{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2021:3U56V7AQTH62QCBPON4M76VN44","short_pith_number":"pith:3U56V7AQ","schema_version":"1.0","canonical_sha256":"dd3beafc1099fda8082f7378cffaade73a32475c0718e303ff2e5984513110f8","source":{"kind":"arxiv","id":"2105.15178","version":4},"attestation_state":"computed","paper":{"title":"Steady state of the KPZ equation on an interval and Liouville quantum mechanics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.dis-nn","cond-mat.stat-mech","math.MP","math.PR","nlin.SI"],"primary_cat":"math-ph","authors_text":"Guillaume Barraquand, Pierre Le Doussal","submitted_at":"2021-05-31T17:41:29Z","abstract_excerpt":"We obtain a simple formula for the stationary measure of the height field evolving according to the Kardar-Parisi-Zhang equation on the interval $[0,L]$ with general Neumann type boundary conditions and any interval size. This is achieved using the recent results of Corwin and Knizel (arXiv:2103.12253) together with Liouville quantum mechanics. Our formula allows to easily determine the stationary measure in various limits: KPZ fixed point on an interval, half-line KPZ equation, KPZ fixed point on a half-line, as well as the Edwards-Wilkinson equation on an interval."},"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":"2105.15178","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2021-05-31T17:41:29Z","cross_cats_sorted":["cond-mat.dis-nn","cond-mat.stat-mech","math.MP","math.PR","nlin.SI"],"title_canon_sha256":"0c88f32784231aec367e8f4fbce2934da81db50d0ef1d1d7fca96583786d3b0c","abstract_canon_sha256":"dac4b86a1e63174cd33a9ac4dcaba92d4daa8efc4afbe598d701de1876907de9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:24:09.384188Z","signature_b64":"yA8EXpLjTQ8+GW2UojuFr60uF9Hj3vSjBvKbTkgu1VaSBNHbJpXf1YIC2MSbBvGM8kiHA23paHKuLAfmABJQDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dd3beafc1099fda8082f7378cffaade73a32475c0718e303ff2e5984513110f8","last_reissued_at":"2026-07-05T04:24:09.383740Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:24:09.383740Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Steady state of the KPZ equation on an interval and Liouville quantum mechanics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.dis-nn","cond-mat.stat-mech","math.MP","math.PR","nlin.SI"],"primary_cat":"math-ph","authors_text":"Guillaume Barraquand, Pierre Le Doussal","submitted_at":"2021-05-31T17:41:29Z","abstract_excerpt":"We obtain a simple formula for the stationary measure of the height field evolving according to the Kardar-Parisi-Zhang equation on the interval $[0,L]$ with general Neumann type boundary conditions and any interval size. This is achieved using the recent results of Corwin and Knizel (arXiv:2103.12253) together with Liouville quantum mechanics. Our formula allows to easily determine the stationary measure in various limits: KPZ fixed point on an interval, half-line KPZ equation, KPZ fixed point on a half-line, as well as the Edwards-Wilkinson equation on an interval."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2105.15178","kind":"arxiv","version":4},"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/2105.15178/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":"2105.15178","created_at":"2026-07-05T04:24:09.383793+00:00"},{"alias_kind":"arxiv_version","alias_value":"2105.15178v4","created_at":"2026-07-05T04:24:09.383793+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2105.15178","created_at":"2026-07-05T04:24:09.383793+00:00"},{"alias_kind":"pith_short_12","alias_value":"3U56V7AQTH62","created_at":"2026-07-05T04:24:09.383793+00:00"},{"alias_kind":"pith_short_16","alias_value":"3U56V7AQTH62QCBP","created_at":"2026-07-05T04:24:09.383793+00:00"},{"alias_kind":"pith_short_8","alias_value":"3U56V7AQ","created_at":"2026-07-05T04:24:09.383793+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2504.18292","citing_title":"Large time cumulants of the KPZ equation on an interval","ref_index":31,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/3U56V7AQTH62QCBPON4M76VN44","json":"https://pith.science/pith/3U56V7AQTH62QCBPON4M76VN44.json","graph_json":"https://pith.science/api/pith-number/3U56V7AQTH62QCBPON4M76VN44/graph.json","events_json":"https://pith.science/api/pith-number/3U56V7AQTH62QCBPON4M76VN44/events.json","paper":"https://pith.science/paper/3U56V7AQ"},"agent_actions":{"view_html":"https://pith.science/pith/3U56V7AQTH62QCBPON4M76VN44","download_json":"https://pith.science/pith/3U56V7AQTH62QCBPON4M76VN44.json","view_paper":"https://pith.science/paper/3U56V7AQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2105.15178&json=true","fetch_graph":"https://pith.science/api/pith-number/3U56V7AQTH62QCBPON4M76VN44/graph.json","fetch_events":"https://pith.science/api/pith-number/3U56V7AQTH62QCBPON4M76VN44/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3U56V7AQTH62QCBPON4M76VN44/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3U56V7AQTH62QCBPON4M76VN44/action/storage_attestation","attest_author":"https://pith.science/pith/3U56V7AQTH62QCBPON4M76VN44/action/author_attestation","sign_citation":"https://pith.science/pith/3U56V7AQTH62QCBPON4M76VN44/action/citation_signature","submit_replication":"https://pith.science/pith/3U56V7AQTH62QCBPON4M76VN44/action/replication_record"}},"created_at":"2026-07-05T04:24:09.383793+00:00","updated_at":"2026-07-05T04:24:09.383793+00:00"}