[
  {
    "id": "ARR-2026-3SDH8JSK73925RXK-v1",
    "type": "article",
    "title": "Reflection Positivity and Exact Gap Certificates from Forgotten Quantum Order",
    "author": [
      {
        "literal": "Lluis Eriksson"
      }
    ],
    "issued": {
      "date-parts": [
        [
          2026,
          8,
          10
        ]
      ]
    },
    "publisher": "AIRR.SCIENCE",
    "archive": "AIRR.SCIENCE",
    "archive_location": "ARR-2026-3SDH8JSK73925RXK",
    "version": "v1",
    "genre": "Archived manuscript",
    "URL": "https://airr.science/papers/ARR-2026-3SDH8JSK73925RXK/versions/v1/",
    "note": "Archived manuscript; ARR-2026-3SDH8JSK73925RXK v1. Not peer reviewed by AIRR. Historical import; not assessed by AIRR.",
    "abstract": "A balanced sequence of short Hamiltonian kicks has no first-order drift, but its order-dependent commutator holonomy survives when the order record is discarded. We prove that a reversal-symmetric average of complete order/reverse echoes is a self-adjoint random-unitary transfer operator and obeys the nonperturbative bound cos(4|y|S) I <= T_y <= I for |y|S < pi/8. This yields site and link reflection positivity and a finite-dimensional Osterwalder-Schrader Hamiltonian. The physical transfer approaches the curvature-frame generator with an explicit sixth-order remainder, giving quantitative O(y^2) convergence of its mass gap. For the regular tetrahedral qubit loop, we derive the exact finite-pulse depolarizing eigenvalue, isolate its first positivity zero at y = 0.455698535295322..., and obtain the mass expansion. We then prove a complete finite-depth Hausdorff criterion for visible transfer edges, with uniformly sharp depth r-1, and give an exact rational four-kick certificate: the true frame gap 10/3 is certified while the false claim 4 has rational witness value -1/64. A Wishart-Loewner band supplies finite-sample type-I control for independent Gaussian correlator sketches, including adaptive witnesses. Exact symbolic and deterministic numerical certificates accompany the manuscript."
  }
]