{
  "base_Hilbert_space_arbitrary": true,
  "grid_is_finite_window": true,
  "input_coordinate": [
    1,
    3
  ],
  "output_coordinate": [
    3,
    1
  ],
  "entry_map": "xi_13 -> S_psi xi_13",
  "complete_operator": "(T xi)_ij=S_psi xi_ji",
  "graph_norm": "sum_ij(||xi_ij||^2+||S_psi xi_ij||^2)",
  "cutoff_order": [
    "finite square F x F",
    "then finite base graph approximants"
  ],
  "filling_example_algebra": "B(ell2(N0)), type I infinity",
  "bijection": "b(j,m)=2^j(2m+1)-1",
  "displayed_table": [
    [
      0,
      2,
      4,
      6
    ],
    [
      1,
      5,
      9,
      13
    ],
    [
      3,
      11,
      19,
      27
    ],
    [
      7,
      23,
      39,
      55
    ]
  ],
  "exact_inverse_sample": [
    {
      "n": 0,
      "j": 0,
      "m": 0
    },
    {
      "n": 1,
      "j": 1,
      "m": 0
    },
    {
      "n": 2,
      "j": 0,
      "m": 1
    },
    {
      "n": 3,
      "j": 2,
      "m": 0
    },
    {
      "n": 4,
      "j": 0,
      "m": 2
    },
    {
      "n": 5,
      "j": 1,
      "m": 1
    },
    {
      "n": 6,
      "j": 0,
      "m": 3
    },
    {
      "n": 7,
      "j": 3,
      "m": 0
    },
    {
      "n": 8,
      "j": 0,
      "m": 4
    },
    {
      "n": 9,
      "j": 1,
      "m": 2
    },
    {
      "n": 10,
      "j": 0,
      "m": 5
    },
    {
      "n": 11,
      "j": 2,
      "m": 1
    },
    {
      "n": 12,
      "j": 0,
      "m": 6
    },
    {
      "n": 13,
      "j": 1,
      "m": 3
    },
    {
      "n": 14,
      "j": 0,
      "m": 7
    },
    {
      "n": 15,
      "j": 4,
      "m": 0
    },
    {
      "n": 16,
      "j": 0,
      "m": 8
    },
    {
      "n": 17,
      "j": 1,
      "m": 4
    },
    {
      "n": 18,
      "j": 0,
      "m": 9
    },
    {
      "n": 19,
      "j": 2,
      "m": 2
    },
    {
      "n": 20,
      "j": 0,
      "m": 10
    },
    {
      "n": 21,
      "j": 1,
      "m": 5
    },
    {
      "n": 22,
      "j": 0,
      "m": 11
    },
    {
      "n": 23,
      "j": 3,
      "m": 1
    },
    {
      "n": 24,
      "j": 0,
      "m": 12
    },
    {
      "n": 25,
      "j": 1,
      "m": 6
    },
    {
      "n": 26,
      "j": 0,
      "m": 13
    },
    {
      "n": 27,
      "j": 2,
      "m": 3
    },
    {
      "n": 28,
      "j": 0,
      "m": 14
    },
    {
      "n": 29,
      "j": 1,
      "m": 7
    },
    {
      "n": 30,
      "j": 0,
      "m": 15
    },
    {
      "n": 31,
      "j": 5,
      "m": 0
    },
    {
      "n": 32,
      "j": 0,
      "m": 16
    },
    {
      "n": 33,
      "j": 1,
      "m": 8
    },
    {
      "n": 34,
      "j": 0,
      "m": 17
    },
    {
      "n": 35,
      "j": 2,
      "m": 4
    },
    {
      "n": 36,
      "j": 0,
      "m": 18
    },
    {
      "n": 37,
      "j": 1,
      "m": 9
    },
    {
      "n": 38,
      "j": 0,
      "m": 19
    },
    {
      "n": 39,
      "j": 3,
      "m": 2
    },
    {
      "n": 40,
      "j": 0,
      "m": 20
    },
