{
  "schema_version": 1,
  "metadata": {
    "title": "What an average hides: exact infinite-temperature autocorrelations",
    "status": "Reproducible numerical benchmark; no experiment replication claim",
    "state": "beta = 0; rho = I16 / 16",
    "beta": 0,
    "dimension": 16,
    "qubits": 4,
    "majoranas": 8,
    "normalization": "psi_i = gamma_i / sqrt(2); {psi_i,psi_j} = delta_ij I; hbar = 1",
    "majorana_spin_mapping": "gamma_(2j-1) = Z tensor ... tensor Z tensor X_j tensor I ...; gamma_(2j) replaces X_j by Y_j; j=1..4, qubit 1 is leftmost tensor factor",
    "observable": "G_i(t) = (2/16) Re Tr[exp(+iHt) psi_i exp(-iHt) psi_i]",
    "time_units": "Inverse Hamiltonian coefficient units, hbar=1; no physical seconds assigned",
    "hamiltonian_terms": [
      {
        "coefficient": -0.36,
        "indices": [
          1,
          2,
          4,
          5
        ]
      },
      {
        "coefficient": 0.19,
        "indices": [
          1,
          3,
          4,
          7
        ]
      },
      {
        "coefficient": -0.71,
        "indices": [
          1,
          3,
          5,
          6
        ]
      },
      {
        "coefficient": 0.22,
        "indices": [
          2,
          3,
          4,
          6
        ]
      },
      {
        "coefficient": 0.49,
        "indices": [
          2,
          3,
          5,
          7
        ]
      }
    ],
    "perturbation": {
      "coefficient": "lambda",
      "indices": [
        1,
        2,
        3,
        5
      ]
    },
    "product_order": "Listed ascending Majorana indices multiplied left to right",
    "rescaling": "None. Original coefficients retained. Lambda changes both commutation structure and energy scales; comparison does not isolate noncommutation.",
    "spectator": "gamma_8 is absent from both H0 and the perturbation; it commutes with either Hamiltonian and G8(t)=1. Active-seven and all-eight averages are both supplied.",
    "array_layout": "times[k]; cases[c].traces[i][k] is G_(i+1)(times[k]); each mean is an array indexed by k",
    "mean_absolute_definition": "Mean of abs(G_i), NOT abs(mean(G_i))",
    "rounding": "Curve outputs rounded to 14 decimal places; validation uses unrounded calculation",
    "limitations": [
      "This one-sided beta=0 calculation illustrates cancellation in averages.",
      "No size-winding, thermalization, teleportation, or gravitational conclusion follows.",
      "No reproduction of finite-temperature experimental curves is claimed."
    ],
    "sources": [
      {
        "title": "Kobrin, Schuster and Yao, Comment on Traversable wormhole dynamics on a quantum processor",
        "date": "2023-02-15",
        "url": "https://arxiv.org/abs/2302.07897",
        "use": "H0 coefficients and normalization"
      },
      {
        "title": "Jafferis et al., Comment on Comment on Traversable wormhole dynamics on a quantum processor",
        "date": "2023-03-27",
        "url": "https://arxiv.org/abs/2303.15423",
        "use": "H0 and the 0.3 psi1 psi2 psi3 psi5 perturbation"
      }
    ],
    "generator": "generate_majorana_data.py; Python standard library and NumPy only",
    "numpy_version": "2.0.2",
    "generator_sha256": "3ddd7ba9123dbb51f47ea99af7c259436b4c27f0ff61cf194dde92cc90038869"
  },
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