[
  {
    "id": "ARR-2026-40S2JAQBBB8GJTN5-v1",
    "type": "article",
    "title": "Constant-precision undecidability for amplified determinants with capacity one",
    "author": [
      {
        "literal": "Lluis Eriksson"
      }
    ],
    "issued": {
      "date-parts": [
        [
          2026,
          10,
          17
        ]
      ]
    },
    "publisher": "AIRR.SCIENCE",
    "archive": "AIRR.SCIENCE",
    "archive_location": "ARR-2026-40S2JAQBBB8GJTN5",
    "version": "v1",
    "genre": "Research preprint",
    "URL": "https://airr.science/papers/ARR-2026-40S2JAQBBB8GJTN5/versions/v1/",
    "note": "Research preprint; ARR-2026-40S2JAQBBB8GJTN5 v1. Not peer reviewed by AIRR. Working paper; not admitted to the AIRR accepted collection.",
    "abstract": "We give a computable reduction from the halting problem to approximating a normalized determinant optimized over matrix coefficients of unrestricted auxiliary dimension. The coefficient matrices are real rational, orthonormal for normalized Hilbert--Schmidt inner product, and have covariance-optimized operator capacity exactly one. Nevertheless, approximating the determinant optimum to one fixed additive precision is undecidable. The proof combines the synchronous linear-game hardness theorem of Taller and Vidick with a homogeneous multiplication block, weighted rational normalization, and two quantitative rounding arguments. A positional-question normalization handles repeated queries without identifying distinct answer positions. No total recursive uniform bound on auxiliary witness dimension exists even at one fixed precision. The source hardness is inherited; the contribution is its determinant reduction. The gap constant is very small, and global priority is not certified."
  }
]