{
  "experiment": "exp_desitter_unification",
  "timestamp": "2026-04-06T07:09:38.803096",
  "piano": 39,
  "tension": "METRIC_TENSOR + BRODY_CROSSOVER + BOUNDARY + GAP_ANTICORR",
  "claim_tested": "De Sitter metric unifies geometric (dR) and statistical (<r>, acf1) observables",
  "N_primes": 5761455,
  "N_windows": 30,
  "W_size": 50000,
  "prime_range": "2 to 99999989",
  "observables_primes": {
    "r_slope_lnp": -0.003690740667945615,
    "r_intercept": 0.5106260382321726,
    "acf1_slope_lnp": 0.0026353136304354523,
    "acf1_intercept": -0.08438762134980968,
    "r_range": [
      0.4655693061205765,
      0.44430135271650567
    ],
    "acf1_range": [
      -0.0474310489920858,
      -0.03149201923698063
    ],
    "dR_norm_range": [
      5.075096079425776e-15,
      5.071604780757338e-16
    ]
  },
  "cross_correlations_primes": {
    "pearson_r_acf1": -0.6181920364399947,
    "pearson_r_dR_std": -0.5405350278567508,
    "pearson_acf1_dR_std": 0.6370997276989258,
    "pearson_r_dR_norm": 0.6082345311543917,
    "spearman_r_dR_norm": 0.6155728587319244,
    "spearman_r_acf1": -0.6338153503893215,
    "spearman_acf1_dR_norm": -0.012235817575083427
  },
  "null_cramer": {
    "n_surrogates": 20,
    "corr_r_dR_mean": -0.5302426302578457,
    "corr_r_dR_std": 0.0781019196878276,
    "z_r_dR": -0.13178162124623422,
    "z_r_acf1": -3.3878983678002674
  },
  "null_shuffled": {
    "n_surrogates": 20,
    "corr_r_dR_mean": 0.08942692269752892,
    "corr_r_dR_std": 0.2239802780197213,
    "z_r_dR": -2.8125777685605517,
    "z_r_acf1": -5.4973348384432645
  },
  "predictive_model": {
    "formula": "<r> = a + b * ln(dR_norm)",
    "a": 0.6463893623456323,
    "b": 0.005439640881675673,
    "R2": 0.4245217078456187
  },
  "windows": [
    {
      "p_center": 300033.0,
      "ln_p": 12.611647747588782,
      "r_mean": 0.4655693061205765,
      "acf1": -0.0474310489920858,
      "dR_std": 0.00011776797426162968,
      "dR_norm": 5.075096079425776e-15,
      "dR_acf1": -0.5352749432757608
    },
    {
      "p_center": 304317.0,
      "ln_p": 12.625825200246407,
      "r_mean": 0.4655001191855309,
      "acf1": -0.04773627172036205,
      "dR_std": 0.00010124551024866007,
      "dR_norm": 4.2427445738744485e-15,
      "dR_acf1": -0.5240233098542821
    },
    {
      "p_center": 310205.0,
      "ln_p": 12.644988648227812,
      "r_mean": 0.4651106759903872,
      "acf1": -0.048372814697931754,
      "dR_std": 8.786892457351819e-05,
      "dR_norm": 3.5476901861412887e-15,
      "dR_acf1": -0.5029080154377255
    },
    {
      "p_center": 318105.0,
      "ln_p": 12.670136795941273,
      "r_mean": 0.46468423607277154,
      "acf1": -0.04975873796228849,
      "dR_std": 7.52746397986098e-05,
      "dR_norm": 2.8930898830501254e-15,
      "dR_acf1": -0.5070269403576322
    },
    {
      "p_center": 328635.0,
      "ln_p": 12.70270299139043,
      "r_mean": 0.4642362572786134,
      "acf1": -0.04904584805221597,
      "dR_std": 6.615738998795051e-05,
      "dR_norm": 2.3830508367055356e-15,
      "dR_acf1": -0.5094420089846435
    },
    {
      "p_center": 343305.0,
      "ln_p": 12.746374543860549,
      "r_mean": 0.4640468339859669,
      "acf1": -0.049615970052672057,
