[
  {
    "id": "ARR-2026-2JJFS9HNTT87DAGC-v1",
    "type": "article",
    "title": "Matrix Isoperimetry and Diffusion from Forgotten Order in Block--Zeno Dynamics",
    "author": [
      {
        "literal": "Lluis Eriksson"
      }
    ],
    "issued": {
      "date-parts": [
        [
          2026,
          8,
          10
        ]
      ]
    },
    "publisher": "AIRR.SCIENCE",
    "archive": "AIRR.SCIENCE",
    "archive_location": "ARR-2026-2JJFS9HNTT87DAGC",
    "version": "v1",
    "genre": "Archived manuscript",
    "URL": "https://airr.science/papers/ARR-2026-2JJFS9HNTT87DAGC/versions/v1/",
    "note": "Archived manuscript; ARR-2026-2JJFS9HNTT87DAGC v1. Not peer reviewed by AIRR. Historical import; not assessed by AIRR.",
    "abstract": "A balanced ordered loop of retained Hamiltonians generates a second-order geometric Hamiltonian. We solve its higher-rank action problem and determine what remains when the order record is erased. For every matrix dimension and every number of kicks `m >= 3`, a gauge-invariant operator action obeys a sharp, dimension-free polygonal bound on the spectral diameter of the geometric Hamiltonian; regular two-level polygons attain the constant in every dimension. A target-sensitive Hilbert--Schmidt companion bound is controlled by the trace norm and has equality exactly for sign-paired nonzero spectra. These laws yield exact diamond-norm ceilings with a physical state witness. For a uniformly forgotten order, we derive an exact `1/12` commutator-frame covariance. The resulting reversal-symmetric random-unitary product converges in diamond norm at rate `O(n^-1)` to a GKLS frame Laplacian whose fixed algebra is the joint commutant of the pair commutators. A tetrahedral Pauli architecture gives exact primitive depolarization with gap `64/3`. Finally, fixed laboratory time `T` and bounded kick amplitude `Lambda` impose a sharp curvature ceiling proportional to `T^2 Lambda^2/n`; maintaining nonzero holonomy requires `Lambda=Omega(sqrt(n))`. Exact symbolic and deterministic numerical certificates accompany the paper."
  }
]