{
  "space": "R",
  "measure_density": "rho(x)=exp(-abs(x))/2",
  "translation_t": 1,
  "Radon_Nikodym_derivative": "r_t(x)=exp(abs(x)-abs(x-t))",
  "unitary_action": "(U_t xi)(x)=sqrt(r_t(x))*xi(x-t)",
  "density_unitary": "(J xi)(x)=sqrt(rho(x))*xi(x)",
  "averaging_domain": "L_infinity(lambda) intersect L_1(dx)",
  "panels": [
    {
      "vector": "xi",
      "support": [
        0,
        1
      ],
      "amplitude_exact": "1",
      "squared_norm_exact": "(1-exp(-1))/2"
    },
    {
      "vector": "B_1 xi",
      "support": [
        1,
        2
      ],
      "amplitude_exact": "1",
      "squared_norm_exact": "exp(-1)*(1-exp(-1))/2"
    },
    {
      "vector": "U_1 xi",
      "support": [
        1,
        2
      ],
      "amplitude_exact": "sqrt(e)",
      "squared_norm_exact": "(1-exp(-1))/2"
    }
  ],
  "constant_vector_distance_squared": "2-2*(1+abs(t)/2)*exp(-abs(t)/2)",
  "proof_locator": "OA-FLOW-L72, (PM1)-(PM12)",
  "drawing": "Graphs show amplitudes. Norm labels are exact integrals against lambda."
}