{
  "proof_locators": [
    "Theorem 5.1, equation (5.9)",
    "Lemma 4.1, equation (4.9)"
  ],
  "original_kernel_support": [
    [
      0.0,
      0.0
    ],
    [
      2.0,
      0.0
    ],
    [
      0.0,
      1.0
    ]
  ],
  "kernel_weights": [
    1,
    2,
    3
  ],
  "reflected_kernel_support": [
    [
      -0.0,
      -0.0
    ],
    [
      -2.0,
      -0.0
    ],
    [
      -0.0,
      -1.0
    ]
  ],
  "analytic_carrier_rectangle": [
    [
      -0.5,
      -0.25
    ],
    [
      0.5,
      -0.25
    ],
    [
      0.5,
      0.25
    ],
    [
      -0.5,
      0.25
    ]
  ],
  "convex_annihilator_carrier": [
    [
      -2.5,
      -0.25
    ],
    [
      -0.5,
      -1.25
    ],
    [
      0.5,
      -1.25
    ],
    [
      0.5,
      0.25
    ],
    [
      -2.5,
      0.25
    ]
  ],
  "open_domain": {
    "x": [
      -3,
      1
    ],
    "y": [
      -2,
      1
    ]
  },
  "open_convolution_domain": {
    "x": [
      -1,
      1
    ],
    "y": [
      -1,
      1
    ]
  },
  "gaussian": {
    "R": 1,
    "interval": [
      -2,
      2
    ],
    "observation": [
      "2/5",
      "1/5"
    ],
    "left_side_bound": "-143/25",
    "right_side_bound": "-63/25",
    "general_side_bound": "-15/16",
    "exponent": "-((Re(z)-Re(w))^2-(Im(z)-Im(w))^2)"
  },
  "authorship": "Original mathematical diagrams; GPT-6.1 Sol (OpenAI), Ultra; CC0 1.0."
}