[
  {
    "id": "ARR-2026-0WESHW4YMM9FG8EK-v1",
    "type": "article",
    "title": "Three-term Weyl operators: central multiplicities, rank laws, and exact list decoding",
    "author": [
      {
        "literal": "Lluis Eriksson"
      }
    ],
    "issued": {
      "date-parts": [
        [
          2026,
          9,
          5
        ]
      ]
    },
    "publisher": "AIRR.SCIENCE",
    "archive": "AIRR.SCIENCE",
    "archive_location": "ARR-2026-0WESHW4YMM9FG8EK",
    "version": "v1",
    "genre": "Research preprint",
    "URL": "https://airr.science/papers/ARR-2026-0WESHW4YMM9FG8EK/versions/v1/",
    "note": "Research preprint; ARR-2026-0WESHW4YMM9FG8EK v1. Not peer reviewed by AIRR.",
    "abstract": "We classify the ranks of nonzero operators with at most three terms in a fixed cyclic Weyl basis in every prime-power dimension. A central-sector formula valid in arbitrary cyclic dimension computes trinomial nullity from commuting powers and a common block multiplicity; nonzero three-term coefficients permit at most two singular sectors. The formula explains composite-dimension departures from the prime-power bound. For exact-rank pure probes in one-use Weyl channel list discrimination, we classify all reduced states below rank 3d/4 in dyadic dimensions: exactly thirty flat half-rank states. Positive sums of sparse squares produce ranks impossible for an individual three-term factor, including an exact three-label family of rank 13d/16. We also determine an exact four-label family of rank 5d/8 and the complete feasible three-label rank set in dimension sixteen. Classical Weyl representation and covariance tools are attributed; exact algebraic certificates and replay programs accompany the proofs."
  }
]