{
  "timestamp": "2026-04-05T09:17:34.255627",
  "experiment": "boundary_excess_growth",
  "tension_id": "BOUNDARY",
  "parameters": {
    "limit": 100000000,
    "n_windows": 25,
    "window_size": 50000,
    "n_cramer_trials": 10
  },
  "summary": {
    "excess_cramer_mean": 0.042737,
    "excess_cramer_slope": -0.002744,
    "excess_shuffled_mean": -0.017853,
    "excess_shuffled_slope": 0.001945,
    "z_cramer_mean": 34.54,
    "z_cramer_slope": -2.3563,
    "all_positive_cramer": true,
    "slope_growing": false,
    "meta_tautology_risk": false,
    "r_small_scale": 0.465569,
    "r_large_scale": 0.444297
  },
  "verdict": "PARTIAL: Excess is positive everywhere but does NOT grow (may shrink)",
  "key_findings": [
    "Excess <r>_prime - <r>_Cramer is positive at ALL 25 scales (z=18 to 50)",
    "But excess SHRINKS with scale: slope = -0.0027 per decade (FALSIFIES growth claim)",
    "<r>_prime < <r>_shuffled at all scales: primes have ANTI-correlated consecutive gaps",
    "<r> moves from 0.466 to 0.444 (toward Poisson, away from GUE) as scale grows",
    "The real signal: primes are more correlated than Cramer but LESS than their own shuffled gaps"
  ]
}