{
  "generated_at": "2026-09-17",
  "scope": "273 independent eligible GSMDC items from the fixed random600 campaign; one OLMo-3-32B-Think checkpoint",
  "metric": {
    "name": "rho",
    "definition": "1 - k*/N",
    "provenance": "Zhai et al., How Much Thinking is Enough? (arXiv:2605.23926)",
    "estimator": "complete-case; all 273 had a measurable critical point"
  },
  "joint": {
    "n": 273,
    "mean_rho": 0.8232917517302294,
    "r2": 0.048494559088229194,
    "adjusted_r2": 0.034292985343277405,
    "oof_r2": 0.008360830023400712,
    "mse_skill": 0.01345523493884726,
    "hc3_joint_p": 0.005581746005715972,
    "coefficients": [
      {
        "key": "ahat",
        "label": "A-hat",
        "beta": -0.0004646241092631905,
        "ci": [
          -0.03506909930469369,
          0.03413985108496731
        ],
        "p": 0.9789298603410709,
        "holm": 0.9789298603410709
      },
      {
        "key": "op",
        "label": "操作量 op",
        "beta": 0.026692640517233756,
        "ci": [
          -0.008217842317058795,
          0.061603123351526304
        ],
        "p": 0.13340111678962258,
        "holm": 0.26680223357924515
      },
      {
        "key": "irrelevant",
        "label": "无关节点数",
        "beta": 0.037231563840078634,
        "ci": [
          0.005593276506832938,
          0.06886985117332434
        ],
        "p": 0.0212618843926143,
        "holm": 0.0637856531778429
      },
      {
        "key": "nll",
        "label": "原始 mean NLL",
        "beta": 0.05676396496327596,
        "ci": [
          0.02032334599786873,
          0.0932045839286832
        ],
        "p": 0.002384137831484356,
        "holm": 0.009536551325937424
      }
    ]
  },
  "checks": {
    "k0_judge_correct": 149,
    "full_prefix_correct": 270,
    "rho_at_least_095": 153,
    "n": 273
  },
  "auxiliary": [
    {
      "label": "Bscaled",
      "r": -0.10488529430476608,
      "p": 0.08366387488964575,
      "holm": 0.2509916246689372
    },
    {
      "label": "A-hat",
      "r": -0.026424078323741607,
      "p": 0.6638019468919294,
      "holm": 0.6717991966082725
    },
    {
      "label": "差值 mismatch",
      "r": -0.0584593772226052,
      "p": 0.33589959830413624,
      "holm": 0.6717991966082725
    }
  ],
  "sources": [
    {
      "label": "模型卡",
      "url": "https://huggingface.co/allenai/Olmo-3-32B-Think"
    },
    {
      "label": "HMTE 指标来源",
      "url": "https://arxiv.org/abs/2605.23926"
    },
    {
      "label": "GSMDC 官方代码",
      "url": "https://github.com/yminglai/GSM-DC"
    }
  ]
}