[
  {
    "id": "ARR-2026-1D2QYXPCVY9H7ANB-v1",
    "type": "article",
    "title": "Exact Rate–Distortion Theory for Complex-Projective Born Prediction: Finite-Dimensional Bingham Frontiers, Thermodynamic Coexistence, and Worst-State Capacity",
    "author": [
      {
        "literal": "Lluis Eriksson"
      }
    ],
    "issued": {
      "date-parts": [
        [
          2026,
          8,
          13
        ]
      ]
    },
    "publisher": "AIRR.SCIENCE",
    "archive": "AIRR.SCIENCE",
    "archive_location": "ARR-2026-1D2QYXPCVY9H7ANB",
    "version": "v1",
    "genre": "Research preprint",
    "URL": "https://airr.science/papers/ARR-2026-1D2QYXPCVY9H7ANB/versions/v1/",
    "note": "Research preprint; ARR-2026-1D2QYXPCVY9H7ANB v1. Not peer reviewed by AIRR.",
    "abstract": "We give a unified exact rate–distortion theory for retaining the complete rank-one Born-probability field of a Haar-random pure state in complex projective space. A constrained root count, a sharp centered power-sum theorem, and Newton's expansion prove an all-degree spectral result: at fixed traceless Frobenius norm the projective Laplace transform is maximized by a one-positive-spike spectrum. This reduces the unrestricted Shannon rate–distortion function to an exact scalar complex-Bingham envelope in every dimension, with covariant channels and independently flagged coexistence mixtures attaining every distortion. For dimension at least three, directional information turns on discontinuously; the qubit curve and the all-dimensional high-fidelity constant are explicit. We then solve the full fixed-normalized-distortion limit. If y_* > 2 solves y_* - 1 = 2 log y_*, the limiting free energy has a unique coexistence point, and the information cost per dimension is a closed two-piece function with a nontrivial linear face. The finite-dimensional onset multiplier equals alpha_* d minus [alpha_*/(2 log y_*)] log d up to an O(1) remainder. Finally, a pointwise Hilbert projection converts every measurable scalar reporter into a physical density-matrix reporter without increasing risk for any pure input. Hence the exact worst-state channel capacity equals the Haar rate–distortion function, arbitrary joint n-state memories cost exactly n times the one-state frontier, and transitivity forces zero rate dispersion with an exponential finite-blocklength strong converse. These results concern reusable calibrated probability fields, not click-only simulation, state update, or intrinsic randomness."
  }
]