{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:IKWB4N6BIE5GWW5GJFLKEHR4HP","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":"d3e247a2e24809c6ad87b5e13f48e6a520767e65cc2807cf56b5daa762bd380d","cross_cats_sorted":["math.MP","physics.flu-dyn"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-11-26T20:11:29Z","title_canon_sha256":"c8c238ffb7cd30f88d2f9dfcdf6b852490b53ae88a7b366a9bdfa0839fa8937c"},"schema_version":"1.0","source":{"id":"1311.6794","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.6794","created_at":"2026-05-18T03:03:46Z"},{"alias_kind":"arxiv_version","alias_value":"1311.6794v3","created_at":"2026-05-18T03:03:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.6794","created_at":"2026-05-18T03:03:46Z"},{"alias_kind":"pith_short_12","alias_value":"IKWB4N6BIE5G","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_16","alias_value":"IKWB4N6BIE5GWW5G","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_8","alias_value":"IKWB4N6B","created_at":"2026-05-18T12:27:46Z"}],"graph_snapshots":[{"event_id":"sha256:e53e6975b2a53371a8809e3a5b72a76ed556f3b23b5008a88a467131159a2877","target":"graph","created_at":"2026-05-18T03:03:46Z","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":"We suggest a new derivation of a kinetic equation of Kolmogorov-Zakharov (KZ) type for the spectrum of the weakly nonlinear Schr\\\"odinger equation with stochastic forcing. The kynetic equation is obtained as a result of a double limiting procedure. Firstly, we consider the equation on a finite box with periodic boundary conditions and send the size of the nonlinearity and of the forcing to zero, while the time is correspondingly rescaled; then, the size of the box is sent to infinity (with a suitable rescaling of the solution). We report here the results of the first limiting procedure, analyz","authors_text":"Alberto Maiocchi, Sergei Kuksin","cross_cats":["math.MP","physics.flu-dyn"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-11-26T20:11:29Z","title":"Derivation of the Kolmogorov-Zakharov equation from the resonant-averaged stochastic NLS equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.6794","kind":"arxiv","version":3},"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":"sha256:74f17441fdad23b4436ccd86623c216251f4fdcc472857f9730f53687c9a9573","target":"record","created_at":"2026-05-18T03:03:46Z","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":"d3e247a2e24809c6ad87b5e13f48e6a520767e65cc2807cf56b5daa762bd380d","cross_cats_sorted":["math.MP","physics.flu-dyn"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-11-26T20:11:29Z","title_canon_sha256":"c8c238ffb7cd30f88d2f9dfcdf6b852490b53ae88a7b366a9bdfa0839fa8937c"},"schema_version":"1.0","source":{"id":"1311.6794","kind":"arxiv","version":3}},"canonical_sha256":"42ac1e37c1413a6b5ba64956a21e3c3bd97e695881e30dcb052fde89f9226b62","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"42ac1e37c1413a6b5ba64956a21e3c3bd97e695881e30dcb052fde89f9226b62","first_computed_at":"2026-05-18T03:03:46.722646Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:03:46.722646Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jBL9X2NJ0sDWheYJZBEOUU8ltTEepQ3rEXD9CYLQkRHNqWsfgYVb4rH6d0UPLgDKxSbwhx4aBvUn7UDPNRMyBA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:03:46.723186Z","signed_message":"canonical_sha256_bytes"},"source_id":"1311.6794","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:74f17441fdad23b4436ccd86623c216251f4fdcc472857f9730f53687c9a9573","sha256:e53e6975b2a53371a8809e3a5b72a76ed556f3b23b5008a88a467131159a2877"],"state_sha256":"656d03f895e10f10681f34d0fd74712c55b6ffa29c3dff1f05fc1b7464c0386a"}