{
  "schema": "AN02-L134-original-diagram-geometry/v1",
  "kernel_convention": "Delta E_n=delta_0; E3=-1/(4*pi*r); E2=log(r)/(2*pi)",
  "cap": {
    "delta_exact": "2/5",
    "capped_kernel": "E_n(max(r,delta))",
    "three_dimensional_L1_error": "delta^2/6",
    "three_dimensional_L2_error_squared": "delta/(12*pi)",
    "two_dimensional_L1_error": "delta^2/4",
    "radial_three_dimensional_L1_error_density": "r-r^2/delta for 0<r<delta; zero otherwise",
    "proof_locators": [
      "SC4.1-SC4.3",
      "SC5.2",
      "SC11 Exercise1"
    ]
  },
  "moving_wells": {
    "domain": "(0,1)^2",
    "observation_exact": [
      "37/100",
      "61/100"
    ],
    "level_definition": "N_m=ceil(exp(m)); all (k/N_m,l/N_m), 0<=k,l<=N_m",
    "value_definition": "log(|x-a|)/m; log(0)=-infinity",
    "finite_block_terms": "(N_m+1)^2",
    "universal_nearest_bound": "sqrt(2)/(2*N_m)<exp(-m)",
    "limits": "limsup=0 and liminf<=-1 everywhere in the open square",
    "plotted_levels": [
      {
        "m": 1,
        "N": 3,
        "block_terms": 16,
        "nearest_indices": [
          1,
          2
        ],
        "nearest_point_exact": [
          "1/3",
          "2/3"
        ],
        "distance_squared_exact": "41/9000",
        "nearest_distance": 0.0674948557710553,
        "distance_bound": 0.23570226039551587,
        "well_radius": 0.36787944117144233,
        "nearest_value": -2.6957038948070244,
        "fixed_far_corner": [
          1,
          0
        ],
        "far_value": -0.13133215473824653
      },
      {
        "m": 2,
        "N": 8,
        "block_terms": 81,
        "nearest_indices": [
          3,
          5
        ],
        "nearest_point_exact": [
          "3/8",
          "5/8"
        ],
        "distance_squared_exact": "1/4000",
        "nearest_distance": 0.015811388300841896,
        "distance_bound": 0.08838834764831845,
        "well_radius": 0.1353352832366127,
        "nearest_value": -2.073512410025507,
        "fixed_far_corner": [
          1,
          0
        ],
        "far_value": -0.06566607736912326
      },
      {
        "m": 3,
        "N": 21,
        "block_terms": 484,
        "nearest_indices": [
          8,
          13
        ],
        "nearest_point_exact": [
          "8/21",
          "13/21"
        ],
        "distance_squared_exact": "89/441000",
        "nearest_distance": 0.014206127514453618,
        "distance_bound": 0.033671751485073696,
        "well_radius": 0.049787068367863944,
        "nearest_value": -1.4180272974494736,
        "fixed_far_corner": [
          1,
          0
        ],
        "far_value": -0.043777384912748844
      },
      {
        "m": 4,
        "N": 55,
        "block_terms": 3136,
        "nearest_indices": [
          20,
          34
        ],
        "nearest_point_exact": [
          "4/11",
          "34/55"
        ],
        "distance_squared_exact": "13/121000",
        "nearest_distance": 0.010365231137264891,
        "distance_bound": 0.0128564869306645,
        "well_radius": 0.01831563888873418,
        "nearest_value": -1.1423245583896677,
        "fixed_far_corner": [
          1,
          0
        ],
        "far_value": -0.03283303868456163
      },
      {
        "m": 5,
        "N": 149,
        "block_terms": 22500,
        "nearest_indices": [
          55,
          91
        ],
        "nearest_point_exact": [
          "55/149",
          "91/149"
        ],
        "distance_squared_exact": "29/22201000",
        "nearest_distance": 0.0011429118366393558,
        "distance_bound": 0.004745683095211729,
        "well_radius": 0.006737946999085467,
        "nearest_value": -1.3548352060886582,
        "fixed_far_corner": [
          1,
          0
        ],
        "far_value": -0.026266430947649307
      },
      {
        "m": 6,
        "N": 404,
        "block_terms": 164025,
        "nearest_indices": [
          149,
          246
        ],
        "nearest_point_exact": [
          "149/404",
          "123/202"
        ],
        "distance_squared_exact": "53/20402000",
        "nearest_distance": 0.0016117644154554165,
        "distance_bound": 0.001750264309867692,
        "well_radius": 0.0024787521766663585,
        "nearest_value": -1.0717376316393732,
        "fixed_far_corner": [
          1,
          0
        ],
        "far_value": -0.021888692456374422
      },
      {
        "m": 7,
        "N": 1097,
        "block_terms": 1205604,
        "nearest_indices": [
          406,
          669
        ],
        "nearest_point_exact": [
          "406/1097",
          "669/1097"
        ],
        "distance_squared_exact": "41/1203409000",
        "nearest_distance": 0.0001845802801396225,
        "distance_bound": 0.0006445822982557407,
        "well_radius": 0.0009118819655545162,
        "nearest_value": -1.2282037237734493,
        "fixed_far_corner": [
          1,
          0
        ],
        "far_value": -0.018761736391178074
      },
      {
        "m": 8,
        "N": 2981,
        "block_terms": 8892324,
        "nearest_indices": [
          1103,
          1818
        ],
        "nearest_point_exact": [
          "1103/2981",
          "1818/2981"
        ],
        "distance_squared_exact": "169/8886361000",
        "nearest_distance": 0.0001379054330164003,
        "distance_bound": 0.00023720455591631922,
        "well_radius": 0.00033546262790251185,
        "nearest_value": -1.1111177969634505,
        "fixed_far_corner": [
          1,
          0
        ],
        "far_value": -0.016416519342280816
      }
    ],
    "proof_locators": [
      "SC9 Example2",
      "SC9.1-SC9.4",
      "SC11 Exercise6"
    ]
  },
  "author": "GPT-6.1 Sol (OpenAI), Ultra; original diagram content CC0-1.0",
  "figure_font_terms": "DejaVu-font-license.txt"
}