{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:2VJQTLPINAE2H7VAAW6F73C5FV","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":"2720366bcdb351ef0364e6efe4ae91ef6eb23aad6db901e2fa842749eba0afc6","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2022-08-25T09:15:55Z","title_canon_sha256":"95c2c938ab5f0831bdcc2a6de0312984db530b10028c511d2f9b69334d7d194f"},"schema_version":"1.0","source":{"id":"2208.11952","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2208.11952","created_at":"2026-07-05T04:51:28Z"},{"alias_kind":"arxiv_version","alias_value":"2208.11952v1","created_at":"2026-07-05T04:51:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2208.11952","created_at":"2026-07-05T04:51:28Z"},{"alias_kind":"pith_short_12","alias_value":"2VJQTLPINAE2","created_at":"2026-07-05T04:51:28Z"},{"alias_kind":"pith_short_16","alias_value":"2VJQTLPINAE2H7VA","created_at":"2026-07-05T04:51:28Z"},{"alias_kind":"pith_short_8","alias_value":"2VJQTLPI","created_at":"2026-07-05T04:51:28Z"}],"graph_snapshots":[{"event_id":"sha256:093f8ee1d875dbf71bca5f4d22390625481ed918a771c4ca8295c4d7ffaec4ff","target":"graph","created_at":"2026-07-05T04:51:28Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2208.11952/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study a simple model for the trajectory of a particle in a turbulent fluid, where a Brownian motion travels through a random Gaussian velocity field. We study the quenched law of the process and prove that in a weak environment setting, the fluctuations at the transition from weak to strong disorder are described by the KPZ equation. We conjecture the same is true without the assumption of a weak environment.","authors_text":"Dom Brockington, Jon Warren","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2022-08-25T09:15:55Z","title":"At the edge of a cloud of Brownian particles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2208.11952","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:fd0f4199f40395d871df4d0463026c5f05314e5b8a86ce637020454d887557da","target":"record","created_at":"2026-07-05T04:51:28Z","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":"2720366bcdb351ef0364e6efe4ae91ef6eb23aad6db901e2fa842749eba0afc6","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2022-08-25T09:15:55Z","title_canon_sha256":"95c2c938ab5f0831bdcc2a6de0312984db530b10028c511d2f9b69334d7d194f"},"schema_version":"1.0","source":{"id":"2208.11952","kind":"arxiv","version":1}},"canonical_sha256":"d55309ade86809a3fea005bc5fec5d2d6d192036fbddc337cac25bf1eb50fce4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d55309ade86809a3fea005bc5fec5d2d6d192036fbddc337cac25bf1eb50fce4","first_computed_at":"2026-07-05T04:51:28.001016Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:51:28.001016Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1CkP+fgTQ9dULaiNW/GGam7jWEJkiew3RIgaC7OCC0o1ly/7R5qh0AVR70eVyduovNhHG5L+bv6EnxyQiIQ3DQ==","signature_status":"signed_v1","signed_at":"2026-07-05T04:51:28.001399Z","signed_message":"canonical_sha256_bytes"},"source_id":"2208.11952","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fd0f4199f40395d871df4d0463026c5f05314e5b8a86ce637020454d887557da","sha256:093f8ee1d875dbf71bca5f4d22390625481ed918a771c4ca8295c4d7ffaec4ff"],"state_sha256":"7858923fcb780e985669b13dadf8d6b5ca6715f15345583d9ff736f4aee4a198"}