{
  "model": "Black-Scholes, European call, no dividends",
  "strike": 100.0,
  "rate": 0.03,
  "time_to_maturity_years": 1.0,
  "spot_range": [
    50,
    150
  ],
  "volatility_range": [
    0.05,
    0.6
  ],
  "grid": [
    128,
    128
  ],
  "grid_spacing": "uniform, inclusive endpoints",
  "selected_rank": 8,
  "retained_fraction": 0.12109375,
  "selected_rows_zero_based": [
    127,
    60,
    29,
    80,
    0,
    50,
    13,
    91
  ],
  "selected_columns_zero_based": [
    127,
    0,
    50,
    17,
    91,
    5,
    31,
    10
  ],
  "selected_spots": [
    150.0,
    97.24409448818898,
    72.83464566929135,
    112.99212598425197,
    50.0,
    89.37007874015748,
    60.23622047244095,
    121.65354330708662
  ],
  "selected_volatilities": [
    0.6,
    0.05,
    0.2665354330708661,
    0.12362204724409448,
    0.4440944881889763,
    0.07165354330708662,
    0.184251968503937,
    0.09330708661417322
  ],
  "singular_values": [
    3348.5801355995995,
    367.3983288175317,
    42.184261849737034,
    9.984869255221868,
    2.261720134679078,
    0.6177058416526389,
    0.16530441683244868,
    0.04194342786892819,
    0.011334897286445132,
    0.0029328402971329835,
    0.0007146912589984793,
    0.00017909409293091343,
    4.17649238526076e-05,
    9.307178755332433e-06,
    2.0558413150486874e-06,
    4.104979216233171e-07,
    8.054171404982927e-08,
    1.4443208105588481e-08,
    2.4203610108880266e-09,
    3.7703656157123593e-10,
    5.2668153000825996e-11,
    6.819310792636753e-12,
    7.562248278489684e-13,
    3.257562903520836e-13,
    3.257562903520836e-13,
    3.257562903520836e-13,
    3.257562903520836e-13,
    3.257562903520836e-13,
    3.257562903520836e-13,
    3.257562903520836e-13,
    3.257562903520836e-13,
    3.257562903520836e-13,
    3.257562903520836e-13,
    3.257562903520836e-13,
    3.257562903520836e-13,
    3.257562903520836e-13,
    3.257562903520836e-13,
    3.257562903520836e-13,
    3.257562903520836e-13,
    3.257562903520836e-13,
    3.257562903520836e-13,
    3.257562903520836e-13,
    3.257562903520836e-13,
    3.257562903520836e-13,
    3.257562903520836e-13,
    3.257562903520836e-13,
    3.257562903520836e-13,
    3.257562903520836e-13,
    3.257562903520836e-13,
    3.257562903520836e-13,
    3.257562903520836e-13,
    3.257562903520836e-13,
    3.257562903520836e-13,
    3.257562903520836e-13,
    3.257562903520836e-13,
    3.257562903520836e-13,
    3.257562903520836e-13,
    3.257562903520836e-13,
    3.257562903520836e-13,
    3.257562903520836e-13,
    3.257562903520836e-13,
    3.257562903520836e-13,
    3.257562903520836e-13,
    3.257562903520836e-13,
    3.257562903520836e-13,
    3.257562903520836e-13,
    3.257562903520836e-13,
    3.257562903520836e-13,
    3.257562903520836e-13,
    3.257562903520836e-13,
    3.257562903520836e-13,
    3.257562903520836e-13,
    3.257562903520836e-13,
    3.257562903520836e-13,
    3.257562903520836e-13,
    3.257562903520836e-13,
    3.257562903520836e-13,
    3.257562903520836e-13,
    3.257562903520836e-13,
    3.257562903520836e-13,
    3.257562903520836e-13,
    3.257562903520836e-13,
    3.257562903520836e-13,
    3.257562903520836e-13,
    3.257562903520836e-13,
    3.257562903520836e-13,
    3.257562903520836e-13,
    3.257562903520836e-13,
    3.257562903520836e-13,
    3.257562903520836e-13,
    3.257562903520836e-13,
    3.257562903520836e-13,
    3.257562903520836e-13,
    3.257562903520836e-13,
    3.257562903520836e-13,
    3.257562903520836e-13,
    3.257562903520836e-13,
    3.257562903520836e-13,
    3.257562903520836e-13,
    3.257562903520836e-13,
    3.257562903520836e-13,
    3.257562903520836e-13,
    3.257562903520836e-13,
    3.257562903520836e-13,
    3.257562903520836e-13,
    3.257562903520836e-13,
    3.257562903520836e-13,
    3.257562903520836e-13,
    3.257562903520836e-13,
    3.257562903520836e-13,
    3.257562903520836e-13,
