{
  "proof": "SDC.A--SDC.J",
  "finite_samples_are_general_proof": false,
  "collar": {
    "input_radius": 0.6,
    "chi_one_through": 0.8,
    "chi_zero_from": 1.25,
    "derivative_support_interval_closed": [
      0.8,
      1.25
    ],
    "polydisc_radius": 1.5,
    "cutoff": "beta(R-r)/(beta(R-r)+beta(r-r0)); beta(t)=0 for t<=0 and exp(-1/t) for t>0",
    "inner_boundary_orientation": "clockwise"
  },
  "residue_matrices": [
    {
      "d": 1,
      "matrix": [
        [
          1
        ]
      ],
      "determinant": 1
    },
    {
      "d": 2,
      "matrix": [
        [
          0,
          1
        ],
        [
          1,
          0
        ]
      ],
      "determinant": -1
    },
    {
      "d": 3,
      "matrix": [
        [
          0,
          0,
          1
        ],
        [
          0,
          1,
          0
        ],
        [
          1,
          0,
          0
        ]
      ],
      "determinant": -1
    },
    {
      "d": 4,
      "matrix": [
        [
          0,
          0,
          0,
          1
        ],
        [
          0,
          0,
          1,
          0
        ],
        [
          0,
          1,
          0,
          0
        ],
        [
          1,
          0,
          0,
          0
        ]
      ],
      "determinant": 1
    },
    {
      "d": 5,
      "matrix": [
        [
          0,
          0,
          0,
          0,
          1
        ],
        [
          0,
          0,
          0,
          1,
          0
        ],
        [
          0,
          0,
          1,
          0,
          0
        ],
        [
          0,
          1,
          0,
          0,
          0
        ],
        [
          1,
          0,
          0,
          0,
          0
        ]
      ],
      "determinant": 1
    },
    {
      "d": 6,
      "matrix": [
        [
          0,
          0,
          0,
          0,
          0,
          1
        ],
        [
          0,
          0,
          0,
          0,
          1,
          0
        ],
        [
          0,
          0,
          0,
          1,
          0,
          0
        ],
        [
          0,
          0,
          1,
          0,
          0,
          0
        ],
        [
          0,
          1,
          0,
          0,
          0,
          0
        ],
        [
          1,
          0,
          0,
          0,
          0,
          0
        ]
      ],
      "determinant": -1
    },
    {
      "d": 7,
      "matrix": [
        [
          0,
          0,
          0,
          0,
          0,
          0,
          1
        ],
        [
          0,
          0,
          0,
          0,
          0,
          1,
          0
        ],
        [
          0,
          0,
          0,
          0,
          1,
          0,
          0
        ],
        [
          0,
          0,
          0,
          1,
          0,
          0,
          0
        ],
        [
          0,
          0,
          1,
          0,
          0,
          0,
          0
        ],
        [
          0,
          1,
          0,
          0,
          0,
          0,
          0
        ],
        [
          1,
          0,
          0,
          0,
          0,
          0,
          0
        ]
      ],
      "determinant": -1
    },
    {
      "d": 8,
      "matrix": [
        [
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          1
        ],
        [
          0,
          0,
          0,
          0,
          0,
          0,
          1,
          0
        ],
        [
          0,
          0,
          0,
          0,
          0,
          1,
          0,
          0
        ],
        [
          0,
          0,
          0,
          0,
          1,
          0,
          0,
          0
        ],
        [
          0,
          0,
          0,
          1,
          0,
          0,
          0,
          0
        ],
        [
          0,
          0,
          1,
