{
  "arithmetic": "exact SymPy rationals",
  "eta": "1/100",
  "Y": 100,
  "t": "1/100000",
  "small_g_distance_squared_from_identity": "5000000001/1562500000000000000",
  "h": "identity",
  "gamma": "gamma1 inverse",
  "cases": [
    {
      "k": 10,
      "gamma1_word": "(S2*S3)^(7*k)",
      "gamma1_congruent_identity_mod_7": true,
      "unperturbed_frobenius_norm_squared": "4",
      "perturbed_frobenius_norm_squared": "8350407013981540561/1562500000000000000",
      "perturbed_outside_Y_ball": false
    },
    {
      "k": 100,
      "gamma1_word": "(S2*S3)^(7*k)",
      "gamma1_congruent_identity_mod_7": true,
      "unperturbed_frobenius_norm_squared": "4",
      "perturbed_frobenius_norm_squared": "14819373062498879323605601/1562500000000000000",
      "perturbed_outside_Y_ball": true
    },
    {
      "k": 1000,
      "gamma1_word": "(S2*S3)^(7*k)",
      "gamma1_congruent_identity_mod_7": true,
      "unperturbed_frobenius_norm_squared": "4",
      "perturbed_frobenius_norm_squared": "1476210977427415104087910960056001/1562500000000000000",
      "perturbed_outside_Y_ball": true
    }
  ],
  "interpretation": "Written inner-range cancellation is false for this small g: gamma1*g^-1*gamma is not controlled by gamma1*gamma. Does not refute the counting-lemma conclusion."
}