{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:5VRLMIUE62VABZUDKLMU3FUI4O","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":"de42847b6edc0a61adb5495a00190938461f5d78fdcff9d77e6b43a5ed25e9f8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-06-05T15:02:13Z","title_canon_sha256":"e7ae84ac3927bdda9538ebe0751655ba3d012ecc0f376e8c842f4dbc590edb06"},"schema_version":"1.0","source":{"id":"2606.07353","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.07353","created_at":"2026-06-08T01:05:21Z"},{"alias_kind":"arxiv_version","alias_value":"2606.07353v1","created_at":"2026-06-08T01:05:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.07353","created_at":"2026-06-08T01:05:21Z"},{"alias_kind":"pith_short_12","alias_value":"5VRLMIUE62VA","created_at":"2026-06-08T01:05:21Z"},{"alias_kind":"pith_short_16","alias_value":"5VRLMIUE62VABZUD","created_at":"2026-06-08T01:05:21Z"},{"alias_kind":"pith_short_8","alias_value":"5VRLMIUE","created_at":"2026-06-08T01:05:21Z"}],"graph_snapshots":[{"event_id":"sha256:84d3fde7ab2f4ffeb47312016908aaba42f3e515aba9f862eb630db56d538cc4","target":"graph","created_at":"2026-06-08T01:05:21Z","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/2606.07353/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the KPZ equation on a circle with an additive spatial perturbation $\\partial_t h=\\tfrac12\\Delta h+\\tfrac12|\\nabla h|^2+\\xi+ V$, where $\\xi$ is a spacetime white noise and $V$ is a smooth spatial function. When $V=0$, it is well-known that the unique invariant measure is the Brownian bridge. In the presence of the perturbation, we show that the equation admits a unique invariant measure that is absolutely continuous with respect to the Brownian bridge. We further prove the measure has a finite relative entropy with respect to the law of the bridge and that, for any $p\\in(1,\\infty)$, th","authors_text":"Tomasz Komorowski, Yu Gu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-06-05T15:02:13Z","title":"The Gaussian structure of a perturbed KPZ"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.07353","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:df1dd9769a4659e018b0dafaa34c560fbfc2c9022974c890d59255387fc43d14","target":"record","created_at":"2026-06-08T01:05:21Z","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":"de42847b6edc0a61adb5495a00190938461f5d78fdcff9d77e6b43a5ed25e9f8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-06-05T15:02:13Z","title_canon_sha256":"e7ae84ac3927bdda9538ebe0751655ba3d012ecc0f376e8c842f4dbc590edb06"},"schema_version":"1.0","source":{"id":"2606.07353","kind":"arxiv","version":1}},"canonical_sha256":"ed62b62284f6aa00e68352d94d9688e3ac44f66a97794522d4aff888662e41e0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ed62b62284f6aa00e68352d94d9688e3ac44f66a97794522d4aff888662e41e0","first_computed_at":"2026-06-08T01:05:21.662166Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-08T01:05:21.662166Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"M9sZuwI/QHUEEpVTpUMcG2JOYZbJuO4Q7Tj78u3OciwWnCfCtitM/t6W0A/KXvAC5+3J4AMdfWZ1Xnidm1P4CA==","signature_status":"signed_v1","signed_at":"2026-06-08T01:05:21.662905Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.07353","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:df1dd9769a4659e018b0dafaa34c560fbfc2c9022974c890d59255387fc43d14","sha256:84d3fde7ab2f4ffeb47312016908aaba42f3e515aba9f862eb630db56d538cc4"],"state_sha256":"a0322201cfc08ea8f92dddfb6becf4d607a8e6506058a181a440ac4d061ee820"}