{
  "kind": "exact integer nilpotent matrices and proof diagram",
  "proofs": [
    "AT.18--AT.24",
    "AT.36--AT.38"
  ],
  "matrix_convention": "Rows and columns ordered e_0 through e_(m-1); column k is z times e_k.",
  "finite_records": [
    {
      "m": 1,
      "basis": [
        "[z^0]"
      ],
      "multiplication_by_z_columns": [
        [
          0
        ]
      ],
      "power_m_is_zero": true,
      "power_m_minus_one_is_nonzero": true,
      "base_disc_contains_zero_rank": 1,
      "base_disc_avoids_zero_rank": 0
    },
    {
      "m": 2,
      "basis": [
        "[z^0]",
        "[z^1]"
      ],
      "multiplication_by_z_columns": [
        [
          0,
          0
        ],
        [
          1,
          0
        ]
      ],
      "power_m_is_zero": true,
      "power_m_minus_one_is_nonzero": true,
      "base_disc_contains_zero_rank": 2,
      "base_disc_avoids_zero_rank": 0
    },
    {
      "m": 3,
      "basis": [
        "[z^0]",
        "[z^1]",
        "[z^2]"
      ],
      "multiplication_by_z_columns": [
        [
          0,
          0,
          0
        ],
        [
          1,
          0,
          0
        ],
        [
          0,
          1,
          0
        ]
      ],
      "power_m_is_zero": true,
      "power_m_minus_one_is_nonzero": true,
      "base_disc_contains_zero_rank": 3,
      "base_disc_avoids_zero_rank": 0
    },
    {
      "m": 4,
      "basis": [
        "[z^0]",
        "[z^1]",
        "[z^2]",
        "[z^3]"
      ],
      "multiplication_by_z_columns": [
        [
          0,
          0,
          0,
          0
        ],
        [
          1,
          0,
          0,
          0
        ],
        [
          0,
          1,
          0,
          0
        ],
        [
          0,
          0,
          1,
          0
        ]
      ],
      "power_m_is_zero": true,
      "power_m_minus_one_is_nonzero": true,
      "base_disc_contains_zero_rank": 4,
      "base_disc_avoids_zero_rank": 0
    },
    {
      "m": 5,
      "basis": [
        "[z^0]",
        "[z^1]",
        "[z^2]",
        "[z^3]",
        "[z^4]"
      ],
      "multiplication_by_z_columns": [
        [
          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
        ]
      ],
      "power_m_is_zero": true,
      "power_m_minus_one_is_nonzero": true,
      "base_disc_contains_zero_rank": 5,
      "base_disc_avoids_zero_rank": 0
    },
    {
      "m": 6,
      "basis": [
        "[z^0]",
        "[z^1]",
        "[z^2]",
        "[z^3]",
        "[z^4]",
        "[z^5]"
      ],
      "multiplication_by_z_columns": [
        [
          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
        ]
      ],
      "power_m_is_zero": true,
      "power_m_minus_one_is_nonzero": true,
      "base_disc_contains_zero_rank": 6,
      "base_disc_avoids_zero_rank": 0
    }
  ],
  "general_proof_is_in_source": true,
  "support_points_are_not_jet_basis_layers": true
}