{
  "abstract": "Asymptotic analysis is one of the classical tools for bridging models across scales. Behind many such derivations lies a common symbolic structure: an ansatz, a substitution, an order-by-order matching procedure, and the extraction of effective equations or interface conditions. This article revisits that structure through two representative bridges: the kinetic-to-fluid limit, illustrated by radiative transfer with interface layers and by neural-network approximations of Boltzmann equations, and the quantum-to-classical limit, illustrated by the Frozen Gaussian Approximation and its Dirac extension. We then explain why such derivations are natural candidates for AI-assisted formalization: their recurring symbolic structures can be organized, verified, and reused. In this sense, a carefully structured expository paper may serve not only as a review, but also as a mathematical seed for future AI-assisted environments.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.10138",
  "author_total": 1,
  "authors": [
    {
      "name": "Xu Yang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7r9fsmdrmrkxj.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.10138",
  "fulltext_url": null,
  "id": "7r9fsmdrmrkxj",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.10138",
  "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",
      "cs.NA"
    ],
    [
      "arxiv",
      "math.NA"
    ],
    [
      "openalex",
      "2604|Gas Dynamics and Kinetic Theory"
    ]
  ],
  "openalex": "W7164122586",
  "pdf_url": "https://arxiv.org/pdf/2606.10138",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-18",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7r9fsmdrmrkxj.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2606.10138",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.10138"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "Bridging Scales: Asymptotic Analysis and AI-Assisted Formalization",
  "title_text": "Bridging Scales: Asymptotic Analysis and AI-Assisted Formalization",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/7r9fsmdrmrkxj",
  "venue": "arXiv",
  "versions": []
}