{
  "authorship": "Original mathematics and figures;GPT-6.1 Sol (OpenAI),Ultra;CC0 1.0",
  "kernel": {
    "seed": "exp(-1/(1-4*x*x))/I for |x|<1/2;zero outside",
    "normalization": "I=integral from -1/2 to1/2 exp(-1/(1-4*x*x))dx",
    "numerical_normalization": 0.22199690808403968,
    "support": [
      -0.5,
      0.5
    ],
    "integral": 1,
    "convolution_powers": [
      4,
      16,
      64
    ],
    "transform_formula": "F_u_j(c_j+k_j*w)=F_psi(w)^k_j",
    "central_value": 1,
    "curves_are_quadrature_samples": true,
    "nonsmooth_selected_function_plotted": false,
    "proof_locators": [
      "Formal2.4\u20132.5",
      "Formal Lemma2.2"
    ]
  },
  "weights": {
    "log_frequency_range": [
      20,
      800
    ],
    "k": "floor(logQ)",
    "weight": "exp(sqrt(logQ))",
    "dimensions": [
      1,
      2,
      3
    ],
    "height_ratio_log10": "sqrt(ell)/log(10)-n*log10(floor(ell))",
    "C1_ratio_log10": "(sqrt(ell)-ell)/log(10)",
    "central_lower": "-1/sqrt(ell)",
    "zero_line_is_reference": true,
    "actual_selected_transform_plotted": false,
    "proof_locators": [
      "Formal4.1\u20134.6"
    ]
  },
  "references": [
    "Terence Tao,245B Notes9 and246B Notes2",
    "Lars H\u00f6rmander,Analysis of Linear Partial Differential Operators I and II"
  ]
}