{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:7LXAJUS7H7ZSP35WJPWDAPKCWS","short_pith_number":"pith:7LXAJUS7","schema_version":"1.0","canonical_sha256":"faee04d25f3ff327efb64bec303d42b49a345f175dd39aa18fcef99414be29c4","source":{"kind":"arxiv","id":"2210.04999","version":6},"attestation_state":"computed","paper":{"title":"Edgeworth-type expansion for the one-point distribution of the KPZ fixed point with a large height at a prior location","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Ron Nissim, Ruixuan Zhang","submitted_at":"2022-10-10T20:05:27Z","abstract_excerpt":"We consider the Kardar-Parisi-Zhang (KPZ) fixed point $\\mathrm{H}(x,\\tau)$ with the narrow-wedge initial condition and investigate the distribution of $\\mathrm{H}(x,\\tau)$ conditioned on a large height at an earlier space-time point $\\mathrm{H}(x',\\tau')$. As $\\mathrm{H}(x',\\tau')$ tends to infinity, we prove that the conditional one-point distribution of $\\mathrm{H}(x,\\tau)$ in the regime $\\tau>\\tau'$ converges to the Gaussian Unitary Ensemble (GUE) Tracy-Widom distribution and that the next two lower-order error terms can be expressed as derivatives of the Tracy-Widom distribution. The lowe "},"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":"2210.04999","kind":"arxiv","version":6},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.PR","submitted_at":"2022-10-10T20:05:27Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"0494f9eaf7309bc518c7cd068d5368931063e82742fa4c8837b49ddd6e946fa5","abstract_canon_sha256":"a7f17772664aae65d52dd799f1f6b0a52b566e8de5a48a3a0ac7494e161657b8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:20:34.149577Z","signature_b64":"T1MgNfmTVxqmU1tNziQIsaivruqZm59PzJlwPmdLxpuTnLuNTdpFCsqZwXTGCPvYk427ULwPn4NUsrPnFVcqCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"faee04d25f3ff327efb64bec303d42b49a345f175dd39aa18fcef99414be29c4","last_reissued_at":"2026-07-05T10:20:34.148982Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:20:34.148982Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Edgeworth-type expansion for the one-point distribution of the KPZ fixed point with a large height at a prior location","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Ron Nissim, Ruixuan Zhang","submitted_at":"2022-10-10T20:05:27Z","abstract_excerpt":"We consider the Kardar-Parisi-Zhang (KPZ) fixed point $\\mathrm{H}(x,\\tau)$ with the narrow-wedge initial condition and investigate the distribution of $\\mathrm{H}(x,\\tau)$ conditioned on a large height at an earlier space-time point $\\mathrm{H}(x',\\tau')$. As $\\mathrm{H}(x',\\tau')$ tends to infinity, we prove that the conditional one-point distribution of $\\mathrm{H}(x,\\tau)$ in the regime $\\tau>\\tau'$ converges to the Gaussian Unitary Ensemble (GUE) Tracy-Widom distribution and that the next two lower-order error terms can be expressed as derivatives of the Tracy-Widom distribution. The lowe "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2210.04999","kind":"arxiv","version":6},"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/2210.04999/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":"2210.04999","created_at":"2026-07-05T10:20:34.149055+00:00"},{"alias_kind":"arxiv_version","alias_value":"2210.04999v6","created_at":"2026-07-05T10:20:34.149055+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2210.04999","created_at":"2026-07-05T10:20:34.149055+00:00"},{"alias_kind":"pith_short_12","alias_value":"7LXAJUS7H7ZS","created_at":"2026-07-05T10:20:34.149055+00:00"},{"alias_kind":"pith_short_16","alias_value":"7LXAJUS7H7ZSP35W","created_at":"2026-07-05T10:20:34.149055+00:00"},{"alias_kind":"pith_short_8","alias_value":"7LXAJUS7","created_at":"2026-07-05T10:20:34.149055+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2501.00932","citing_title":"An upper tail field of the KPZ fixed point","ref_index":2021,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/7LXAJUS7H7ZSP35WJPWDAPKCWS","json":"https://pith.science/pith/7LXAJUS7H7ZSP35WJPWDAPKCWS.json","graph_json":"https://pith.science/api/pith-number/7LXAJUS7H7ZSP35WJPWDAPKCWS/graph.json","events_json":"https://pith.science/api/pith-number/7LXAJUS7H7ZSP35WJPWDAPKCWS/events.json","paper":"https://pith.science/paper/7LXAJUS7"},"agent_actions":{"view_html":"https://pith.science/pith/7LXAJUS7H7ZSP35WJPWDAPKCWS","download_json":"https://pith.science/pith/7LXAJUS7H7ZSP35WJPWDAPKCWS.json","view_paper":"https://pith.science/paper/7LXAJUS7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2210.04999&json=true","fetch_graph":"https://pith.science/api/pith-number/7LXAJUS7H7ZSP35WJPWDAPKCWS/graph.json","fetch_events":"https://pith.science/api/pith-number/7LXAJUS7H7ZSP35WJPWDAPKCWS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7LXAJUS7H7ZSP35WJPWDAPKCWS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7LXAJUS7H7ZSP35WJPWDAPKCWS/action/storage_attestation","attest_author":"https://pith.science/pith/7LXAJUS7H7ZSP35WJPWDAPKCWS/action/author_attestation","sign_citation":"https://pith.science/pith/7LXAJUS7H7ZSP35WJPWDAPKCWS/action/citation_signature","submit_replication":"https://pith.science/pith/7LXAJUS7H7ZSP35WJPWDAPKCWS/action/replication_record"}},"created_at":"2026-07-05T10:20:34.149055+00:00","updated_at":"2026-07-05T10:20:34.149055+00:00"}