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Let $H_N$ denote the Hamiltonian of the system and let $\\psi_{N,t}$ be the solution to the Schr\\\"odinger equation. Suppose that the initial data $\\psi_{N,0}$ satisfies the energy condition \\[ < \\psi_{N,0}, H_N \\psi_{N,0} > \\leq C N >. \\] and that the one-particle density matrix converges to a projection as $N \\to \\infty$. Then, we prove that the $k$-particle density matrices of $\\psi_{N,t}$ factorize "},"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":"0802.3877","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2008-02-26T19:11:50Z","cross_cats_sorted":["math.AP","math.MP"],"title_canon_sha256":"99527f300fcf591772d8b7d88a585a59ce1336aebd156ad0bd4f7090d5b23a20","abstract_canon_sha256":"643f821e9b818f9d4c5f1cd2f1430af17aee5ad5f1e5b75f34bd2eebb6dca053"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:16:00.834005Z","signature_b64":"aaQLohjlf8dyDa7g48E5oMzaMeCFfWIgbYx/LoOzgDNleM+LMffsoLz1BxAw99CyZ86d0tk0CtBLKWa2z0BwAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"01788fa01ddfdeee3ab9b9d18b8332bb905c93fd0e4dfef151c48c548954f8dd","last_reissued_at":"2026-05-18T02:16:00.833579Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:16:00.833579Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Rigorous Derivation of the Gross-Pitaevskii Equation with a Large Interaction Potential","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.MP"],"primary_cat":"math-ph","authors_text":"Benjamin Schlein, Horng-Tzer Yau, Laszlo Erdos","submitted_at":"2008-02-26T19:11:50Z","abstract_excerpt":"Consider a system of $N$ bosons in three dimensions interacting via a repulsive short range pair potential $N^2V(N(x_i-x_j))$, where $\\bx=(x_1, >..., x_N)$ denotes the positions of the particles. 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