      "dR_std": 5.68807378940337e-05,
      "dR_norm": 1.8828500029144555e-15,
      "dR_acf1": -0.5108373727025638
    },
    {
      "p_center": 363064.0,
      "ln_p": 12.802334406246409,
      "r_mean": 0.46407386465111106,
      "acf1": -0.04820113259217795,
      "dR_std": 4.9758103016135234e-05,
      "dR_norm": 1.4768266501528846e-15,
      "dR_acf1": -0.510589499471383
    },
    {
      "p_center": 390022.0,
      "ln_p": 12.87395842677124,
      "r_mean": 0.4638671772482982,
      "acf1": -0.04661925692416786,
      "dR_std": 4.4097928176704287e-05,
      "dR_norm": 1.1388317209182212e-15,
      "dR_acf1": -0.497800458996819
    },
    {
      "p_center": 426306.0,
      "ln_p": 12.96291267724961,
      "r_mean": 0.4639633591920612,
      "acf1": -0.0475250993341703,
      "dR_std": 4.0018785071125034e-05,
      "dR_norm": 8.677970203187234e-16,
      "dR_acf1": -0.485441191700922
    },
    {
      "p_center": 475410.0,
      "ln_p": 13.071932868604964,
      "r_mean": 0.4638304360422358,
      "acf1": -0.04677786397820886,
      "dR_std": 3.819278024037445e-05,
      "dR_norm": 6.675848331108941e-16,
      "dR_acf1": -0.4761023399993174
    },
    {
      "p_center": 542202.0,
      "ln_p": 13.203393904715664,
      "r_mean": 0.46366782501594167,
      "acf1": -0.04457359659384229,
      "dR_std": 4.005890763277879e-05,
      "dR_norm": 5.395751930303047e-16,
      "dR_acf1": -0.4550423957094974
    },
    {
      "p_center": 633570.0,
      "ln_p": 13.35912576987653,
      "r_mean": 0.4618554120917833,
      "acf1": -0.05018713951766598,
      "dR_std": 4.576537724030955e-05,
      "dR_norm": 4.529010559469494e-16,
      "dR_acf1": -0.43971159527819426
    },
    {
      "p_center": 758373.0,
      "ln_p": 13.538930628023387,
      "r_mean": 0.45970116973592784,
      "acf1": -0.054458669692122,
      "dR_std": 5.870660563728685e-05,
      "dR_norm": 4.0664493394524513e-16,
      "dR_acf1": -0.43718113535299735
    },
    {
      "p_center": 927785.0,
      "ln_p": 13.740555303891657,
      "r_mean": 0.4582639162344058,
      "acf1": -0.055190876963176566,
      "dR_std": 7.956474130859146e-05,
      "dR_norm": 3.682458261682641e-16,
      "dR_acf1": -0.42719795088795504
    },
    {
      "p_center": 1161021.0,
      "ln_p": 13.964810348371742,
      "r_mean": 0.45635149107679024,
      "acf1": -0.058206201956840155,
      "dR_std": 0.00011836765837368006,
      "dR_norm": 3.5058016183285125e-16,
      "dR_acf1": -0.4233093833842448
    },
    {
      "p_center": 1479730.0,
      "ln_p": 14.207370196665044,
      "r_mean": 0.45529749423050686,
      "acf1": -0.05476002236219264,
      "dR_std": 0.00018614503351467557,
      "dR_norm": 3.3952143190988445e-16,
      "dR_acf1": -0.42338602441933704
    },
    {
      "p_center": 1917054.0,
      "ln_p": 14.466300190645127,
      "r_mean": 0.45430436785820355,
      "acf1": -0.0551862219857334,
      "dR_std": 0.00029843412579368497,
      "dR_norm": 3.2447285623994084e-16,
      "dR_acf1": -0.42681495244818757
    },
    {
      "p_center": 2518290.0,
      "ln_p": 14.739090657725239,
      "r_mean": 0.454996116046496,
      "acf1": -0.0444016186942626,
      "dR_std": 0.0005026010940835939,
      "dR_norm": 3.1698261352215034e-16,
