{
  "abstract": "How much initial-state precision is required to predict a nonlinear system to a prescribed accuracy over a finite horizon? We formulate this inverse prediction problem through a one-shot resource $B_N$, defined as the number of binary refinement bits required in the initial state by a specified local sensing architecture. Within a common scale-separable error-growth regime, changing a fixed tolerance changes $B_N$ only by an $N$-independent offset. An exactly solvable circle/Chebyshev map provides the chaotic calibration $B_N=N\\log_2 m+O(1)$. We then apply the framework to the quasiperiodically forced logistic map under phase-only initial uncertainty. Over the resolved horizons, representative smooth-torus, strange-nonchaotic-attractor (SNA), and chaotic regimes exhibit a three-level precision-resource hierarchy: bounded, logarithmic-like, and linear-like growth, respectively. For the SNA, algebraic phase sensitivity $G_N^{\\mathrm{op}}\\sim N^μ$ implies an admissible initial uncertainty of order $N^{-μ}$, and therefore a precision cost proportional to $\\log N$. Phase-grid refinement shows that the sampled worst-case maxima are numerically stable with increasing phase resolution. Near the torus--SNA fractalization point, derivative-based phase sensitivity can already grow while finite perturbations remain below a fixed operational tolerance for more than $10^6$ iterations, revealing exceptionally long activation horizons. Thus an SNA can occupy an intermediate finite-precision resource class between a smooth torus and ordinary chaos, while its operational manifestation can occur on a much longer timescale than its derivative-based sensitivity.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.38674",
  "author_total": 1,
  "authors": [
    {
      "name": "Song-Ju Kim"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/aq72varq1qfh9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.38674",
  "fulltext_url": null,
  "id": "aq72varq1qfh9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.38674",
  "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",
      "2610|Mathematical Dynamics and Fractals"
    ]
  ],
  "openalex": "W7215081656",
  "pdf_url": "https://arxiv.org/pdf/2609.38674",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/aq72varq1qfh9.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:49Z",
      "native_id": "2609.38674",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.38674"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:nlin.CD",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Initial-State Precision as a Predictive Resource: From Tori to Strange Nonchaotic Attractors and Chaos",
  "title_text": "Initial-State Precision as a Predictive Resource: From Tori to Strange Nonchaotic Attractors and Chaos",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:49Z",
  "url": "https://research.draconitic.com/paper/aq72varq1qfh9",
  "venue": "arXiv",
  "versions": []
}