{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:LPBEUKFUWUPBT2SZH7HJPZHZZI","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"70a96cb30c01d3f5f385a60e9a522af2704bd5477aeb9d1353c4ebbbf5616a17","cross_cats_sorted":["math.DS","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2009-01-21T14:37:02Z","title_canon_sha256":"59fb091e13b9a0b98043835fcb57903420dcc592a722b1e737bde9878df1fcba"},"schema_version":"1.0","source":{"id":"0901.3283","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0901.3283","created_at":"2026-05-18T04:30:37Z"},{"alias_kind":"arxiv_version","alias_value":"0901.3283v2","created_at":"2026-05-18T04:30:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0901.3283","created_at":"2026-05-18T04:30:37Z"},{"alias_kind":"pith_short_12","alias_value":"LPBEUKFUWUPB","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_16","alias_value":"LPBEUKFUWUPBT2SZ","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_8","alias_value":"LPBEUKFU","created_at":"2026-05-18T12:26:00Z"}],"graph_snapshots":[{"event_id":"sha256:509fd7d295dc90de879d31589d6bc841a4f50d47421708a3837bd156c3dc1649","target":"graph","created_at":"2026-05-18T04:30:37Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"It is common practice to approximate a weakly nonlinear wave equation through a kinetic transport equation, thus raising the issue of controlling the validity of the kinetic limit for a suitable choice of the random initial data. While for the general case a proof of the kinetic limit remains open, we report on first progress. As wave equation we consider the nonlinear Schrodinger equation discretized on a hypercubic lattice. Since this is a Hamiltonian system, a natural choice of random initial data is distributing them according to the corresponding Gibbs measure with a chemical potential ch","authors_text":"Herbert Spohn, Jani Lukkarinen","cross_cats":["math.DS","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2009-01-21T14:37:02Z","title":"Weakly nonlinear Schr\\\"odinger equation with random initial data"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0901.3283","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:fe4414b381400a58bbbc8c50cbfff2f58137a6aaf7eee4630581d9df20acfee8","target":"record","created_at":"2026-05-18T04:30:37Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"70a96cb30c01d3f5f385a60e9a522af2704bd5477aeb9d1353c4ebbbf5616a17","cross_cats_sorted":["math.DS","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2009-01-21T14:37:02Z","title_canon_sha256":"59fb091e13b9a0b98043835fcb57903420dcc592a722b1e737bde9878df1fcba"},"schema_version":"1.0","source":{"id":"0901.3283","kind":"arxiv","version":2}},"canonical_sha256":"5bc24a28b4b51e19ea593fce97e4f9ca38bd814bdac64bc9e1cafe2d5beca4ce","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5bc24a28b4b51e19ea593fce97e4f9ca38bd814bdac64bc9e1cafe2d5beca4ce","first_computed_at":"2026-05-18T04:30:37.087559Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:30:37.087559Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hs3j/QpJCk6269h9Z7OBpevJL4uUeuJIjZzrYPudQtlJ5CK6oFExEJRRAIsGBdE5/2RKLeJgXPKTbHz2s7HpDg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:30:37.088288Z","signed_message":"canonical_sha256_bytes"},"source_id":"0901.3283","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fe4414b381400a58bbbc8c50cbfff2f58137a6aaf7eee4630581d9df20acfee8","sha256:509fd7d295dc90de879d31589d6bc841a4f50d47421708a3837bd156c3dc1649"],"state_sha256":"1256fa060da7a208c94e9848d24b459b157c6460ca5067392f64463fd4026484"}