{
  "title": "One trace across Fourier charts",
  "license": "CC0-1.0 to the extent of rights held; DejaVu Sans has separate retained terms",
  "normalization": {
    "positive_fourier": "lambda_t(p)=exp(i*t*p)",
    "measure": "dp/(2*pi)",
    "theta": "theta_s f(p)=f(p-s)",
    "generator": "h(p)=exp(p)",
    "trace_density_relative_to_measure": "exp(-p)"
  },
  "scalar": {
    "s_exact": "log(2)",
    "original_interval": "[0,1)",
    "translated_interval": "[log(2),1+log(2))",
    "original_integral_exact": "(1 - exp(-1))/(2*pi)",
    "translated_integral_exact": "(1 - exp(-1))/(4*pi)",
    "ratio_exact": "1/2",
    "original_integral_decimal": 0.10060511156757618,
    "translated_integral_decimal": 0.05030255578378809,
    "curve_formula": "exp(-p)",
    "curve_domain": [
      -0.12,
      1.9
    ],
    "curve_sample_count": 801,
    "fill_samples_per_interval": 401,
    "endpoint_marker_convention": "filled left and open right show half-open interval; endpoint choices do not affect the integral"
  },
  "matrices": {
    "H": [
      [
        4,
        0
      ],
      [
        0,
        1
      ]
    ],
    "K": [
      [
        2,
        1
      ],
      [
        1,
        2
      ]
    ],
    "commutator_HK_minus_KH": [
      [
        0,
        3
      ],
      [
        -3,
        0
      ]
    ],
    "H_eigenvalues": [
      4,
      1
    ],
    "K_eigenvalues": [
      3,
      1
    ],
    "H_power": "diag(4^(it),1)",
    "K_power": "(1/2)*[[3^(it)+1,3^(it)-1],[3^(it)-1,3^(it)+1]]",
    "cocycle_order": "K^(it) H^(-it)",
    "checked_symbolic_identity": "(K^(it) H^(-it)) H^(it) = K^(it)",
    "symbolic_parameter_substitutions": {
      "z": "3^(it)",
      "w": "4^(it)"
    },
    "inverse_density_limit": "D*(r*D+epsilon*I)^(-1) -> r^(-1)*I, D=H,K",
    "whole_positive_cone_trace": "integral exp(-p)*Tr(Y(p))*dp/(2*pi)"
  },
  "cutoff": {
    "h": [
      [
        1,
        0
      ],
      [
        0,
        4
      ]
    ],
    "X": [
      [
        1,
        1
      ],
      [
        1,
        1
      ]
    ],
    "weight": "Phi(Y)=Tr(hY)",
    "B": "v_epsilon*v_epsilon^*, v_epsilon=((1+epsilon)^(-1/2),(4+epsilon)^(-1/2))^T",
    "scalar_formula": "1/(1+epsilon)+4/(4+epsilon)",
    "values_exact": {
      "epsilon=4": "7/10",
      "epsilon=1": "13/10",
      "epsilon->0+": "2"
    },
    "difference_determinant_exact": "-1/400",
    "difference_eigenvalues_exact": [
      "(15-sqrt(241))/80",
      "(15+sqrt(241))/80"
    ],
    "scalar_derivative": "-1/(1+epsilon)^2-4/(4+epsilon)^2 < 0",
    "parameter_axis": "decreases from left to right",
    "curve_sample_count": 801,
    "curve_domain": [
      0,
      4
    ],
    "scope": "centralizer perturbation model; not a finite-dimensional scaling core"
  },
  "render": {
    "size_inches": [
      16,
      12
    ],
    "dpi": 160,
    "png_pixels": [
      2560,
      1920
    ],
    "font": "DejaVu Sans",
    "svg_fonttype": "path",
    "axes_bounds": {
      "scalar_original": [
        0.075,
        0.565,
        0.385,
        0.295
      ],
      "scalar_translated": [
        0.075,
        0.115,
        0.385,
        0.295
      ],
      "ordered_chart": [
        0.535,
        0.545,
        0.41,
        0.34
      ],
      "cutoff": [
        0.58,
        0.115,
        0.365,
        0.29
      ]
    }
  },
  "proof_locators": [
    "CORE.9.b",
    "CORE.9.h",
    "CORE.9.j",
    "CORE.10.e",
    "CORE.10.g",
    "CORE.3.b"
  ],
  "symbolic_checks": {
    "scalar_ratio": true,
    "ordered_factor_cancellation": true,
    "both_matrix_resolvent_limits": true,
    "cutoff_determinant": true,
    "cutoff_values_and_limit": true,
    "cutoff_scalar_derivative": true
  },
  "runtime": {
    "matplotlib": "3.10.9",
    "numpy": "2.4.4",
    "sympy": "1.13.1"
  }
}