outputs/claim3_structure.json

{
 "checks": {
  "IPGS is a probability kernel for all gamma>0, K>=2": {
   "pass": true,
   "detail": "2e5 random draws: p >= 0 and sums to 1"
  },
  "IPGS satisfies p_t(b_t) >= 1/K (used in Part I of Eq. C.15)": {
   "pass": true,
   "detail": "min over 2e5 draws of K*p(b_t) = 1.000000 >= 1"
  },
  "Organic recommendations do not increment N_i or S_i": {
   "pass": true,
   "detail": "313 organic rounds, 0 wrongly counted"
  },
  "Both stages of the mechanism are exercised": {
   "pass": true,
   "detail": "MPASC=28 RASC-promote=32 RASC-organic=313 IPGS=19627"
  },
  "Every arm reaches the saturation threshold N before Stage 2": {
   "pass": true,
   "detail": "N_i at transition = [15, 15, 15, 15], N = 15"
  },
  "RASC explores with frequency 1/L": {
   "pass": true,
   "detail": "measured 0.1226 over 41714 RASC rounds vs 1/L = 0.1250 (3 s.e. = 0.0049)"
  },
  "Exploitation starts at epoch m0 = ceil(2 + log2 N)": {
   "pass": true,
   "detail": "checked N in {1..1.8e5}"
  },
  "Cold-start DBIC bound Eq. (C.7) holds at the prescribed L": {
   "pass": true,
   "detail": "min over 2e5 random (eps,tau,rho,Delta0) of LHS+eps = -1.221e-15 >= 0"
  },
  "Cold start is linear in K (paper: O(K L N))": {
   "pass": true,
   "detail": "fitted exponent in K = 1.042"
  },
  "Cold start is linear in L": {
   "pass": true,
   "detail": "fitted exponent in L = 0.941"
  },
  "Cold start is linear in N": {
   "pass": true,
   "detail": "fitted exponent in N = 0.985"
  },
  "Algorithm 2 per-round cost grows sub-cubically in d (per-round work is O(Kd))": {
   "pass": true,
   "detail": "fitted exponent in d = 0.051; per-round us = [21.9, 28.3, 29.4, 48.1, 30.0, 24.5]"
  },
  "Oracle linear solve scales close to the paper's stated O(d^3)": {
   "pass": true,
   "detail": "fitted exponent in d = 2.321 (theory 3, wall-clock fit); us = [60.4, 235.4, 1137.4, 7622.4]"
  },
  "Oracle Gram formation scales close to O(n d^2), the true dominant cost": {
   "pass": true,
   "detail": "fitted exponent in d = 2.295 (theory 2, wall-clock fit); us = [157.2, 860.8, 5509.9, 17003.5]"
  }
 },
 "phases": {
  "MPASC": 28,
  "RASC-promote": 32,
  "RASC-organic": 313,
  "IPGS": 19627
 },
 "cold_start_complexity": {
  "K": {
   "x": [
    8,
    16,
    32,
    64
   ],
   "y": [
    1402.6666666666667,
    2879.3333333333335,
    6084.666666666667,
    12133.666666666666
   ],
   "slope": 1.0417757838667079
  },
  "L": {
   "x": [
    4.0,
    8.0,
    16.0,
    32.0
   ],
   "y": [
    304.3333333333333,
    589.0,
    1241.0,
    2086.0
   ],
   "slope": 0.9406208256069987
  },
  "N": {
   "x": [
    10,
    20,
    40,
    80
   ],
   "y": [
    352.0,
    754.0,
    1475.0,
    2737.6666666666665
   ],
   "slope": 0.984597691600608
  }
 },
 "per_round_us": {
  "d": [
   2,
   4,
   8,
   16,
   32,
   64
  ],
  "us": [
   21.869932243134826,
   28.299682249780744,
   29.41534886485897,
   48.06129159987904,
   30.009807262104005,
   24.454427126329392
  ],
  "slope": 0.050513870214334886
 },
 "refit_us": {
  "d": [
   128,
   256,
   512,
   1024
  ],
  "solve_us": [
   60.44333800673485,
   235.37165950983763,
   1137.4174989759922,
   7622.4433444440365
  ],
  "gram_us": [
   157.1832923218608,
   860.7916999608278,
   5509.941698983312,
   17003.46670113504
  ],
  "slope_solve": 2.320832850778965,
  "slope_gram": 2.295001267189097
 },
 "n_fail": 0,
 "failed": []
}