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          "squared_map_gap": "1",
          "vertices": [
            [
              "-1/16777216",
              "0"
            ],
            [
              "-1/16777216",
              "-1"
            ],
            [
              "-1/33554432",
              "-1"
            ]
          ]
        },
        {
          "first_cell": 2,
          "second_cell": 1,
          "mass": "1/268435456",
          "squared_map_gap": "1",
          "vertices": [
            [
              "1/33554432",
              "-1"
            ],
            [
              "1/16777216",
              "-1"
            ],
            [
              "1/16777216",
              "0"
            ]
          ]
        },
        {
          "first_cell": 2,
          "second_cell": 2,
          "mass": "7/134217728",
          "squared_map_gap": "1/1125899906842624",
          "vertices": [
            [
              "-1/16777216",
              "0"
            ],
            [
              "-1/33554432",
              "-1"
            ],
            [
              "1/33554432",
              "-1"
            ],
            [
              "1/16777216",
              "0"
            ],
            [
              "1/16777216",
              "1"
            ],
            [
              "-1/16777216",
              "1"
            ]
          ]
        }
      ],
      "central_cell_symmetric_difference_mass": "1/67108864",
      "squared_map_distance": "281474976710657/18889465931478580854784",
      "squared_target_w2": "1/18889465931478580854784",
      "target_w1": "1/562949953421312",
      "target_w2": "1/137438953472",
      "target_distance_justification": "Matching equal-mass atoms attains the second-coordinate lower bound; no general transport optimization was run.",
      "required_half_exponent_constant_squared": "281474976710657/137438953472",
      "one_third_exponent_ratio_sixth_power": "22300745198530860826023261066505567067963393/356811923176489970264571492362373784095686656",
      "source_constant_squared_rational_upper_bound": "9464",
      "constant_bound_justification": "For K=Y=[-1,1]^2 choose R^2=L^2=2, P_K/volume(K)=1 and sqrt(162)<=13 in the paper formula.",
      "interpretation": "Exact finite reproduction of the continuous two-dimensional counterexample formulas; extra cube coordinates factor out as described by the source. It neither proves the general stability theorem nor certifies a learned, discrete or entropic transport solver."
    }
  ]
}