      "dR_acf1": -0.431474129582102
    },
    {
      "p_center": 3341570.0,
      "ln_p": 15.021951314389586,
      "r_mean": 0.45276250371570415,
      "acf1": -0.041182289631620024,
      "dR_std": 0.0008681904180040132,
      "dR_norm": 3.108082483767937e-16,
      "dR_acf1": -0.4278382923902426
    },
    {
      "p_center": 4474695.0,
      "ln_p": 15.313948750943757,
      "r_mean": 0.45322434650889976,
      "acf1": -0.04866438878461713,
      "dR_std": 0.0014717273260819934,
      "dR_norm": 2.939402924793379e-16,
      "dR_acf1": -0.41092437075906985
    },
    {
      "p_center": 6030060.0,
      "ln_p": 15.612267518902621,
      "r_mean": 0.4525583787042679,
      "acf1": -0.042621586356574113,
      "dR_std": 0.002649087214813211,
      "dR_norm": 2.913265883302158e-16,
      "dR_acf1": -0.41874778066512836
    },
    {
      "p_center": 8167655.0,
      "ln_p": 15.915692399932631,
      "r_mean": 0.4500214874822105,
      "acf1": -0.0456271585941302,
      "dR_std": 0.004893754954924466,
      "dR_norm": 2.934213741611806e-16,
      "dR_acf1": -0.4117416723028543
    },
    {
      "p_center": 11102331.0,
      "ln_p": 16.22266564423565,
      "r_mean": 0.45199466382728665,
      "acf1": -0.03571023651350359,
      "dR_std": 0.017755291561237497,
      "dR_norm": 5.76108912030588e-16,
      "dR_acf1": -0.4138347893392894
    },
    {
      "p_center": 15135112.0,
      "ln_p": 16.532527900476648,
      "r_mean": 0.4477716066917081,
      "acf1": -0.03990481853556306,
      "dR_std": 0.032123689795015196,
      "dR_norm": 5.60939702750156e-16,
      "dR_acf1": -0.413587424085543
    },
    {
      "p_center": 20670535.0,
      "ln_p": 16.844219814245104,
      "r_mean": 0.44834505445367334,
      "acf1": -0.039227362381218045,
      "dR_std": 0.058801485982184286,
      "dR_norm": 5.505076371522853e-16,
      "dR_acf1": -0.4068692143978108
    },
    {
      "p_center": 28268459.0,
      "ln_p": 17.157257218102686,
      "r_mean": 0.44739786780097235,
      "acf1": -0.044012256853370804,
      "dR_std": 0.10665799894470136,
      "dR_norm": 5.338806297222821e-16,
      "dR_acf1": -0.4163054314503495
    },
    {
      "p_center": 38699122.0,
      "ln_p": 17.471327470404148,
      "r_mean": 0.4474158581378746,
      "acf1": -0.04081731465189688,
      "dR_std": 0.1996893242983151,
      "dR_norm": 5.333769087642022e-16,
      "dR_acf1": -0.40538834208213514
    },
    {
      "p_center": 53004138.0,
      "ln_p": 17.78588054394036,
      "r_mean": 0.4449280782761393,
      "acf1": -0.03270037677972819,
      "dR_std": 0.3643461086507622,
      "dR_norm": 5.18745822317499e-16,
      "dR_acf1": -0.39818098261136264
    },
    {
      "p_center": 72626757.0,
      "ln_p": 18.100843965614793,
      "r_mean": 0.44729766951914707,
      "acf1": -0.03385586908634045,
      "dR_std": 0.6868992715533309,
      "dR_norm": 5.209099916655784e-16,
      "dR_acf1": -0.40456596090031116
    },
    {
      "p_center": 99540899.0,
      "ln_p": 18.416079162899006,
      "r_mean": 0.44430135271650567,
      "acf1": -0.03149201923698063,
      "dR_std": 1.2562647799879714,
      "dR_norm": 5.071604780757338e-16,
      "dR_acf1": -0.39419255532539427
    }
  ]
}