{
  "authored_diagonal_matrix": [
    [
      -3,
      0
    ],
    [
      0,
      1
    ]
  ],
  "start": [
    1,
    1
  ],
  "eight_exact_steps": [
    {
      "step": 1,
      "normalized_vector": [
        "-1",
        "1/3"
      ],
      "nonnegative_normalization_scale": "3",
      "signed_Rayleigh": "-13/5",
      "residual_infinity": "6/5"
    },
    {
      "step": 2,
      "normalized_vector": [
        "1",
        "1/9"
      ],
      "nonnegative_normalization_scale": "3",
      "signed_Rayleigh": "-121/41",
      "residual_infinity": "18/41"
    },
    {
      "step": 3,
      "normalized_vector": [
        "-1",
        "1/27"
      ],
      "nonnegative_normalization_scale": "3",
      "signed_Rayleigh": "-1093/365",
      "residual_infinity": "54/365"
    },
    {
      "step": 4,
      "normalized_vector": [
        "1",
        "1/81"
      ],
      "nonnegative_normalization_scale": "3",
      "signed_Rayleigh": "-9841/3281",
      "residual_infinity": "162/3281"
    },
    {
      "step": 5,
      "normalized_vector": [
        "-1",
        "1/243"
      ],
      "nonnegative_normalization_scale": "3",
      "signed_Rayleigh": "-88573/29525",
      "residual_infinity": "486/29525"
    },
    {
      "step": 6,
      "normalized_vector": [
        "1",
        "1/729"
      ],
      "nonnegative_normalization_scale": "3",
      "signed_Rayleigh": "-797161/265721",
      "residual_infinity": "1458/265721"
    },
    {
      "step": 7,
      "normalized_vector": [
        "-1",
        "1/2187"
      ],
      "nonnegative_normalization_scale": "3",
      "signed_Rayleigh": "-7174453/2391485",
      "residual_infinity": "4374/2391485"
    },
    {
      "step": 8,
      "normalized_vector": [
        "1",
        "1/6561"
      ],
      "nonnegative_normalization_scale": "3",
      "signed_Rayleigh": "-64570081/21523361",
      "residual_infinity": "13122/21523361"
    }
  ],
  "status": "budget_exhausted",
  "known_dominant_eigenvalue": -3,
  "normalization_scale_is_not_signed_eigenvalue": true,
  "closed_form_power_oracle": "[(-3)^k,1] normalized by infinity norm, checked every step",
  "missing_dominant_start_component": {
    "start": [
      0,
      1
    ],
    "steps": [
      {
        "step": 1,
        "normalized_vector": [
          "0",
          "1"
        ],
        "nonnegative_normalization_scale": "1",
        "signed_Rayleigh": "1",
        "residual_infinity": "0"
      }
    ],
    "status": "eigenpair_residual_tolerance_not_dominance_proof"
  },
  "equal_absolute_eigenvalues": {
    "matrix": [
      [
        1,
        0
      ],
      [
        0,
        -1
      ]
    ],
    "steps": [
      {
        "step": 1,
        "normalized_vector": [
          "1",
          "-1"
        ],
        "nonnegative_normalization_scale": "1",
        "signed_Rayleigh": "0",
        "residual_infinity": "1"
      },
      {
        "step": 2,
        "normalized_vector": [
          "1",
          "1"
        ],
        "nonnegative_normalization_scale": "1",
        "signed_Rayleigh": "0",
        "residual_infinity": "1"
      },
      {
        "step": 3,
        "normalized_vector": [
          "1",
          "-1"
        ],
        "nonnegative_normalization_scale": "1",
        "signed_Rayleigh": "0",
        "residual_infinity": "1"
      },
      {
        "step": 4,
        "normalized_vector": [
          "1",
          "1"
        ],
        "nonnegative_normalization_scale": "1",
        "signed_Rayleigh": "0",
        "residual_infinity": "1"
      }
    ],
    "status": "budget_exhausted"
  },
  "zero_image_status": "zero_image",
  "invalid_cases_rejected": [
    "zero_start",
    "ragged",
    "nonfinite",
    "cap_bool",
    "tol_zero"
  ],
  "scope": "no universal convergence, PCA/model training/benchmark; norm ratio positive3 differs from negative dominant eigenvalue;8steps do not pass chosen1e-8residual tolerance"
}