[
  {
    "id": "ARR-2026-418PW0QXGN812RDC-v1",
    "type": "article",
    "title": "Sharpness of the universal capacity bound for amplified determinants",
    "author": [
      {
        "literal": "Lluis Eriksson"
      }
    ],
    "issued": {
      "date-parts": [
        [
          2026,
          10,
          17
        ]
      ]
    },
    "publisher": "AIRR.SCIENCE",
    "archive": "AIRR.SCIENCE",
    "archive_location": "ARR-2026-418PW0QXGN812RDC",
    "version": "v1",
    "genre": "Research preprint",
    "URL": "https://airr.science/papers/ARR-2026-418PW0QXGN812RDC/versions/v1/",
    "note": "Research preprint; ARR-2026-418PW0QXGN812RDC v1. Not peer reviewed by AIRR. Working paper; not admitted to the AIRR accepted collection.",
    "abstract": "For a finite tuple of square complex matrices, let F_infinity be the supremum of the normalized determinant over all matrix amplifications and Hilbert-Schmidt unit coefficient tuples, and let C be the maximum operator capacity over coefficient covariances of trace one. The previously established comparison C/e <= F_infinity <= C has the optimal universal constant: we construct finite tuples with C/F_infinity arbitrarily close to e. The tuples may have exactly identity Hilbert-Schmidt Gram matrix; their capacities tend to one and their amplified determinant values tend to e^(-1). The construction uses independent complex Gaussian coefficients with a fixed number of coefficients before the matrix dimension tends to infinity. A balance property of determinant maximizers makes polynomial moment comparison uniform over every amplification. A separate cut criterion turns Gaussian expansion estimates into a dimension-independent capacity lower bound. For each fixed number of Gaussian coefficients, scalar and arbitrarily amplified optima both converge in probability to e^(-1)."
  }
]