{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:O6BSQ6R225TB45WLI6IYOH2NNE","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":"6b6f4f81f19713c8d1c1b4559208bc82b6b162d131e3e26d47f9929b6bfb5bf4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-06-25T05:30:51Z","title_canon_sha256":"f0732703305c2f0cd757d736d340b4936c059d5d0d9457dbb29d98f0e90ecb7d"},"schema_version":"1.0","source":{"id":"2606.26619","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.26619","created_at":"2026-06-26T01:15:36Z"},{"alias_kind":"arxiv_version","alias_value":"2606.26619v1","created_at":"2026-06-26T01:15:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.26619","created_at":"2026-06-26T01:15:36Z"},{"alias_kind":"pith_short_12","alias_value":"O6BSQ6R225TB","created_at":"2026-06-26T01:15:36Z"},{"alias_kind":"pith_short_16","alias_value":"O6BSQ6R225TB45WL","created_at":"2026-06-26T01:15:36Z"},{"alias_kind":"pith_short_8","alias_value":"O6BSQ6R2","created_at":"2026-06-26T01:15:36Z"}],"graph_snapshots":[{"event_id":"sha256:d41a2b9f60f20bf9e84a004cf1badfb222922b67bb96d9f88d3c58baca917e7e","target":"graph","created_at":"2026-06-26T01:15:36Z","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/2606.26619/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider the stochastic reaction-diffusion equation on the whole space: \\begin{align*}\n  \\left\\{\n  \\begin{aligned}\n  du(t,x) &=\\frac{1}{2}\\partial_{xx} u(t,x) dt+b(u(t,x))dt+ \\sigma(u(t,x)) W(dt,dx),\\quad t\\geq 0,\\ x\\in \\mathbb{R},\\\\\n  u(0,x)&=u_0(x), \\quad x\\in \\mathbb{R},\n  \\end{aligned}\n  \\right. \\end{align*} where $W(dt,dx)$ is a space-time white noise, $b$, $\\sigma$ are measurable coefficients. We first show that the solution is not strong Feller, and then establish the existence and uniqueness of invariant measures, exponential mixing as well as irreducibility for the solutions. To ov","authors_text":"Jianliang Zhai, Shijie Shang, Tusheng Zhang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-06-25T05:30:51Z","title":"Ergodicity of stochastic reaction-diffusion equations on unbounded domains driven by space-time white noise"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.26619","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":"sha256:499c7394f41bf831b24c2a856d3c48fba0afd1db99b4efc4042f3d74e0ed110f","target":"record","created_at":"2026-06-26T01:15:36Z","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":"6b6f4f81f19713c8d1c1b4559208bc82b6b162d131e3e26d47f9929b6bfb5bf4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-06-25T05:30:51Z","title_canon_sha256":"f0732703305c2f0cd757d736d340b4936c059d5d0d9457dbb29d98f0e90ecb7d"},"schema_version":"1.0","source":{"id":"2606.26619","kind":"arxiv","version":1}},"canonical_sha256":"7783287a3ad7661e76cb4791871f4d69079e8b32bee7a4c0c47a0adf13aac6e9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7783287a3ad7661e76cb4791871f4d69079e8b32bee7a4c0c47a0adf13aac6e9","first_computed_at":"2026-06-26T01:15:36.401803Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-26T01:15:36.401803Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JdmN2VYZw1Fj1TE63Xe2/EU/xfYh65VlgtfCPA2cU9Z1uE9MkTVNqZd64iVXLYd/wDdQ3JILmo1wz2Cn6R5ECA==","signature_status":"signed_v1","signed_at":"2026-06-26T01:15:36.402162Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.26619","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:499c7394f41bf831b24c2a856d3c48fba0afd1db99b4efc4042f3d74e0ed110f","sha256:d41a2b9f60f20bf9e84a004cf1badfb222922b67bb96d9f88d3c58baca917e7e"],"state_sha256":"3e60ed4de7659320c6b6e746f49a5c055a21963013bbff1078a0aae6a502d7fb"}