{
  "pair_factor": {
    "ring": "R = Z_3[eta]/(eta^2 - 3 eta) \u2245 {(a,b) in Z_3^2 : a \u2261 b mod 3}",
    "normalization": "Z_3 \u00d7 Z_3",
    "maximal_ideal": "m = (3,eta) = 3(Z_3 \u00d7 Z_3)",
    "radical_power_formula": "m^r = 3^r (Z_3 \u00d7 Z_3)",
    "principal_chain": "3^r R = {(a,b): a,b in 3^r Z_3 and a \u2261 b mod 3^(r+1)}"
  },
  "layers": [
    {
      "r": 1,
      "layer": "m^1/m^2",
      "dimension_F3": 2,
      "intermediate_ideals": [
        "m^2",
        "m^2 + Z_3\u00b7(3^1,0)",
        "m^2 + Z_3\u00b7(0,3^1)",
        "m^2 + Z_3\u00b7(3^1,3^1) = 3^1R",
        "m^2 + Z_3\u00b7(3^1,-3^1)",
        "m^1"
      ],
      "one_dimensional_lines_mod_layer": [
        "[ (1,0) ]",
        "[ (0,1) ]",
        "[ (1,1) ]",
        "[ (1,-1) ]"
      ],
      "ideal_count_between_layers": 6
    },
    {
      "r": 2,
      "layer": "m^2/m^3",
      "dimension_F3": 2,
      "intermediate_ideals": [
        "m^3",
        "m^3 + Z_3\u00b7(3^2,0)",
        "m^3 + Z_3\u00b7(0,3^2)",
        "m^3 + Z_3\u00b7(3^2,3^2) = 3^2R",
        "m^3 + Z_3\u00b7(3^2,-3^2)",
        "m^2"
      ],
      "one_dimensional_lines_mod_layer": [
        "[ (1,0) ]",
        "[ (0,1) ]",
        "[ (1,1) ]",
        "[ (1,-1) ]"
      ],
      "ideal_count_between_layers": 6
    },
    {
      "r": 3,
      "layer": "m^3/m^4",
      "dimension_F3": 2,
      "intermediate_ideals": [
        "m^4",
        "m^4 + Z_3\u00b7(3^3,0)",
        "m^4 + Z_3\u00b7(0,3^3)",
        "m^4 + Z_3\u00b7(3^3,3^3) = 3^3R",
        "m^4 + Z_3\u00b7(3^3,-3^3)",
        "m^3"
      ],
      "one_dimensional_lines_mod_layer": [
        "[ (1,0) ]",
        "[ (0,1) ]",
        "[ (1,1) ]",
        "[ (1,-1) ]"
      ],
      "ideal_count_between_layers": 6
    },
    {
      "r": 4,
      "layer": "m^4/m^5",
      "dimension_F3": 2,
      "intermediate_ideals": [
        "m^5",
        "m^5 + Z_3\u00b7(3^4,0)",
        "m^5 + Z_3\u00b7(0,3^4)",
        "m^5 + Z_3\u00b7(3^4,3^4) = 3^4R",
        "m^5 + Z_3\u00b7(3^4,-3^4)",
        "m^4"
      ],
      "one_dimensional_lines_mod_layer": [
        "[ (1,0) ]",
        "[ (0,1) ]",
        "[ (1,1) ]",
        "[ (1,-1) ]"
      ],
      "ideal_count_between_layers": 6
    },
    {
      "r": 5,
      "layer": "m^5/m^6",
      "dimension_F3": 2,
      "intermediate_ideals": [
        "m^6",
        "m^6 + Z_3\u00b7(3^5,0)",
        "m^6 + Z_3\u00b7(0,3^5)",
        "m^6 + Z_3\u00b7(3^5,3^5) = 3^5R",
        "m^6 + Z_3\u00b7(3^5,-3^5)",
        "m^5"
      ],
      "one_dimensional_lines_mod_layer": [
        "[ (1,0) ]",
        "[ (0,1) ]",
        "[ (1,1) ]",
        "[ (1,-1) ]"
      ],
      "ideal_count_between_layers": 6
    },
    {
      "r": 6,
      "layer": "m^6/m^7",
      "dimension_F3": 2,
      "intermediate_ideals": [
        "m^7",
        "m^7 + Z_3\u00b7(3^6,0)",
        "m^7 + Z_3\u00b7(0,3^6)",
        "m^7 + Z_3\u00b7(3^6,3^6) = 3^6R",
        "m^7 + Z_3\u00b7(3^6,-3^6)",
        "m^6"
      ],
      "one_dimensional_lines_mod_layer": [
        "[ (1,0) ]",
        "[ (0,1) ]",
        "[ (1,1) ]",
        "[ (1,-1) ]"
      ],
      "ideal_count_between_layers": 6
    }
  ]
}