{
  "y": [
    "1/5",
    "-3/10",
    "17/10"
  ],
  "x": [
    "0",
    "0",
    "1"
  ],
  "theta": "7/10",
  "sorted_threshold_trace": [
    {
      "j": 1,
      "u_j": "17/10",
      "theta_candidate": "7/10",
      "positive": true
    },
    {
      "j": 2,
      "u_j": "1/5",
      "theta_candidate": "9/20",
      "positive": false
    },
    {
      "j": 3,
      "u_j": "-3/10",
      "theta_candidate": "1/5",
      "positive": false
    }
  ],
  "objective_half_squared": "31/100",
  "wrong_clip_normalize": [
    "2/19",
    "0",
    "17/19"
  ],
  "wrong_objective": "13491/36100",
  "all125_grid_support_oracles_and_shift": 125,
  "all_negative": [
    "1",
    "0",
    "0"
  ],
  "all_zero": [
    "1/3",
    "1/3",
    "1/3"
  ],
  "invalid_cases_rejected": [
    "empty",
    "bool",
    "float",
    "too_many",
    "value_budget",
    "denominator_budget"
  ],
  "scope": "Euclidean simplex projection, not softmax/probability calibration. Exact local rational subset max4; own KKT and support enumeration, no optimizer/model/librarybenchmark."
}