{
  "kernel": "1+x*z, prior f(x)=a+b*x with independent standard-normal a,b",
  "one_training_point": {
    "train_X": [
      "0"
    ],
    "train_y": [
      "1"
    ],
    "training_noise_variance": "1",
    "query_X": [
      "0",
      "1"
    ],
    "K_train_with_noise": [
      [
        "2"
      ]
    ],
    "cross_query_train": [
      [
        "1"
      ],
      [
        "1"
      ]
    ],
    "K_query_prior": [
      [
        "1",
        "1"
      ],
      [
        "1",
        "2"
      ]
    ],
    "alpha_solved_from_K_y": [
      "1/2"
    ],
    "solves_K_cross_columns": [
      [
        "1/2"
      ],
      [
        "1/2"
      ]
    ],
    "posterior_mean": [
      "1/2",
      "1/2"
    ],
    "latent_joint_covariance": [
      [
        "1/2",
        "1/2"
      ],
      [
        "1/2",
        "3/2"
      ]
    ],
    "independent_future_measurement_noise_variance": "1",
    "future_observation_joint_covariance": [
      [
        "3/2",
        "1/2"
      ],
      [
        "1/2",
        "5/2"
      ]
    ],
    "latent_sum_variance_full": "3",
    "latent_sum_variance_if_independence_wrongly_assumed": "2"
  },
  "independent_coefficient_posterior_covariance_check": [
    [
      "1/2",
      "1/2"
    ],
    [
      "1/2",
      "3/2"
    ]
  ],
  "changed_y_fixed_kernel_and_noise": {
    "train_X": [
      "0"
    ],
    "train_y": [
      "3"
    ],
    "training_noise_variance": "1",
    "query_X": [
      "0",
      "1"
    ],
    "K_train_with_noise": [
      [
        "2"
      ]
    ],
    "cross_query_train": [
      [
        "1"
      ],
      [
        "1"
      ]
    ],
    "K_query_prior": [
      [
        "1",
        "1"
      ],
      [
        "1",
        "2"
      ]
    ],
    "alpha_solved_from_K_y": [
      "3/2"
    ],
    "solves_K_cross_columns": [
      [
        "1/2"
      ],
      [
        "1/2"
      ]
    ],
    "posterior_mean": [
      "3/2",
      "3/2"
    ],
    "latent_joint_covariance": [
      [
        "1/2",
        "1/2"
      ],
      [
        "1/2",
        "3/2"
      ]
    ],
    "independent_future_measurement_noise_variance": "1",
    "future_observation_joint_covariance": [
      [
        "3/2",
        "1/2"
      ],
      [
        "1/2",
        "5/2"
      ]
    ],
    "latent_sum_variance_full": "3",
    "latent_sum_variance_if_independence_wrongly_assumed": "2"
  },
  "repeated_X_positive_noise": {
    "train_X": [
      "0",
      "0"
    ],
    "train_y": [
      "1",
      "3"
    ],
    "training_noise_variance": "1",
    "query_X": [
      "0",
      "1"
    ],
    "K_train_with_noise": [
      [
        "2",
        "1"
      ],
      [
        "1",
        "2"
      ]
    ],
    "cross_query_train": [
      [
        "1",
        "1"
      ],
      [
        "1",
        "1"
      ]
    ],
    "K_query_prior": [
      [
        "1",
        "1"
      ],
      [
        "1",
        "2"
      ]
    ],
    "alpha_solved_from_K_y": [
      "-1/3",
      "5/3"
    ],
    "solves_K_cross_columns": [
      [
        "1/3",
        "1/3"
      ],
      [
        "1/3",
        "1/3"
      ]
    ],
    "posterior_mean": [
      "4/3",
      "4/3"
    ],
    "latent_joint_covariance": [
      [
        "1/3",
        "1/3"
      ],
      [
        "1/3",
        "4/3"
      ]
    ],
    "independent_future_measurement_noise_variance": "1",
    "future_observation_joint_covariance": [
      [
        "4/3",
        "1/3"
      ],
      [
        "1/3",
        "7/3"
      ]
    ],
    "latent_sum_variance_full": "7/3",
    "latent_sum_variance_if_independence_wrongly_assumed": "5/3"
  },
  "repeated_X_zero_noise_ordinary_solve_rejected": "singular ordinary linear solve; not a general GP invalidity verdict",
  "hyperparameters_or_noise_estimated": false,
  "acquisition_optimization_or_sklearn_executed": false
}