{
  "abstract": "How much precision must be allocated, and to which uncertainty channels, to meet a prediction requirement? We formulate a minimum one-shot specification cost over initial state variables and persistent forcing parameters. The central result is that prediction accuracy can select the horizon-scaling law of this resource by activating different physical uncertainty channels. Within any common uniformly scale-separable regime with the same active channels, changing a fixed tolerance changes the required precision by only $\\cO(1)$ bits. An exactly solvable multiscale toral system shows that one fixed dynamics and target can nevertheless switch from $B_N(\\eps_c)=\\Th(\\log N)$ to $B_N(\\eps_f)=\\Th(N)$ when finer accuracy activates an expanding channel. A forced Lorenz--84 calculation then realizes the same channel-switching mechanism numerically over finite horizons in a single two-scale diagnostic field: a sampled post-transient eddy envelope supports a coarse branch controlled by the phase rate of a large-scale forcing, whereas finer accuracy activates exponentially sensitive atmospheric degrees of freedom and produces an approximately linear increase of the linearized one-shot cost over the resolved window. Thus accuracy can determine not only how much predictive precision is required, but which physical channel controls its growth with horizon.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.00352",
  "author_total": 1,
  "authors": [
    {
      "name": "Song-Ju Kim"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/etbrrjd5ddqd5.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.00352",
  "fulltext_url": null,
  "id": "etbrrjd5ddqd5",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.00352",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "nlin.CD"
    ],
    [
      "openalex",
      "1902|Meteorological Phenomena and Simulations"
    ]
  ],
  "openalex": "W7215980639",
  "pdf_url": "https://arxiv.org/pdf/2610.00352",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/etbrrjd5ddqd5.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:03Z",
      "native_id": "2610.00352",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.00352"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:nlin.CD",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Prediction Accuracy Can Select the Scaling Law of Required Precision",
  "title_text": "Prediction Accuracy Can Select the Scaling Law of Required Precision",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:03Z",
  "url": "https://research.draconitic.com/paper/etbrrjd5ddqd5",
  "venue": "arXiv",
  "versions": []
}