          0,
          0,
          0,
          0,
          0
        ],
        [
          0,
          1,
          0,
          0,
          0,
          0,
          0,
          0
        ],
        [
          1,
          0,
          0,
          0,
          0,
          0,
          0,
          0
        ]
      ],
      "determinant": 1
    }
  ],
  "finite_local_shift_sign_samples": [
    {
      "n": 1,
      "hom_degree": 0,
      "pairing_factor": 1,
      "compact_differential_coefficient": 1,
      "continuous_dual_differential_coefficient": -1
    },
    {
      "n": 1,
      "hom_degree": 1,
      "pairing_factor": -1,
      "compact_differential_coefficient": -1,
      "continuous_dual_differential_coefficient": 1
    },
    {
      "n": 2,
      "hom_degree": 0,
      "pairing_factor": 1,
      "compact_differential_coefficient": -1,
      "continuous_dual_differential_coefficient": -1
    },
    {
      "n": 2,
      "hom_degree": 1,
      "pairing_factor": 1,
      "compact_differential_coefficient": 1,
      "continuous_dual_differential_coefficient": 1
    },
    {
      "n": 2,
      "hom_degree": 2,
      "pairing_factor": 1,
      "compact_differential_coefficient": -1,
      "continuous_dual_differential_coefficient": -1
    },
    {
      "n": 3,
      "hom_degree": 0,
      "pairing_factor": 1,
      "compact_differential_coefficient": 1,
      "continuous_dual_differential_coefficient": -1
    },
    {
      "n": 3,
      "hom_degree": 1,
      "pairing_factor": -1,
      "compact_differential_coefficient": -1,
      "continuous_dual_differential_coefficient": 1
    },
    {
      "n": 3,
      "hom_degree": 2,
      "pairing_factor": 1,
      "compact_differential_coefficient": 1,
      "continuous_dual_differential_coefficient": -1
    },
    {
      "n": 3,
      "hom_degree": 3,
      "pairing_factor": -1,
      "compact_differential_coefficient": -1,
      "continuous_dual_differential_coefficient": 1
    },
    {
      "n": 4,
      "hom_degree": 0,
      "pairing_factor": 1,
      "compact_differential_coefficient": -1,
      "continuous_dual_differential_coefficient": -1
    },
    {
      "n": 4,
      "hom_degree": 1,
      "pairing_factor": 1,
      "compact_differential_coefficient": 1,
      "continuous_dual_differential_coefficient": 1
    },
    {
      "n": 4,
      "hom_degree": 2,
      "pairing_factor": 1,
      "compact_differential_coefficient": -1,
      "continuous_dual_differential_coefficient": -1
    },
    {
      "n": 4,
      "hom_degree": 3,
      "pairing_factor": 1,
      "compact_differential_coefficient": 1,
      "continuous_dual_differential_coefficient": 1
    },
    {
      "n": 4,
      "hom_degree": 4,
      "pairing_factor": 1,
      "compact_differential_coefficient": -1,
      "continuous_dual_differential_coefficient": -1
    },
    {
      "n": 5,
      "hom_degree": 0,
      "pairing_factor": 1,
      "compact_differential_coefficient": 1,
      "continuous_dual_differential_coefficient": -1
    },
    {
      "n": 5,
      "hom_degree": 1,
      "pairing_factor": -1,
      "compact_differential_coefficient": -1,
      "continuous_dual_differential_coefficient": 1
    },
    {
      "n": 5,
      "hom_degree": 2,
      "pairing_factor": 1,
      "compact_differential_coefficient": 1,
      "continuous_dual_differential_coefficient": -1
    },
    {
      "n": 5,
      "hom_degree": 3,
      "pairing_factor": -1,
      "compact_differential_coefficient": -1,
      "continuous_dual_differential_coefficient": 1
    },
    {
      "n": 5,
      "hom_degree": 4,
      "pairing_factor": 1,
      "compact_differential_coefficient": 1,
      "continuous_dual_differential_coefficient": -1
    },
    {
      "n": 5,
      "hom_degree": 5,
      "pairing_factor": -1,
      "compact_differential_coefficient": -1,
      "continuous_dual_differential_coefficient": 1
    }
  ],
  "trace": "(2*pi*i)^(-n) times integral",
  "density": "omega_X[n]",
  "bar_dual_factor": "(-1)^p"
}