{
  "alpha_exact": "(sqrt(5)-1)/2",
  "circle_samples": [
    {
      "circle_coordinates_sample": [
        0.6084388609788614,
        -0.7936007512916969
      ],
      "label": 3,
      "m": 4,
      "return_error_exact": "(-1)^(4-1)*alpha^4",
      "return_error_sample": -0.14589803375031551
    },
    {
      "circle_coordinates_sample": [
        0.9910694127331605,
        -0.1333469877603103
      ],
      "label": 21,
      "m": 8,
      "return_error_exact": "(-1)^(8-1)*alpha^8",
      "return_error_sample": -0.021286236252208202
    },
    {
      "circle_coordinates_sample": [
        0.9998096238259333,
        -0.019511947751204243
      ],
      "label": 144,
      "m": 12,
      "return_error_exact": "(-1)^(12-1)*alpha^12",
      "return_error_sample": -0.0031056200151418616
    }
  ],
  "fibonacci_identity": "F_m*alpha-F_(m-1)=(-1)^(m-1)*alpha^m",
  "graph_samples": [
    {
      "jet_kernel_exact": "4*sin(pi*alpha^2)^2",
      "jet_kernel_sample": 3.4747377561566406,
      "label": 1,
      "label_kernel_exact": 1,
      "m": 2
    },
    {
      "jet_kernel_exact": "4*sin(pi*alpha^3)^2",
      "jet_kernel_sample": 1.8251485505660796,
      "label": 2,
      "label_kernel_exact": 4,
      "m": 3
    },
    {
      "jet_kernel_exact": "4*sin(pi*alpha^4)^2",
      "jet_kernel_sample": 0.7831222780422773,
      "label": 3,
      "label_kernel_exact": 9,
      "m": 4
    },
    {
      "jet_kernel_exact": "4*sin(pi*alpha^5)^2",
      "jet_kernel_sample": 0.3124894103752048,
      "label": 5,
      "label_kernel_exact": 25,
      "m": 5
    },
    {
      "jet_kernel_exact": "4*sin(pi*alpha^6)^2",
      "jet_kernel_sample": 0.12135740735176548,
      "label": 8,
      "label_kernel_exact": 64,
      "m": 6
    },
    {
      "jet_kernel_exact": "4*sin(pi*alpha^7)^2",
      "jet_kernel_sample": 0.046648452743646596,
      "label": 13,
      "label_kernel_exact": 169,
      "m": 7
    },
    {
      "jet_kernel_exact": "4*sin(pi*alpha^8)^2",
      "jet_kernel_sample": 0.017861174533678977,
      "label": 21,
      "label_kernel_exact": 441,
      "m": 8
    },
    {
      "jet_kernel_exact": "4*sin(pi*alpha^9)^2",
      "jet_kernel_sample": 0.006828651046705321,
      "label": 34,
      "label_kernel_exact": 1156,
      "m": 9
    },
    {
      "jet_kernel_exact": "4*sin(pi*alpha^10)^2",
      "jet_kernel_sample": 0.002609230688947188,
      "label": 55,
      "label_kernel_exact": 3025,
      "m": 10
    },
    {
      "jet_kernel_exact": "4*sin(pi*alpha^11)^2",
      "jet_kernel_sample": 0.000996771411750865,
      "label": 89,
      "label_kernel_exact": 7921,
      "m": 11
    },
    {
      "jet_kernel_exact": "4*sin(pi*alpha^12)^2",
      "jet_kernel_sample": 0.0003807523481333766,
      "label": 144,
      "label_kernel_exact": 20736,
      "m": 12
    },
    {
      "jet_kernel_exact": "4*sin(pi*alpha^13)^2",
      "jet_kernel_sample": 0.00014543730776571737,
      "label": 233,
      "label_kernel_exact": 54289,
      "m": 13
    },
    {
      "jet_kernel_exact": "4*sin(pi*alpha^14)^2",
      "jet_kernel_sample": 5.555252445088507e-05,
      "label": 377,
      "label_kernel_exact": 142129,
      "m": 14
    },
    {
      "jet_kernel_exact": "4*sin(pi*alpha^15)^2",
      "jet_kernel_sample": 2.1219236890232407e-05,
      "label": 610,
      "label_kernel_exact": 372100,
      "m": 15
    },
    {
      "jet_kernel_exact": "4*sin(pi*alpha^16)^2",
      "jet_kernel_sample": 8.105036134341378e-06,
      "label": 987,
      "label_kernel_exact": 974169,
      "m": 16
    },
    {
      "jet_kernel_exact": "4*sin(pi*alpha^17)^2",
      "jet_kernel_sample": 3.095849615580751e-06,
      "label": 1597,
      "label_kernel_exact": 2550409,
      "m": 17
    },
    {
      "jet_kernel_exact": "4*sin(pi*alpha^18)^2",
      "jet_kernel_sample": 1.1825095176388503e-06,
      "label": 2584,
      "label_kernel_exact": 6677056,
      "m": 18
    }
  ],
  "inverse_character_55": {
    "central_exponent_mod_10": 5,
    "derivative": 1,
    "determinant_exponent_mod_10": 0
  },
  "metric_exact": "dx^2 on R/Z",
  "proof_locators": [
    "GK.2",
    "GK.4",
    "GK.5",
    "GK.6",
    "GK.7",
    "GK.8",
    "GK.9"
  ],
  "schema": "labelled-geometric-kernel-figure/v1",
  "schematic_scope": "GK.4 conditional input; GK.5-GK.7 proved implication; GK.8 actual actions; GK.9 general eligible geometry proved by EG/EK in Section 11AF"
}