[
  {
    "id": "ARR-2026-3H0ZKWJMH18MH9FX-v1",
    "type": "article",
    "title": "Strictly Scalable Exterior Decoders for Quantum Lists: Exact Full-Spark Widths and Fixed-Probe Weyl Bayes Curves",
    "author": [
      {
        "literal": "Lluis Eriksson"
      }
    ],
    "issued": {
      "date-parts": [
        [
          2026,
          8,
          24
        ]
      ]
    },
    "publisher": "AIRR.SCIENCE",
    "archive": "AIRR.SCIENCE",
    "archive_location": "ARR-2026-3H0ZKWJMH18MH9FX",
    "version": "v1",
    "genre": "Research preprint",
    "URL": "https://airr.science/papers/ARR-2026-3H0ZKWJMH18MH9FX/versions/v1/",
    "note": "Research preprint; ARR-2026-3H0ZKWJMH18MH9FX v1. Not peer reviewed by AIRR.",
    "abstract": "A quantum list measurement succeeds when its output contains the prepared label. Building on the known equivalence between learning width and Gram-matrix factor width, this paper closes an exact realization-sensitive branch. Every full-spark ensemble of N pure-state rays spanning C^r that admits strictly positive tight representatives has minimum zero-error list size N-r+1. Weighted Hodge duals of all (r-1)-fold frame wedges give an explicit attaining POVM, and a physical-space annihilator-cone formulation gives constructive compression to at most r^2 outcomes. A smallest-eigenvalue functional supplies a positive and perturbatively stable Bayes-error floor below threshold. For a flat consecutive-support Schmidt-rank-r probe of the complete d-dimensional Weyl-channel ensemble, the fixed-probe threshold is d-r+1. When r divides d, an arithmetic-support construction and dimension converse close the optimization over all pure Schmidt-rank-r probes at d/r. For the consecutive rank-two probe, the complete one-shot Bayes list curve is determined exactly. The nondivisible probe optimum, adaptive or multiuse testers, asymptotic capacity, arbitrary mixed states, and non-scalable full-spark ensembles remain outside scope."
  }
]