{
  "ridge_sweep": [
    {
      "lambda_": 0.0001,
      "condition": 9999.000199974857,
      "sqrt_condition": 99.99500087491802,
      "active_cg_matvecs": 56,
      "pivots": 0,
      "active_free": 16,
      "pg_steps": 3239,
      "active_objective": -105.40781739382753,
      "pg_objective": -105.40781739382759,
      "simplex_error": 4.729550084903167e-13,
      "min_x": 0.0,
      "kkt_free": 2.461248982399411e-10,
      "kkt_bound_min": -2.3039348207021249e-10,
      "active_time": 0.0034129239993490046,
      "pg_time": 0.2553559389998554
    },
    {
      "lambda_": 0.001,
      "condition": 9990.010989017504,
      "sqrt_condition": 99.95004246631166,
      "active_cg_matvecs": 55,
      "pivots": 0,
      "active_free": 16,
      "pg_steps": 3239,
      "active_objective": -105.40798164382757,
      "pg_objective": -105.40798164382753,
      "simplex_error": 1.3871126469666706e-12,
      "min_x": 0.0,
      "kkt_free": 3.213749266706145e-10,
      "kkt_bound_min": -6.067857327707316e-10,
      "active_time": 0.003321640000649495,
      "pg_time": 0.2504232419996697
    },
    {
      "lambda_": 0.01,
      "condition": 9900.999999998474,
      "sqrt_condition": 99.50376877283831,
      "active_cg_matvecs": 55,
      "pivots": 0,
      "active_free": 16,
      "pg_steps": 3238,
      "active_objective": -105.40962414382756,
      "pg_objective": -105.40962414382757,
      "simplex_error": 1.2466694343515883e-12,
      "min_x": 0.0,
      "kkt_free": 6.832223675701243e-11,
      "kkt_bound_min": -1.042721464727947e-11,
      "active_time": 0.003294611000455916,
      "pg_time": 0.24821845299993583
    },
    {
      "lambda_": 0.1,
      "condition": 9090.999999994923,
      "sqrt_condition": 95.34673565463541,
      "active_cg_matvecs": 55,
      "pivots": 0,
      "active_free": 16,
      "pg_steps": 3233,
      "active_objective": -105.42604914382761,
      "pg_objective": -105.42604914382756,
      "simplex_error": 8.881784197001252e-15,
      "min_x": 0.0,
      "kkt_free": 1.866240495473903e-11,
      "kkt_bound_min": -1.0278000672769849e-11,
      "active_time": 0.0032702349999453872,
      "pg_time": 0.24844830499932868
    },
    {
      "lambda_": 1.0,
      "condition": 5000.5000000019445,
      "sqrt_condition": 70.7142135641905,
      "active_cg_matvecs": 53,
      "pivots": 0,
      "active_free": 16,
      "pg_steps": 3178,
      "active_objective": -105.59029914382761,
      "pg_objective": -105.59029914382755,
      "simplex_error": 8.44035952241029e-12,
      "min_x": 0.0,
      "kkt_free": 1.5955627929997718e-08,
      "kkt_bound_min": -1.4328826125620253e-08,
      "active_time": 0.003214570999261923,
      "pg_time": 0.2523497069996665
    }
  ],
  "spectrum_sweep": [
    {
      "raw_ratio": 1,
      "condition": 1.000000000000004,
      "sqrt_condition": 1.000000000000002,
      "cg_matvecs": 2,
      "pg_steps": 2,
      "objective_gap": 2.7755575615628914e-17
    },
    {
      "raw_ratio": 10,
      "condition": 9.991008991008988,
      "sqrt_condition": 3.160855737139705,
      "cg_matvecs": 32,
      "pg_steps": 94,
      "objective_gap": -1.1102230246251565e-16
    },
    {
      "raw_ratio": 100,
      "condition": 99.9010989010994,
      "sqrt_condition": 9.995053721771555,
      "cg_matvecs": 39,
      "pg_steps": 340,
      "objective_gap": 4.440892098500626e-16
    },
    {
      "raw_ratio": 1000,
      "condition": 999.0019980020144,
      "sqrt_condition": 31.60699286553554,
      "cg_matvecs": 46,
      "pg_steps": 1102,
      "objective_gap": -1.0658141036401503e-14
    },
    {
      "raw_ratio": 10000,
      "condition": 9990.010989017504,
      "sqrt_condition": 99.95004246631166,
      "cg_matvecs": 55,
      "pg_steps": 3239,
      "objective_gap": 4.263256414560601e-14
    }
  ],
  "predictions": [
    "Increasing ridge decreases kappa(A) monotonically and should reduce CG work.",
    "Across spectra, CG work should track sqrt(kappa) more closely than projected-gradient steps track kappa.",
    "The active-set output should have exact simplex feasibility and nonnegative coefficients, with sparse support."
  ]
}