1{
  2  "seed": 2184,
  3  "prediction_checks": {
  4    "weak_noise_scaling": {
  5      "predicted_loglog_slope": -0.5,
  6      "observed_loglog_slope": -0.48114411850291106,
  7      "tolerance": 0.12,
  8      "passed": true,
  9      "n": [
 10        8,
 11        16,
 12        32,
 13        64,
 14        128,
 15        256
 16      ],
 17      "std": [
 18        0.4245481667462415,
 19        0.33853416469623837,
 20        0.21744622617264295,
 21        0.16226827000783398,
 22        0.11905282477270107,
 23        0.08162000556664657
 24      ]
 25    },
 26    "consensus_transition": {
 27      "prediction": "majority improves for p>0.5 and worsens for p<0.5",
 28      "rows": [
 29        {
 30          "p": 0.4,
 31          "m": 3,
 32          "observed_error": 0.6497,
 33          "hoeffding_bound": 0.9417645335842487
 34        },
 35        {
 36          "p": 0.4,
 37          "m": 7,
 38          "observed_error": 0.7038333333333333,
 39          "hoeffding_bound": 0.8693582353988059
 40        },
 41        {
 42          "p": 0.4,
 43          "m": 15,
 44          "observed_error": 0.7860666666666667,
 45          "hoeffding_bound": 0.740818220681718
 46        },
 47        {
 48          "p": 0.4,
 49          "m": 31,
 50          "observed_error": 0.8718,
 51          "hoeffding_bound": 0.5379444375946747
 52        },
 53        {
 54          "p": 0.55,
 55          "m": 3,
 56          "observed_error": 0.4246333333333333,
 57          "hoeffding_bound": 0.9851119396030626
 58        },
 59        {
 60          "p": 0.55,
 61          "m": 7,
 62          "observed_error": 0.3939666666666667,
 63          "hoeffding_bound": 0.9656054162575665
 64        },
 65        {
 66          "p": 0.55,
 67          "m": 15,
 68          "observed_error": 0.3486666666666667,
 69          "hoeffding_bound": 0.9277434863285527
 70        },
 71        {
 72          "p": 0.55,
 73          "m": 31,
 74          "observed_error": 0.2853,
 75          "hoeffding_bound": 0.8564151774836133
 76        },
 77        {
 78          "p": 0.7,
 79          "m": 3,
 80          "observed_error": 0.21806666666666666,
 81          "hoeffding_bound": 0.7866278610665535
 82        },
 83        {
 84          "p": 0.7,
 85          "m": 7,
 86          "observed_error": 0.1255,
 87          "hoeffding_bound": 0.5712090638488151
 88        },
 89        {
 90          "p": 0.7,
 91          "m": 15,
 92          "observed_error": 0.049433333333333336,
 93          "hoeffding_bound": 0.3011942119122023
 94        },
 95        {
 96          "p": 0.7,
 97          "m": 31,
 98          "observed_error": 0.007833333333333333,
 99          "hoeffding_bound": 0.08374322559219607
100        },
101        {
102          "p": 0.85,
103          "m": 3,
104          "observed_error": 0.061533333333333336,
105          "hoeffding_bound": 0.47950545897489416
106        },
107        {
108          "p": 0.85,
109          "m": 7,
110          "observed_error": 0.012533333333333334,
111          "hoeffding_bound": 0.1799637207131122
112        },
113        {
114          "p": 0.85,
115          "m": 15,
116          "observed_error": 0.0005666666666666667,
117          "hoeffding_bound": 0.025349405522724956
118        },
119        {
120          "p": 0.85,
121          "m": 31,
122          "observed_error": 0.0,
123          "hoeffding_bound": 0.0005029599566898495
124        }
125      ],
126      "passed": true
127    },
128    "patch_count_scaling": {
129      "prediction": "error decreases with m for p=.70 and stays below Hoeffding upper bound",
130      "rows": [
131        {
132          "p": 0.7,
133          "m": 3,
134          "observed_error": 0.21806666666666666,
135          "hoeffding_bound": 0.7866278610665535
136        },
137        {
138          "p": 0.7,
139          "m": 7,
140          "observed_error": 0.1255,
141          "hoeffding_bound": 0.5712090638488151
142        },
143        {
144          "p": 0.7,
145          "m": 15,
146          "observed_error": 0.049433333333333336,
147          "hoeffding_bound": 0.3011942119122023
148        },
149        {
150          "p": 0.7,
151          "m": 31,
152          "observed_error": 0.007833333333333333,
153          "hoeffding_bound": 0.08374322559219607
154        }
155      ],
156      "monotonic_with_sampling_tolerance": true,
157      "below_bound_with_sampling_tolerance": true,
158      "passed": true
159    }
160  },
161  "secondary_mvp": {
162    "local_exact_support_accuracy_mean": 0.997125,
163    "modal_consensus_exact_accuracy": 1.0,
164    "interpretation": "consensus converts noisy local support votes into a region-level decision"
165  },
166  "all_mechanism_checks_passed": true
167}