{
  "kind": "original mathematical diagram and rigorously bounded real sample",
  "panels": {
    "A": {
      "proof": "RF.A; RF.7--RF.9",
      "rings": [
        "D",
        "E",
        "Ehat"
      ],
      "formal_correcting_series_declared_actual": false,
      "descent": "exact faithful normal completion on finite actual E-modules"
    },
    "B": {
      "proof": "RF.C; RF.17--RF.20",
      "lambda": {
        "numerator": 2,
        "denominator": 5
      },
      "operator": "sum_{n>=0} n! D_t^{-n}",
      "input": "t^(2/5)",
      "coefficient": "a_n=n! / product_{s=1}^n(s+2/5)",
      "recurrence": "a_0=1; a_n=a_(n-1)*5*n/(5*n+2)",
      "exact_coefficients": [
        {
          "n": 0,
          "numerator": "1",
          "denominator": "1"
        },
        {
          "n": 1,
          "numerator": "5",
          "denominator": "7"
        },
        {
          "n": 2,
          "numerator": "25",
          "denominator": "42"
        },
        {
          "n": 3,
          "numerator": "125",
          "denominator": "238"
        },
        {
          "n": 4,
          "numerator": "625",
          "denominator": "1309"
        },
        {
          "n": 5,
          "numerator": "15625",
          "denominator": "35343"
        },
        {
          "n": 6,
          "numerator": "78125",
          "denominator": "188496"
        },
        {
          "n": 7,
          "numerator": "390625",
          "denominator": "996336"
        },
        {
          "n": 8,
          "numerator": "1953125",
          "denominator": "5230764"
        },
        {
          "n": 9,
          "numerator": "9765625",
          "denominator": "27316212"
        },
        {
          "n": 10,
          "numerator": "244140625",
          "denominator": "710221512"
        },
        {
          "n": 11,
          "numerator": "1220703125",
          "denominator": "3680238744"
        },
        {
          "n": 12,
          "numerator": "6103515625",
          "denominator": "19014566844"
        },
        {
          "n": 13,
          "numerator": "30517578125",
          "denominator": "97998152196"
        },
        {
          "n": 14,
          "numerator": "152587890625",
          "denominator": "503990497008"
        },
        {
          "n": 15,
          "numerator": "3814697265625",
          "denominator": "12935756089872"
        },
        {
          "n": 16,
          "numerator": "19073486328125",
          "denominator": "66295749960594"
        },
        {
          "n": 17,
          "numerator": "95367431640625",
          "denominator": "339278249798334"
        },
        {
          "n": 18,
          "numerator": "476837158203125",
          "denominator": "1734088832302596"
        },
        {
          "n": 19,
          "numerator": "2384185791015625",
          "denominator": "8852979828071148"
        },
        {
          "n": 20,
          "numerator": "59604644775390625",
          "denominator": "225750985615814274"
        },
        {
          "n": 21,
          "numerator": "298023223876953125",
          "denominator": "1150255021947244158"
        },
        {
          "n": 22,
          "numerator": "1490116119384765625",
          "denominator": "5855843748095061168"
        },
        {
          "n": 23,
          "numerator": "7450580596923828125",
          "denominator": "29788422544657485072"
        },
        {
          "n": 24,
          "numerator": "37252902984619140625",
          "denominator": "151424481268675549116"
        }
      ],
      "plotted_terms": 200,
      "largest_plotted_index": 199,
      "domain": {
        "real_min_exclusive": 0,
        "real_max_numerator": 3,
        "real_max_denominator": 4
      },
      "coefficient_bound": "0<a_n<=1",
      "tail_bound": "0<=P f-S_N<=t^(2/5)*t^(N+1)/(1-t), 0<t<1",
      "plotted_sum_tail_bound": "t^(2/5)*t^200/(1-t)",
      "plot_is_a_real_sample_of_a_complex_multivalued_function": true
    },
    "C": {
      "proof": "RF.H; RF.28--RF.33",
      "identity": "phi*mu=E tensor_D e_prime",
      "mu": "P tensor u maps to P*u",
      "finite_flatness_used": true,
      "mixed_E_infinity_over_D_infinity_flatness_used": false
    }
  },
  "geometry_scale": "panels A and C are algebraic diagrams with no geometric scale",
  "sources": [
    "https://www.kurims.kyoto-u.ac.jp/~kenkyubu/kashiwara/HolIII.pdf"
  ]
}