{
  "experiment": "exp_geodesic_deviation_primes",
  "timestamp": "2026-04-05T12:07:44.263663",
  "piano": 39,
  "tension": "METRIC_TENSOR",
  "claim_tested": "g=(p/2)^2 de Sitter \u2014 is R=2 specific to primes?",
  "answer": "NO. R=2 is tautological. The FLUCTUATIONS dR=R-2 encode prime structure.",
  "N_primes": 664579,
  "prime_dR_std": 0.00476875,
  "prime_acf_lag1": -0.417203,
  "prime_acf_lag2": 0.045462,
  "shuffled_baseline": {
    "n_surrogates": 20,
    "dR_std_mean": 0.00633108,
    "z_score_std": -12.71,
    "z_score_acf1": -2.16,
    "z_score_acf2": 0.62
  },
  "cramer_baseline": {
    "n_surrogates": 20,
    "dR_std_mean": 0.00950148,
    "z_score_std": -46.49,
    "z_score_acf1": -8.07
  },
  "psd_ratios_by_band": [
    0.0165,
    0.0572,
    0.0365,
    0.0911,
    0.2991
  ],
  "verdict": "CONSTRAINT",
  "finding": "R=2 tautological. Curvature fluctuations encode gap correlations."
}