{
  "claim": "Claim 5: beta* sqrt speedup + ADePM > DePM/DeEPCA (Sec 4)",
  "partA_real_data": {
    "dataset": "SNAP ego-Facebook (n=d=50 subgraph)",
    "ADePM_beats_DePM": true,
    "ADePM_beats_DeEPCA": true,
    "DeEPCA_over_ADePM_bstar": {
      "20": 8.178394353297831,
      "40": 1243911.2309841341
    },
    "DeEPCA_final_L20": 0.003553243467635026,
    "DeEPCA_final_L40": 0.003552721959639524,
    "ADePM_bstar_final_L20": 0.00043446712326879015,
    "ADePM_bstar_final_L40": 2.856089623717561e-09,
    "DeEPCA_plateaus_with_L": true,
    "ADePM_keeps_improving_with_L": true
  },
  "partB_sqrt_speedup": {
    "exponent": 1.0006978285692545,
    "rows": [
      {
        "gap": 0.1,
        "Delta": 0.09999999999999998,
        "1_over_Delta": 10.000000000000002,
        "1_over_sqrtDelta": 3.16227766016838,
        "T_beta_star": 36,
        "T_beta_0": 131,
        "speedup_ratio": 3.638888888888889
      },
      {
        "gap": 0.03,
        "Delta": 0.030000000000000027,
        "1_over_Delta": 33.33333333333331,
        "1_over_sqrtDelta": 5.773502691896255,
        "T_beta_star": 71,
        "T_beta_0": 456,
        "speedup_ratio": 6.422535211267606
      },
      {
        "gap": 0.01,
        "Delta": 0.010000000000000009,
        "1_over_Delta": 99.99999999999991,
        "1_over_sqrtDelta": 9.999999999999995,
        "T_beta_star": 115,
        "T_beta_0": 1383,
        "speedup_ratio": 12.02608695652174
      },
      {
        "gap": 0.003,
        "Delta": 0.0030000000000000027,
        "1_over_Delta": 333.33333333333303,
        "1_over_sqrtDelta": 18.25741858350553,
        "T_beta_star": 211,
        "T_beta_0": 4627,
        "speedup_ratio": 21.928909952606634
      },
      {
        "gap": 0.001,
        "Delta": 0.0010000000000000009,
        "1_over_Delta": 999.9999999999991,
        "1_over_sqrtDelta": 31.622776601683782,
        "T_beta_star": 382,
        "T_beta_0": 13894,
        "speedup_ratio": 36.3717277486911
      },
      {
        "gap": 0.0003,
        "Delta": 0.00029999999999996696,
        "1_over_Delta": 3333.3333333337005,
        "1_over_sqrtDelta": 57.73502691896576,
        "T_beta_star": 709,
        "T_beta_0": 46334,
        "speedup_ratio": 65.35119887165021
      }
    ],
    "theory": 1.0
  },
  "verdict": "VERIFIED"
}