{
  "abstract": "Scientific autoformalization turns verbal accounts into executable mathematics, but executable code does not settle which model has been constructed. We examine two sources of structural uncertainty: the formalizer that generates a response law, and the recurrence that turns that law into trajectories. In secondary analyses of an openly archived crossed experiment, we studied 320 response maps generated by two pinned language-model formalizers from five engineered cognitive accounts within one sparse quadratic grammar and 16 randomized blocks. With whole blocks held out, source-account identity was recovered at 78.8% accuracy (chance 20.0%) and formalizer identity at 96.3% (chance 50.0%; both p < 0.001). Program size was the stronger single feature family; a pre-specified exploratory comparison found no stable source-account predictive gain from local geometry beyond size. Holding every response map fixed, we then evaluated five recurrence families spanning 33 configurations and 1,013,760 finite-horizon trajectories. Added feedback, projection and leak produced sharply different outcome distributions. The consequential distinction was which comparisons survived: median cross-recurrence rank concordance was 0.73 for endpoint magnitude but 0.05 for settling, among the configuration pairs with defined rankings. Thus a common mathematical language did not erase translation provenance, and robust ordering under one observable did not transfer to another. Scientific autoformalization is usefully studied as model-space construction: the generated ensemble and its dynamical embedding are both part of the specification supporting a scientific claim.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.14808",
  "author_total": 1,
  "authors": [
    {
      "name": "Andre Panossian"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/b2gjdpbyjvcpr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.14808",
  "fulltext_url": null,
  "id": "b2gjdpbyjvcpr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.14808",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.SE"
    ],
    [
      "arxiv",
      "physics.comp-ph"
    ],
    [
      "openalex",
      "1702|Diverse Interdisciplinary Research Studies"
    ]
  ],
  "openalex": "W7213256188",
  "pdf_url": "https://arxiv.org/pdf/2609.14808",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/b2gjdpbyjvcpr.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:25Z",
      "native_id": "2609.14808",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.14808"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:physics.comp-ph",
      "subfield": "computational"
    }
  ],
  "title": "Transformed in Translation: Two-Stage Structural Uncertainty in LLM-Based Scientific Autoformalization",
  "title_text": "Transformed in Translation: Two-Stage Structural Uncertainty in LLM-Based Scientific Autoformalization",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:25Z",
  "url": "https://research.draconitic.com/paper/b2gjdpbyjvcpr",
  "venue": "arXiv",
  "versions": []
}