{"paper":{"title":"Intrinsic Instantaneous Coarse-to-Fine Recoverability in the Lorenz-96 System","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["physics.data-an"],"primary_cat":"nlin.CD","authors_text":"Junfeng Chen, Zhongfeng Xu","submitted_at":"2026-07-09T10:07:46Z","abstract_excerpt":"In multiscale chaotic systems, a basic closure question is how much of the unresolved fine scales is instantaneously determined by the resolved coarse scales on the attractor. In a Fourier description, we formalize this by asking, given a target mode $k$ and a lower-mode cutoff $k_{\\rm cut}<k$, how much of mode $k$ is determined by the retained modes $0,\\ldots,k_{\\rm cut}$. We quantify this relation by the correlation-ratio functional $R(k\\mid k_{\\rm cut})$, interpreted as conditional-mean explained variance, and use it to build a scale-resolved recoverability map $(k,k_{\\rm cut})\\mapsto R(k\\m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.08323","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.08323/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}