{
  "abstract": "This paper proposes a radical shift in the foundations of classical calculus\n\nand computational mathematics — a transition from approximate linear computations\n\nunder the IEEE 754 standard to Vernier Calculus. Within this paradigm, the\n\ncontinuous field is replaced by the interference effect of two dynamically shifting\n\nnumerical scales, transforming mathematics from a process of counting infinite\n\nfractions into a search for absolute nodes of harmony. The paper derives a monolithic\n\niterative formula for the dynamic vernier, which completely eliminates the accumulation\n\nof digital rounding noise in computer systems. Using a comprehensive end-to-end\n\ncalculation of a base quantum (the number four), we demonstrate how root, logarithm,\n\nand integral functions simultaneously unfold from a single numerical log. A fundamental\n\nfeature of autofixation is revealed: as the flow approaches the precision of unity,\n\nit naturally hits a prime number, scanning the structural matrix of space. This work\n\njustifies the urgency of the new mathematics for applications in supercomputers,\n\nquantum computing, and resonant neural networks.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "name": "Saltykov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/20s1kd2f73n7z.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23574023",
  "fulltext_url": null,
  "id": "20s1kd2f73n7z",
  "issns": [],
  "landing_url": "https://zenodo.org/records/23574023",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [],
  "openalex": null,
  "pdf_url": "https://zenodo.org/api/records/23574023/files/%D0%BD%D0%BE%D0%BD%D0%B8%D1%83%D1%81.pdf/content",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/20s1kd2f73n7z.ris",
  "sources": [
    {
      "first_seen": "2026-11-05T12:20:24Z",
      "native_id": "23574023",
      "source": "zenodo",
      "url": "https://zenodo.org/records/23574023"
    }
  ],
  "subjects": [],
  "title": "The Concept of Vernier Calculus and Absolute Discretization of Computational Fields via Dynamic Autoresonant Flow",
  "title_text": "The Concept of Vernier Calculus and Absolute Discretization of Computational Fields via Dynamic Autoresonant Flow",
  "type": "preprint",
  "updated_at": "2026-11-05T12:20:24Z",
  "url": "https://research.draconitic.com/paper/20s1kd2f73n7z",
  "venue": "Zenodo",
  "versions": []
}