{
  "schema": "AN02-LP045-exact-original-diagrams/v1",
  "source": "local-polynomial-annihilator-proof.md",
  "figures": {
    "moments-to-local-quotient": {
      "kind": "exact-map schematic",
      "proof_locators": [
        "LP2–LP7",
        "LP15–LP21"
      ],
      "transpose_divisor": "P(-z)",
      "D": "-i partial",
      "algebraic_domain_V": "complex polynomials in n real variables",
      "restricted_functional": "mu restricted to V = T* a",
      "no_formal_functional_growth_assumed": true
    },
    "root-circle-and-analytic-unit": {
      "kind": "three exact samples of complex t-plane",
      "Q": "(1+t)(t^2-w)",
      "q": "t^2-w",
      "b": "1+t",
      "parameter_disk_radius": 0.0625,
      "circle_R": 0.5,
      "inner_radius_r": 0.25,
      "sample_parameters": [
        -0.0625,
        0,
        0.0625
      ],
      "roots": [
        [
          [
            0,
            -0.25
          ],
          [
            0,
            0.25
          ]
        ],
        [
          [
            0,
            0
          ]
        ],
        [
          [
            -0.25,
            0
          ],
          [
            0.25,
            0
          ]
        ]
      ],
      "root_multiplicities": [
        [
          1,
          1
        ],
        [
          2
        ],
        [
          1,
          1
        ]
      ],
      "additional_root": [
        -1,
        0
      ],
      "q_boundary_lower_bound": 0.1875,
      "Q_boundary_lower_bound": 0.09375,
      "proof_locators": [
        "LP10–LP14",
        "LP26–LP27"
      ]
    },
    "local-quotient-global-pole": {
      "kind": "real slice with certified complex disk bounds",
      "F": "t^2-w",
      "Q": "(1+t)(t^2-w)",
      "G": "1/(1+t)",
      "sample_t_interval": [
        -0.9,
        0.9
      ],
      "sample_points": 1600,
      "pole": -1,
      "certified_disk_radius": 0.25,
      "R": 0.5,
      "M": 1,
      "beta": 0.75,
      "contour_bound": 2.6666666666666665,
      "sharp_bound": 1.3333333333333333,
      "proof_locators": [
        "LP23",
        "LP27",
        "Exercise5"
      ]
    }
  },
  "authorship": "GPT-6.1 Sol (OpenAI), Ultra, October2026",
  "original_drawing_license": "CC0-1.0",
  "font": "DejaVu Sans; existing reader font notices apply",
  "diagram_sources_retained": true
}