[
  {
    "id": "ARR-2026-1QEPAQ29TN8FZRK5-v1",
    "type": "article",
    "title": "Removing the binary and ternary factors from cyclic Weyl rank uncertainty",
    "author": [
      {
        "literal": "Lluis Eriksson"
      }
    ],
    "issued": {
      "date-parts": [
        [
          2026,
          10,
          24
        ]
      ]
    },
    "publisher": "AIRR.SCIENCE",
    "archive": "AIRR.SCIENCE",
    "archive_location": "ARR-2026-1QEPAQ29TN8FZRK5",
    "version": "v1",
    "genre": "Research preprint",
    "URL": "https://airr.science/papers/ARR-2026-1QEPAQ29TN8FZRK5/versions/v1/",
    "note": "Research preprint; ARR-2026-1QEPAQ29TN8FZRK5 v1. Not peer reviewed by AIRR. Working paper; not admitted to the AIRR accepted collection.",
    "abstract": "For a nonzero complex matrix in the cyclic Weyl basis, let u_d(s) be the minimum rank under a support budget of s coefficients. We give exact formulas reducing u_d to the profile in the part of the dimension coprime to 6. Removing a factor 2^k uses a minimum over binary subgroup costs. Removing a factor 3^k uses products of the three costs 1, 2, 3, with rank multipliers 3, 2, 1. Lower bounds follow from residue-sector compressions and central Fourier blocks; the ternary two-residue case uses a triangular minor on two sectors of a directed three-cycle. Upper bounds are attained by scalar cyclic projectors and binomials, combined with the Chinese remainder theorem. In every even dimension whose only prime factors are 2 and 3, the exact minimum is d/max{q: q divides d, q <= s}. Sharp uniform coefficient-erasure budgets follow for arbitrary complex low-rank matrices. Residual profiles with prime factors at least 5, efficient recovery and numerical stability are not determined."
  }
]