{
  "description": "Cross-case ranking recomputed under the co-dominance p-value and the joint 2D magnitude ||D||_2, with look-elsewhere correction.",
  "p_floor": 0.0002,
  "cases": {
    "special_relativity": {
      "label": "Special relativity",
      "nulls": {
        "random_removal": {
          "label": "Random removal",
          "n_draws": 5000,
          "observed_D_I": 7.611536823493907,
          "observed_D_P": -0.3557613576970711,
          "null_mean_D_I": -0.07226772315366134,
          "null_mean_D_P": -0.08501798575204461,
          "p_co": 0.0,
          "p_co_is_floor": true,
          "l2_observed": 7.6198463868397095
        },
        "scrambled_assignment": {
          "label": "Scrambled assignment",
          "n_draws": 5000,
          "observed_D_I": 7.611536823493907,
          "observed_D_P": -0.3557613576970711,
          "null_mean_D_I": -0.058589271892877694,
          "null_mean_D_P": -0.1934679997999546,
          "p_co": 0.0,
          "p_co_is_floor": true,
          "l2_observed": 7.6198463868397095
        }
      },
      "look_elsewhere": {
        "observed_global_max_l2": 7.6198463868397095,
        "global_p": 0.0007998400319936012,
        "z_score": 7.91255249766178,
        "argmax_concept": "special_relativity",
        "argmax_year": 1902,
        "target_concept": "special_relativity",
        "argmax_is_target": true,
        "n_perm": 5000,
        "null_mean": 2.2664867323385525,
        "null_max": 7.88753206448518
      }
    },
    "higgs": {
      "label": "Higgs mechanism",
      "nulls": {
        "random_removal": {
          "label": "Random removal",
          "n_draws": 5000,
          "observed_D_I": -3.2530730762360744,
          "observed_D_P": -14.56884937431579,
          "null_mean_D_I": -0.18948144455208626,
          "null_mean_D_P": -0.17967726326649233,
          "p_co": 0.0,
          "p_co_is_floor": true,
          "l2_observed": 14.927620591736433
        },
        "scrambled_assignment": {
          "label": "Scrambled assignment",
          "n_draws": 5000,
          "observed_D_I": -3.2530730762360744,
          "observed_D_P": -14.56884937431579,
          "null_mean_D_I": -2.0723873404049695,
          "null_mean_D_P": 0.606785143994134,
          "p_co": 0.0,
          "p_co_is_floor": true,
          "l2_observed": 14.927620591736433
        }
      },
      "look_elsewhere": {
        "observed_global_max_l2": 14.927620591736433,
        "global_p": 0.020195960807838434,
        "z_score": 2.6746041126909645,
        "argmax_concept": "higgs_mechanism",
        "argmax_year": 1959,
        "target_concept": "higgs_mechanism",
        "argmax_is_target": true,
        "n_perm": 5000,
        "null_mean": 7.666755082009165,
        "null_max": 33.05535295688414
      }
    },
    "godel": {
      "label": "Godel incompleteness",
      "nulls": {
        "random_removal": {
          "label": "Random removal",
          "n_draws": 5000,
          "observed_D_I": 0.4959255785702684,
          "observed_D_P": 2.4955344782426976,
          "null_mean_D_I": -0.07484884823126907,
          "null_mean_D_P": -0.41004396600209686,
          "p_co": 0.0,
          "p_co_is_floor": true,
          "l2_observed": 2.544333805061417
        },
        "scrambled_assignment": {
          "label": "Scrambled assignment",
          "n_draws": 5000,
          "observed_D_I": 0.4959255785702684,
          "observed_D_P": 2.4955344782426976,
          "null_mean_D_I": 0.041103562594427365,
          "null_mean_D_P": -0.34498451191701124,
          "p_co": 0.0004,
          "p_co_is_floor": false,
          "l2_observed": 2.544333805061417
        }
      },
      "look_elsewhere": {
        "observed_global_max_l2": 2.8476241794006807,
        "global_p": 0.15076984603079385,
        "z_score": 0.8691889772529079,
        "argmax_concept": "type_theory",
        "argmax_year": 1940,
        "target_concept": "incompleteness",
        "argmax_is_target": false,
        "n_perm": 5000,
        "null_mean": 2.33546126468608,
        "null_max": 9.090869434411061
      }
    },
    "deep_learning": {
      "label": "Deep learning",
      "nulls": {
        "random_removal": {
          "label": "Random removal",
          "n_draws": 5000,
          "observed_D_I": -1.545786135845599,
          "observed_D_P": -3.1268117102101227,
          "null_mean_D_I": -1.20558918087578,
          "null_mean_D_P": -1.1540867877820533,
          "p_co": 0.0232,
          "p_co_is_floor": false,
          "l2_observed": 3.4880375928134177
        },
        "scrambled_assignment": {
          "label": "Scrambled assignment",
          "n_draws": 5000,
          "observed_D_I": -1.545786135845599,
          "observed_D_P": -3.1268117102101227,
          "null_mean_D_I": -1.7068815839039517,
          "null_mean_D_P": 1.8650071876226066,
          "p_co": 0.0,
          "p_co_is_floor": true,
          "l2_observed": 3.4880375928134177
        }
      },
      "look_elsewhere": {
        "observed_global_max_l2": 20.627173300084717,
        "global_p": 0.08818236352729454,
        "z_score": 1.2178820155919705,
        "argmax_concept": "feature_engineering",
        "argmax_year": 2008,
        "target_concept": "deep_learning",
        "argmax_is_target": false,
        "n_perm": 5000,
        "null_mean": 12.393603855755268,
        "null_max": 150.97709265771653
      }
    },
    "attention": {
      "label": "Attention mechanism",
      "nulls": {
        "random_removal": {
          "label": "Random removal",
          "n_draws": 5000,
          "observed_D_I": 1.6401378730172,
          "observed_D_P": 0.8986035662761397,
          "null_mean_D_I": -0.12261437960195612,
          "null_mean_D_P": -0.12192991511981845,
          "p_co": 0.0006,
          "p_co_is_floor": false,
          "l2_observed": 1.8701712787414904
        },
        "scrambled_assignment": {
          "label": "Scrambled assignment",
          "n_draws": 5000,
          "observed_D_I": 1.6401378730172,
          "observed_D_P": 0.8986035662761397,
          "null_mean_D_I": -0.7328929040518997,
          "null_mean_D_P": -0.2565547095678798,
          "p_co": 0.0156,
          "p_co_is_floor": false,
          "l2_observed": 1.8701712787414904
        }
      },
      "look_elsewhere": {
        "observed_global_max_l2": 6.023091233803916,
        "global_p": 0.9646070785842832,
        "z_score": -1.1540671334768489,
        "argmax_concept": "reinforcement_learning",
        "argmax_year": 2008,
        "target_concept": "attention_mechanism",
        "argmax_is_target": false,
        "n_perm": 5000,
        "null_mean": 9.083562453074485,
        "null_max": 38.74262793055992
      }
    }
  }
}