{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:3YVWKE3YXOWMUHUJD63OMPTNUG","short_pith_number":"pith:3YVWKE3Y","schema_version":"1.0","canonical_sha256":"de2b651378bbacca1e891fb6e63e6da1805f2fa505793e71129403897ce9417e","source":{"kind":"arxiv","id":"2607.21443","version":1},"attestation_state":"computed","paper":{"title":"The critical KPZ scale for the Averaging Process","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Federico Sau, Hindy Drillick, Shalin Parekh","submitted_at":"2026-07-23T15:50:08Z","abstract_excerpt":"KPZ-type extremal fluctuations have recently been proved for several models of random walks in space-time random environments (RWRE) in $1+1$ dimensions. A general moment criterion predicts the spatial scale at which this behavior should occur, but does not by itself guarantee non-trivial fluctuations at that scale.\n  In this paper, we show that the averaging process provides an instance in which this criterion is not sharp: because of a degeneracy in the update mechanism, the actual KPZ limit appears only beyond the predicted scale. The relevant critical contribution arises from the interplay"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2607.21443","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2026-07-23T15:50:08Z","cross_cats_sorted":[],"title_canon_sha256":"cc502806f756c88473e0d0df319f535800557d7970ed62977f6f75fb8c4a494c","abstract_canon_sha256":"161269381271e3dfe72248c9a4d7860ba1dfb9e41b7fd72b964600fd00e7f7bb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-24T01:24:32.871818Z","signature_b64":"wPlz+1//7rLkezYAk8GMfYu21iUXKtu9Q+mEay6kAP2viifWoWW7OorJv7C21E+TSBdu/51vNeUHnp0jEXHHAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"de2b651378bbacca1e891fb6e63e6da1805f2fa505793e71129403897ce9417e","last_reissued_at":"2026-07-24T01:24:32.870961Z","signature_status":"signed_v1","first_computed_at":"2026-07-24T01:24:32.870961Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The critical KPZ scale for the Averaging Process","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Federico Sau, Hindy Drillick, Shalin Parekh","submitted_at":"2026-07-23T15:50:08Z","abstract_excerpt":"KPZ-type extremal fluctuations have recently been proved for several models of random walks in space-time random environments (RWRE) in $1+1$ dimensions. A general moment criterion predicts the spatial scale at which this behavior should occur, but does not by itself guarantee non-trivial fluctuations at that scale.\n  In this paper, we show that the averaging process provides an instance in which this criterion is not sharp: because of a degeneracy in the update mechanism, the actual KPZ limit appears only beyond the predicted scale. The relevant critical contribution arises from the interplay"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.21443","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.21443/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2607.21443","created_at":"2026-07-24T01:24:32.871408+00:00"},{"alias_kind":"arxiv_version","alias_value":"2607.21443v1","created_at":"2026-07-24T01:24:32.871408+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.21443","created_at":"2026-07-24T01:24:32.871408+00:00"},{"alias_kind":"pith_short_12","alias_value":"3YVWKE3YXOWM","created_at":"2026-07-24T01:24:32.871408+00:00"},{"alias_kind":"pith_short_16","alias_value":"3YVWKE3YXOWMUHUJ","created_at":"2026-07-24T01:24:32.871408+00:00"},{"alias_kind":"pith_short_8","alias_value":"3YVWKE3Y","created_at":"2026-07-24T01:24:32.871408+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/3YVWKE3YXOWMUHUJD63OMPTNUG","json":"https://pith.science/pith/3YVWKE3YXOWMUHUJD63OMPTNUG.json","graph_json":"https://pith.science/api/pith-number/3YVWKE3YXOWMUHUJD63OMPTNUG/graph.json","events_json":"https://pith.science/api/pith-number/3YVWKE3YXOWMUHUJD63OMPTNUG/events.json","paper":"https://pith.science/paper/3YVWKE3Y"},"agent_actions":{"view_html":"https://pith.science/pith/3YVWKE3YXOWMUHUJD63OMPTNUG","download_json":"https://pith.science/pith/3YVWKE3YXOWMUHUJD63OMPTNUG.json","view_paper":"https://pith.science/paper/3YVWKE3Y","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2607.21443&json=true","fetch_graph":"https://pith.science/api/pith-number/3YVWKE3YXOWMUHUJD63OMPTNUG/graph.json","fetch_events":"https://pith.science/api/pith-number/3YVWKE3YXOWMUHUJD63OMPTNUG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3YVWKE3YXOWMUHUJD63OMPTNUG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3YVWKE3YXOWMUHUJD63OMPTNUG/action/storage_attestation","attest_author":"https://pith.science/pith/3YVWKE3YXOWMUHUJD63OMPTNUG/action/author_attestation","sign_citation":"https://pith.science/pith/3YVWKE3YXOWMUHUJD63OMPTNUG/action/citation_signature","submit_replication":"https://pith.science/pith/3YVWKE3YXOWMUHUJD63OMPTNUG/action/replication_record"}},"created_at":"2026-07-24T01:24:32.871408+00:00","updated_at":"2026-07-24T01:24:32.871408+00:00"}