{
  "experiment": "number_variance_multi_scale",
  "timestamp": "2026-04-05T11:45:22.782355",
  "claim_under_test": "BOUNDARY: GUE->Poisson drift in primes",
  "method": "Number variance Sigma^2(L) at 5 scales, compared with GUE and Poisson predictions",
  "L_values": [
    2,
    5,
    10,
    20,
    50,
    100,
    200
  ],
  "results": {
    "p~1e+03": {
      "n_primes": 4965,
      "p_start": 1000,
      "log_slope_prime": 5.641581985527148,
      "log_slope_shuffled": 18.871692833403298,
      "lin_slope_prime": 0.1402813684747755,
      "lin_slope_shuffled": 0.48602363229588125,
      "r2_log": 0.8294869969860744,
      "r2_lin": 0.988807958006435,
      "better_fit": "linear"
    },
    "p~1e+05": {
      "n_primes": 4256,
      "p_start": 100000,
      "log_slope_prime": 7.281290262250898,
      "log_slope_shuffled": 21.059044391969984,
      "lin_slope_prime": 0.1627211926684012,
      "lin_slope_shuffled": 0.545510681525602,
      "r2_log": 0.9229243895584269,
      "r2_lin": 0.8886727487885985,
      "better_fit": "log"
    },
    "p~1e+06": {
      "n_primes": 3636,
      "p_start": 1000000,
      "log_slope_prime": 7.622765856174489,
      "log_slope_shuffled": 26.304765728410274,
      "lin_slope_prime": 0.1727823934252702,
      "lin_slope_shuffled": 0.6973788477220926,
      "r2_log": 0.920921423558583,
      "r2_lin": 0.9122220758481309,
      "better_fit": "log"
    },
    "p~1e+07": {
      "n_primes": 3130,
      "p_start": 10000000,
      "log_slope_prime": 7.570219513831313,
      "log_slope_shuffled": 24.752993655891814,
      "lin_slope_prime": 0.19217027952705348,
      "lin_slope_shuffled": 0.6522117690675411,
      "r2_log": 0.7844006625554336,
      "r2_lin": 0.9745354465274412,
      "better_fit": "linear"
    },
    "p~5e+07": {
      "n_primes": 2792,
      "p_start": 50000000,
      "log_slope_prime": 19.398628884441422,
      "log_slope_shuffled": 27.357032807136125,
      "lin_slope_prime": 0.5135624403673104,
      "lin_slope_shuffled": 0.721335667895747,
      "r2_log": 0.7383141808911973,
      "r2_lin": 0.9976767216167644,
      "better_fit": "linear"
    }
  },
  "gue_log_slope": 0.20264236728467555
}