{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:MWRDZ5DA2E2OHEYQ5MLHTLNQXT","short_pith_number":"pith:MWRDZ5DA","schema_version":"1.0","canonical_sha256":"65a23cf460d134e39310eb1679adb0bce5640777c7218035392269863f2bf945","source":{"kind":"arxiv","id":"1904.08137","version":2},"attestation_state":"computed","paper":{"title":"A microscopic derivation of Gibbs measures for nonlinear Schr\\\"{o}dinger equations with unbounded interaction potentials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.PR"],"primary_cat":"math.AP","authors_text":"Vedran Sohinger","submitted_at":"2019-04-17T08:44:14Z","abstract_excerpt":"We study the derivation of the Gibbs measure for the nonlinear Schr\\\"{o}dinger equation (NLS) from many-body quantum thermal states in the high-temperature limit. In this paper, we consider the nonlocal NLS with defocusing and unbounded $L^p$ interaction potentials on $\\mathbb{T}^d$ for $d=1,2,3$. This extends the author's earlier joint work with Fr\\\"{o}hlich, Knowles, and Schlein, where the regime of defocusing and bounded interaction potentials was considered. When $d=1$, we give an alternative proof of a result previously obtained by Lewin, Nam, and Rougerie.\n  Our proof is based on a pertu"},"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":"1904.08137","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-04-17T08:44:14Z","cross_cats_sorted":["math-ph","math.MP","math.PR"],"title_canon_sha256":"5b1ff9a62678d4f624233848a000edf1c2d24c6b0cfa458fa3f66c667325afeb","abstract_canon_sha256":"80cb401ef3851828dd52ad8fcdd8cfdcd7a15654b8a92fe02de48868f2fb9793"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:43:42.299625Z","signature_b64":"Ifa/U7Jyqa4s4hS/YQy+Mkd2gee1Tzf30y3Wtjoq4QfI5DhHwsahrAc6o1qtXSQtGB4+7fcOaSr9/KlXv+R/DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"65a23cf460d134e39310eb1679adb0bce5640777c7218035392269863f2bf945","last_reissued_at":"2026-05-17T23:43:42.299081Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:43:42.299081Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A microscopic derivation of Gibbs measures for nonlinear Schr\\\"{o}dinger equations with unbounded interaction potentials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.PR"],"primary_cat":"math.AP","authors_text":"Vedran Sohinger","submitted_at":"2019-04-17T08:44:14Z","abstract_excerpt":"We study the derivation of the Gibbs measure for the nonlinear Schr\\\"{o}dinger equation (NLS) from many-body quantum thermal states in the high-temperature limit. In this paper, we consider the nonlocal NLS with defocusing and unbounded $L^p$ interaction potentials on $\\mathbb{T}^d$ for $d=1,2,3$. This extends the author's earlier joint work with Fr\\\"{o}hlich, Knowles, and Schlein, where the regime of defocusing and bounded interaction potentials was considered. When $d=1$, we give an alternative proof of a result previously obtained by Lewin, Nam, and Rougerie.\n  Our proof is based on a pertu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.08137","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":"1904.08137","created_at":"2026-05-17T23:43:42.299160+00:00"},{"alias_kind":"arxiv_version","alias_value":"1904.08137v2","created_at":"2026-05-17T23:43:42.299160+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.08137","created_at":"2026-05-17T23:43:42.299160+00:00"},{"alias_kind":"pith_short_12","alias_value":"MWRDZ5DA2E2O","created_at":"2026-05-18T12:33:24.271573+00:00"},{"alias_kind":"pith_short_16","alias_value":"MWRDZ5DA2E2OHEYQ","created_at":"2026-05-18T12:33:24.271573+00:00"},{"alias_kind":"pith_short_8","alias_value":"MWRDZ5DA","created_at":"2026-05-18T12:33:24.271573+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2012.05110","citing_title":"Interacting loop ensembles and Bose gases","ref_index":32,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/MWRDZ5DA2E2OHEYQ5MLHTLNQXT","json":"https://pith.science/pith/MWRDZ5DA2E2OHEYQ5MLHTLNQXT.json","graph_json":"https://pith.science/api/pith-number/MWRDZ5DA2E2OHEYQ5MLHTLNQXT/graph.json","events_json":"https://pith.science/api/pith-number/MWRDZ5DA2E2OHEYQ5MLHTLNQXT/events.json","paper":"https://pith.science/paper/MWRDZ5DA"},"agent_actions":{"view_html":"https://pith.science/pith/MWRDZ5DA2E2OHEYQ5MLHTLNQXT","download_json":"https://pith.science/pith/MWRDZ5DA2E2OHEYQ5MLHTLNQXT.json","view_paper":"https://pith.science/paper/MWRDZ5DA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1904.08137&json=true","fetch_graph":"https://pith.science/api/pith-number/MWRDZ5DA2E2OHEYQ5MLHTLNQXT/graph.json","fetch_events":"https://pith.science/api/pith-number/MWRDZ5DA2E2OHEYQ5MLHTLNQXT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MWRDZ5DA2E2OHEYQ5MLHTLNQXT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MWRDZ5DA2E2OHEYQ5MLHTLNQXT/action/storage_attestation","attest_author":"https://pith.science/pith/MWRDZ5DA2E2OHEYQ5MLHTLNQXT/action/author_attestation","sign_citation":"https://pith.science/pith/MWRDZ5DA2E2OHEYQ5MLHTLNQXT/action/citation_signature","submit_replication":"https://pith.science/pith/MWRDZ5DA2E2OHEYQ5MLHTLNQXT/action/replication_record"}},"created_at":"2026-05-17T23:43:42.299160+00:00","updated_at":"2026-05-17T23:43:42.299160+00:00"}