    3.257562903520836e-13,
    3.257562903520836e-13,
    3.257562903520836e-13,
    3.257562903520836e-13,
    3.257562903520836e-13,
    3.257562903520836e-13,
    3.257562903520836e-13,
    3.257562903520836e-13,
    3.257562903520836e-13,
    3.257562903520836e-13,
    3.257562903520836e-13,
    3.257562903520836e-13,
    3.257562903520836e-13,
    3.257562903520836e-13,
    3.257562903520836e-13,
    3.257562903520836e-13,
    3.257562903520836e-13
  ],
  "errors_by_rank": [
    {
      "rank": 1,
      "svd_relative_frobenius": 0.10981282190695986,
      "mci_relative_frobenius": 0.23763576603446265,
      "mci_max_absolute": 17.423763483824285,
      "retained_unique_entries": 255,
      "pivot_condition_number": 1.0
    },
    {
      "rank": 2,
      "svd_relative_frobenius": 0.01288635438941629,
      "mci_relative_frobenius": 0.03997880976272836,
      "mci_max_absolute": 2.481355913400699,
      "retained_unique_entries": 508,
      "pivot_condition_number": 6.49915521998354
    },
    {
      "rank": 3,
      "svd_relative_frobenius": 0.0030448210880202504,
      "mci_relative_frobenius": 0.007314711781371536,
      "mci_max_absolute": 0.6770726819688129,
      "retained_unique_entries": 759,
      "pivot_condition_number": 54.92538536612853
    },
    {
      "rank": 4,
      "svd_relative_frobenius": 0.0006977769235535919,
      "mci_relative_frobenius": 0.0026596615612898117,
      "mci_max_absolute": 0.3266179341207225,
      "retained_unique_entries": 1008,
      "pivot_condition_number": 287.84112073334245
    },
    {
      "rank": 5,
      "svd_relative_frobenius": 0.00019024402954286374,
      "mci_relative_frobenius": 0.0004962408729179727,
      "mci_max_absolute": 0.07432581133209576,
      "retained_unique_entries": 1255,
      "pivot_condition_number": 862.9713334733616
    },
    {
      "rank": 6,
      "svd_relative_frobenius": 5.074146298190493e-05,
      "mci_relative_frobenius": 0.00023669268271863902,
      "mci_max_absolute": 0.03202041858561472,
      "retained_unique_entries": 1500,
      "pivot_condition_number": 3467.2014241295037
    },
    {
      "rank": 7,
      "svd_relative_frobenius": 1.2927795022844317e-05,
      "mci_relative_frobenius": 2.9724710098686295e-05,
      "mci_max_absolute": 0.005685619047252288,
      "retained_unique_entries": 1743,
      "pivot_condition_number": 11579.713235963934
    },
    {
      "rank": 8,
      "svd_relative_frobenius": 3.4822128039589017e-06,
      "mci_relative_frobenius": 1.0378095764997841e-05,
      "mci_max_absolute": 0.0016681758148022197,
      "retained_unique_entries": 1984,
      "pivot_condition_number": 83043.74025296538
    },
    {
      "rank": 9,
      "svd_relative_frobenius": 8.976897674171991e-07,
      "mci_relative_frobenius": 2.514082150344296e-06,
      "mci_max_absolute": 0.0007729141825549846,
      "retained_unique_entries": 2223,
      "pivot_condition_number": 294822.9726935349
    },
    {
      "rank": 10,
      "svd_relative_frobenius": 2.1906903010068418e-07,
      "mci_relative_frobenius": 8.015208036638968e-07,
      "mci_max_absolute": 0.00018514531452416133,
      "retained_unique_entries": 2460,
      "pivot_condition_number": 898995.4268949952
    },
    {
      "rank": 11,
      "svd_relative_frobenius": 5.465991041045366e-08,
      "mci_relative_frobenius": 1.4917817474360746e-07,
      "mci_max_absolute": 5.0755100843957734e-05,
      "retained_unique_entries": 2695,
      "pivot_condition_number": 4158805.3621378154
    },
    {
      "rank": 12,
      "svd_relative_frobenius": 1.2716348180919315e-08,
      "mci_relative_frobenius": 6.070983320696019e-08,
      "mci_max_absolute": 1.3209922241408378e-05,
      "retained_unique_entries": 2928,
      "pivot_condition_number": 23111096.553459935
    }
  ],
  "pivot_search": "full residual; all 16384 grid entries evaluated",
  "error_scope": "128 x 128 grid only; no off-grid or Greek accuracy claim"
}