{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:J4MF2LDKVM36O2IWNSZDFEMOXF","short_pith_number":"pith:J4MF2LDK","schema_version":"1.0","canonical_sha256":"4f185d2c6aab37e769166cb232918eb94afc40cc48fb1dbb842d7aa3e92905bb","source":{"kind":"arxiv","id":"1002.1879","version":2},"attestation_state":"computed","paper":{"title":"Exact height distributions for the KPZ equation with narrow wedge initial condition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"cond-mat.stat-mech","authors_text":"Herbert Spohn, Tomohiro Sasamoto","submitted_at":"2010-02-09T15:48:24Z","abstract_excerpt":"We consider the KPZ equation in one space dimension with narrow wedge initial condition, $h(x,t=0)=- |x|/\\delta$, $\\delta\\ll 1$. Based on previous results for the weakly asymmetric simple exclusion process with step initial conditions, we obtain a determinantal formula for the one-point distribution of the solution $h(x,t)$ valid for any $x$ and $t>0$. The corresponding distribution function converges in the long time limit, $t\\to\\infty$, to the Tracy-Widom distribution. The first order correction is a shift of order $t^{-1/3}$. We provide numerical computations based on the exact formula."},"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":"1002.1879","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2010-02-09T15:48:24Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"41deb72e77f97baa1b05c765cf61a7ace206904a5344580db4e25ab63828db74","abstract_canon_sha256":"85abe223e84cc5e62276245b9763efd2d93e46e3b8466f25f57f91c71eff44b5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:09:10.776883Z","signature_b64":"qoc2a3FR988DiP//hKKZWy36TSrmM5uQ3sBD5d/9FzQUKg7OwbumUxZr9pSlR5pFVdkHQuTEoq2z8PCFKPNEDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4f185d2c6aab37e769166cb232918eb94afc40cc48fb1dbb842d7aa3e92905bb","last_reissued_at":"2026-05-18T02:09:10.776038Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:09:10.776038Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Exact height distributions for the KPZ equation with narrow wedge initial condition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"cond-mat.stat-mech","authors_text":"Herbert Spohn, Tomohiro Sasamoto","submitted_at":"2010-02-09T15:48:24Z","abstract_excerpt":"We consider the KPZ equation in one space dimension with narrow wedge initial condition, $h(x,t=0)=- |x|/\\delta$, $\\delta\\ll 1$. Based on previous results for the weakly asymmetric simple exclusion process with step initial conditions, we obtain a determinantal formula for the one-point distribution of the solution $h(x,t)$ valid for any $x$ and $t>0$. The corresponding distribution function converges in the long time limit, $t\\to\\infty$, to the Tracy-Widom distribution. The first order correction is a shift of order $t^{-1/3}$. We provide numerical computations based on the exact formula."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1002.1879","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"1002.1879","created_at":"2026-05-18T02:09:10.776174+00:00"},{"alias_kind":"arxiv_version","alias_value":"1002.1879v2","created_at":"2026-05-18T02:09:10.776174+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1002.1879","created_at":"2026-05-18T02:09:10.776174+00:00"},{"alias_kind":"pith_short_12","alias_value":"J4MF2LDKVM36","created_at":"2026-05-18T12:26:09.077623+00:00"},{"alias_kind":"pith_short_16","alias_value":"J4MF2LDKVM36O2IW","created_at":"2026-05-18T12:26:09.077623+00:00"},{"alias_kind":"pith_short_8","alias_value":"J4MF2LDK","created_at":"2026-05-18T12:26:09.077623+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/J4MF2LDKVM36O2IWNSZDFEMOXF","json":"https://pith.science/pith/J4MF2LDKVM36O2IWNSZDFEMOXF.json","graph_json":"https://pith.science/api/pith-number/J4MF2LDKVM36O2IWNSZDFEMOXF/graph.json","events_json":"https://pith.science/api/pith-number/J4MF2LDKVM36O2IWNSZDFEMOXF/events.json","paper":"https://pith.science/paper/J4MF2LDK"},"agent_actions":{"view_html":"https://pith.science/pith/J4MF2LDKVM36O2IWNSZDFEMOXF","download_json":"https://pith.science/pith/J4MF2LDKVM36O2IWNSZDFEMOXF.json","view_paper":"https://pith.science/paper/J4MF2LDK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1002.1879&json=true","fetch_graph":"https://pith.science/api/pith-number/J4MF2LDKVM36O2IWNSZDFEMOXF/graph.json","fetch_events":"https://pith.science/api/pith-number/J4MF2LDKVM36O2IWNSZDFEMOXF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/J4MF2LDKVM36O2IWNSZDFEMOXF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/J4MF2LDKVM36O2IWNSZDFEMOXF/action/storage_attestation","attest_author":"https://pith.science/pith/J4MF2LDKVM36O2IWNSZDFEMOXF/action/author_attestation","sign_citation":"https://pith.science/pith/J4MF2LDKVM36O2IWNSZDFEMOXF/action/citation_signature","submit_replication":"https://pith.science/pith/J4MF2LDKVM36O2IWNSZDFEMOXF/action/replication_record"}},"created_at":"2026-05-18T02:09:10.776174+00:00","updated_at":"2026-05-18T02:09:10.776174+00:00"}