{
  "gauge_noninvariance": [
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      "M": 0,
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      "diagonal_mass": 7.25,
      "off_diagonal_total": 0.0,
      "reconstructed_J": 7.25,
      "abs_error": 0.0
    },
    {
      "M": 0.5,
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      "diagonal_mass": 3.625,
      "off_diagonal_total": 3.625,
      "reconstructed_J": 7.25,
      "abs_error": 0.0
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    {
      "M": 1,
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      "diagonal_mass": 7.25,
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      "reconstructed_J": 7.25,
      "abs_error": 0.0
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    {
      "M": 2,
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      "diagonal_mass": 36.25,
      "off_diagonal_total": -29.0,
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      "abs_error": 0.0
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    {
      "M": 5,
      "target_J": 7.25,
      "diagonal_mass": 297.25,
      "off_diagonal_total": -290.0,
      "reconstructed_J": 7.25,
      "abs_error": 0.0
    },
    {
      "M": 20,
      "target_J": 7.25,
      "diagonal_mass": 5517.25,
      "off_diagonal_total": -5510.0,
      "reconstructed_J": 7.25,
      "abs_error": 0.0
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  ],
  "finite_depth_gap": [
    {
      "N": 1000,
      "profile": "fixed",
      "depth": 5,
      "lambda": 0.8,
      "factor": 0.3276800000000001,
      "effective_kappa": 0.16151668834676067
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    {
      "N": 1000,
      "profile": "loglog",
      "depth": 1,
      "lambda": 0.8,
      "factor": 0.8,
      "effective_kappa": 0.03230333766935213
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    {
      "N": 1000,
      "profile": "half_log",
      "depth": 3,
      "lambda": 0.8,
      "factor": 0.5120000000000001,
      "effective_kappa": 0.09691001300805638
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    {
      "N": 1000000,
      "profile": "fixed",
      "depth": 5,
      "lambda": 0.8,
      "factor": 0.3276800000000001,
      "effective_kappa": 0.08075834417338033
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    {
      "N": 1000000,
      "profile": "loglog",
      "depth": 2,
      "lambda": 0.8,
      "factor": 0.6400000000000001,
      "effective_kappa": 0.032303337669352124
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    {
      "N": 1000000,
      "profile": "half_log",
      "depth": 6,
      "lambda": 0.8,
      "factor": 0.2621440000000001,
      "effective_kappa": 0.09691001300805639
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    {
      "N": 1000000000000,
      "profile": "fixed",
      "depth": 5,
      "lambda": 0.8,
      "factor": 0.3276800000000001,
      "effective_kappa": 0.04037917208669017
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    {
      "N": 1000000000000,
      "profile": "loglog",
      "depth": 3,
      "lambda": 0.8,
      "factor": 0.5120000000000001,
      "effective_kappa": 0.024227503252014095
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    {
      "N": 1000000000000,
      "profile": "half_log",
      "depth": 13,
      "lambda": 0.8,
      "factor": 0.054975581388800036,
      "effective_kappa": 0.10498584742539444
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    {
      "N": 1000000000000000000000000,
      "profile": "fixed",
      "depth": 5,
      "lambda": 0.8,
      "factor": 0.3276800000000001,
      "effective_kappa": 0.020189586043345083
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    {
      "N": 1000000000000000000000000,
      "profile": "loglog",
      "depth": 4,
      "lambda": 0.8,
      "factor": 0.4096000000000001,
      "effective_kappa": 0.016151668834676065
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    {
      "N": 1000000000000000000000000,
      "profile": "half_log",
      "depth": 27,
      "lambda": 0.8,
      "factor": 0.002417851639229262,
      "effective_kappa": 0.10902376463406345
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  ],
  "mobius_strength": [
    {
      "theta": 0.95,
      "assumption": "M(x)=O_epsilon(x^(0.95+epsilon))",
      "implied_zero_free_half_plane": "Re(s)>0.95",
      "fixed_strip_width_from_1": 0.050000000000000044
    },
    {
      "theta": 0.9,
      "assumption": "M(x)=O_epsilon(x^(0.9+epsilon))",
      "implied_zero_free_half_plane": "Re(s)>0.9",
      "fixed_strip_width_from_1": 0.09999999999999998
    },
    {
      "theta": 0.75,
      "assumption": "M(x)=O_epsilon(x^(0.75+epsilon))",
      "implied_zero_free_half_plane": "Re(s)>0.75",
      "fixed_strip_width_from_1": 0.25
    },
    {
      "theta": 0.6,
      "assumption": "M(x)=O_epsilon(x^(0.6+epsilon))",
      "implied_zero_free_half_plane": "Re(s)>0.6",
      "fixed_strip_width_from_1": 0.4
    },
    {
      "theta": 0.5,
      "assumption": "M(x)=O_epsilon(x^(0.5+epsilon))",
      "implied_zero_free_half_plane": "Re(s)>0.5",
      "fixed_strip_width_from_1": 0.5
    }
  ],
  "status": "PASS"
}