e16fe78ef920ad4cb7753707","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-07-30T13:05:30Z","title_canon_sha256":"8a13feaa45d32c7be77cdb03b5ce4102119a3aaa29a3c8b8df5a4e76b919118b"},"schema_version":"1.0","source":{"id":"2607.28167","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.28167","created_at":"2026-07-31T01:36:10Z"},{"alias_kind":"arxiv_version","alias_value":"2607.28167v1","created_at":"2026-07-31T01:36:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.28167","created_at":"2026-07-31T01:36:10Z"},{"alias_kind":"pith_short_12","alias_value":"RT57NTTPRTBX","created_at":"2026-07-31T01:36:10Z"},{"alias_kind":"pith_short_16","alias_value":"RT57NTTPRTBX2G33","created_at":"2026-07-31T01:36:10Z"},{"alias_kind":"pith_short_8","alias_value":"RT57NTTP","created_at":"2026-07-31T01:36:10Z"}],"graph_snapshots":[{"event_id":"sha256:715d310b5354b4f4971cb15e07b8e37cb8a3b4572fde996d2d660b219182473c","target":"graph","created_at":"2026-07-31T01:36:10Z","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/2607.28167/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper investigates the nonlinear stochastic fractional heat equation driven by a Gaussian noise that is white in time and fractional in space with a Hurst parameter $H \\in \\big(\\frac{3-\\alpha}{4}, \\frac{1}{2}\\big)$. Specifically, the driving operator is the fractional Laplacian of order $\\alpha/2 \\in (1/2, 1)$. We characterize the asymptotic behavior of the temporal increment $u(t+\\varepsilon,x)-u(t,x)$ for fixed $t\\ge 0$ and $x\\in\\mathbb{R}$ as $\\varepsilon\\downarrow 0$. Utilizing these precise asymptotic estimates, we establish Khinchin's and Chung's laws of the iterated logarithm for t","authors_text":"Beibei Zhang, Bin Qian","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-07-30T13:05:30Z","title":"Temporal properties of the stochastic fractional heat equation with rough dependence in space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.28167","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:a90d93f350a1973fc8a47d9d6547a5064cccea9722a186bb1807f623fe98d83a","target":"record","created_at":"2026-07-31T01:36:10Z","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":"9a24dc8cdda9cf8470ec0b2a2ccd88d2ad0ba507e16fe78ef920ad4cb7753707","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-07-30T13:05:30Z","title_canon_sha256":"8a13feaa45d32c7be77cdb03b5ce4102119a3aaa29a3c8b8df5a4e76b919118b"},"schema_version":"1.0","source":{"id":"2607.28167","kind":"arxiv","version":1}},"canonical_sha256":"8cfbf6ce6f8cc37d1b7bf85dec9a248d04093fd8067c0b8e083e1ff41a1bbe8b","receipt":{"builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8cfbf6ce6f8cc37d1b7bf85dec9a248d04093fd8067c0b8e083e1ff41a1bbe8b","first_computed_at":"2026-07-31T01:36:10.252136Z","kind":"pith_receipt","last_reissued_at":"2026-07-31T01:36:10.252136Z","receipt_version":"0.3","signature_status":"unsigned_v0"},"source_id":"2607.28167","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a90d93f350a1973fc8a47d9d6547a5064cccea9722a186bb1807f623fe98d83a","sha256:715d310b5354b4f4971cb15e07b8e37cb8a3b4572fde996d2d660b219182473c"],"state_sha256":"6dd8828c8dc96203bffa33160fda812776858c377d2fe914de54d8e196aa8f8c"}