{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:TLYMJLYQSDJDGJPLV6ENYON5NA","short_pith_number":"pith:TLYMJLYQ","schema_version":"1.0","canonical_sha256":"9af0c4af1090d23325ebaf88dc39bd680d656f894ffb3073f6942356e1e78fb4","source":{"kind":"arxiv","id":"1606.08702","version":3},"attestation_state":"computed","paper":{"title":"Nonlinear Luttinger liquid: Exact result for the Green function in terms of the fourth Painlev\\'e transcendent","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"cond-mat.quant-gas","authors_text":"Austen Lamacraft, D. L. Kovrizhin, Tom Price","submitted_at":"2016-06-28T13:51:00Z","abstract_excerpt":"We show that exact time dependent single particle Green function in the Imambekov-Glazman theory of nonlinear Luttinger liquids can be written, for any value of the Luttinger parameter, in terms of a particular solution of the Painlev\\'e IV equation. Our expression for the Green function has a form analogous to the celebrated Tracy-Widom result connecting the Airy kernel with Painlev\\'e II. The asymptotic power law of the exact solution as a function of a single scaling variable $x/\\sqrt{t}$ agrees with the mobile impurity results. The full shape of the Green function in the thermodynamic limi"},"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":"1606.08702","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.quant-gas","submitted_at":"2016-06-28T13:51:00Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"24694400cbec4b615e921308fba544c398f16950fd95316278d01d73c7e87e85","abstract_canon_sha256":"4ba9b559f15a66449a01cffff1455cb5885d43a3e973b0caaeda226030591b65"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:18:04.355516Z","signature_b64":"22Nc8tgYyM6iFl0lTzOIUxZkYpQQyrZ6GkxBYg1mXwRkCiFTB0R71Q85tZ/hUCQgI2WeTDNjVl9KiHpCAu3IBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9af0c4af1090d23325ebaf88dc39bd680d656f894ffb3073f6942356e1e78fb4","last_reissued_at":"2026-05-18T00:18:04.354984Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:18:04.354984Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Nonlinear Luttinger liquid: Exact result for the Green function in terms of the fourth Painlev\\'e transcendent","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"cond-mat.quant-gas","authors_text":"Austen Lamacraft, D. L. Kovrizhin, Tom Price","submitted_at":"2016-06-28T13:51:00Z","abstract_excerpt":"We show that exact time dependent single particle Green function in the Imambekov-Glazman theory of nonlinear Luttinger liquids can be written, for any value of the Luttinger parameter, in terms of a particular solution of the Painlev\\'e IV equation. Our expression for the Green function has a form analogous to the celebrated Tracy-Widom result connecting the Airy kernel with Painlev\\'e II. The asymptotic power law of the exact solution as a function of a single scaling variable $x/\\sqrt{t}$ agrees with the mobile impurity results. The full shape of the Green function in the thermodynamic limi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.08702","kind":"arxiv","version":3},"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":"1606.08702","created_at":"2026-05-18T00:18:04.355070+00:00"},{"alias_kind":"arxiv_version","alias_value":"1606.08702v3","created_at":"2026-05-18T00:18:04.355070+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.08702","created_at":"2026-05-18T00:18:04.355070+00:00"},{"alias_kind":"pith_short_12","alias_value":"TLYMJLYQSDJD","created_at":"2026-05-18T12:30:44.179134+00:00"},{"alias_kind":"pith_short_16","alias_value":"TLYMJLYQSDJDGJPL","created_at":"2026-05-18T12:30:44.179134+00:00"},{"alias_kind":"pith_short_8","alias_value":"TLYMJLYQ","created_at":"2026-05-18T12:30:44.179134+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/TLYMJLYQSDJDGJPLV6ENYON5NA","json":"https://pith.science/pith/TLYMJLYQSDJDGJPLV6ENYON5NA.json","graph_json":"https://pith.science/api/pith-number/TLYMJLYQSDJDGJPLV6ENYON5NA/graph.json","events_json":"https://pith.science/api/pith-number/TLYMJLYQSDJDGJPLV6ENYON5NA/events.json","paper":"https://pith.science/paper/TLYMJLYQ"},"agent_actions":{"view_html":"https://pith.science/pith/TLYMJLYQSDJDGJPLV6ENYON5NA","download_json":"https://pith.science/pith/TLYMJLYQSDJDGJPLV6ENYON5NA.json","view_paper":"https://pith.science/paper/TLYMJLYQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1606.08702&json=true","fetch_graph":"https://pith.science/api/pith-number/TLYMJLYQSDJDGJPLV6ENYON5NA/graph.json","fetch_events":"https://pith.science/api/pith-number/TLYMJLYQSDJDGJPLV6ENYON5NA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TLYMJLYQSDJDGJPLV6ENYON5NA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TLYMJLYQSDJDGJPLV6ENYON5NA/action/storage_attestation","attest_author":"https://pith.science/pith/TLYMJLYQSDJDGJPLV6ENYON5NA/action/author_attestation","sign_citation":"https://pith.science/pith/TLYMJLYQSDJDGJPLV6ENYON5NA/action/citation_signature","submit_replication":"https://pith.science/pith/TLYMJLYQSDJDGJPLV6ENYON5NA/action/replication_record"}},"created_at":"2026-05-18T00:18:04.355070+00:00","updated_at":"2026-05-18T00:18:04.355070+00:00"}