    {
      "n": 41,
      "j": 1,
      "m": 10
    },
    {
      "n": 42,
      "j": 0,
      "m": 21
    },
    {
      "n": 43,
      "j": 2,
      "m": 5
    },
    {
      "n": 44,
      "j": 0,
      "m": 22
    },
    {
      "n": 45,
      "j": 1,
      "m": 11
    },
    {
      "n": 46,
      "j": 0,
      "m": 23
    },
    {
      "n": 47,
      "j": 4,
      "m": 1
    },
    {
      "n": 48,
      "j": 0,
      "m": 24
    },
    {
      "n": 49,
      "j": 1,
      "m": 12
    },
    {
      "n": 50,
      "j": 0,
      "m": 25
    },
    {
      "n": 51,
      "j": 2,
      "m": 6
    },
    {
      "n": 52,
      "j": 0,
      "m": 26
    },
    {
      "n": 53,
      "j": 1,
      "m": 13
    },
    {
      "n": 54,
      "j": 0,
      "m": 27
    },
    {
      "n": 55,
      "j": 3,
      "m": 3
    },
    {
      "n": 56,
      "j": 0,
      "m": 28
    },
    {
      "n": 57,
      "j": 1,
      "m": 14
    },
    {
      "n": 58,
      "j": 0,
      "m": 29
    },
    {
      "n": 59,
      "j": 2,
      "m": 7
    },
    {
      "n": 60,
      "j": 0,
      "m": 30
    },
    {
      "n": 61,
      "j": 1,
      "m": 15
    },
    {
      "n": 62,
      "j": 0,
      "m": 31
    },
    {
      "n": 63,
      "j": 6,
      "m": 0
    },
    {
      "n": 64,
      "j": 0,
      "m": 32
    },
    {
      "n": 65,
      "j": 1,
      "m": 16
    },
    {
      "n": 66,
      "j": 0,
      "m": 33
    },
    {
      "n": 67,
      "j": 2,
      "m": 8
    },
    {
      "n": 68,
      "j": 0,
      "m": 34
    },
    {
      "n": 69,
      "j": 1,
      "m": 17
    },
    {
      "n": 70,
      "j": 0,
      "m": 35
    },
    {
      "n": 71,
      "j": 3,
      "m": 4
    },
    {
      "n": 72,
      "j": 0,
      "m": 36
    },
    {
      "n": 73,
      "j": 1,
      "m": 18
    },
    {
      "n": 74,
      "j": 0,
      "m": 37
    },
    {
      "n": 75,
      "j": 2,
      "m": 9
    },
    {
      "n": 76,
      "j": 0,
      "m": 38
    },
    {
      "n": 77,
      "j": 1,
      "m": 19
    },
    {
      "n": 78,
      "j": 0,
      "m": 39
    },
    {
      "n": 79,
      "j": 4,
      "m": 2
    },
    {
      "n": 80,
      "j": 0,
      "m": 40
    },
    {
      "n": 81,
      "j": 1,
      "m": 20
    },
    {
      "n": 82,
      "j": 0,
      "m": 41
    },
    {
      "n": 83,
      "j": 2,
      "m": 10
    },
    {
      "n": 84,
      "j": 0,
      "m": 42
    },
    {
      "n": 85,
      "j": 1,
      "m": 21
    },
    {
      "n": 86,
      "j": 0,
      "m": 43
    },
    {
      "n": 87,
      "j": 3,
      "m": 5
    },
    {
      "n": 88,
      "j": 0,
      "m": 44
    },
    {
      "n": 89,
      "j": 1,
      "m": 22
    },
    {
      "n": 90,
      "j": 0,
      "m": 45
    },
    {
      "n": 91,
      "j": 2,
      "m": 11
    },
    {
      "n": 92,
      "j": 0,
      "m": 46
    },
    {
      "n": 93,
      "j": 1,
      "m": 23
    },
    {
      "n": 94,
      "j": 0,
      "m": 47
    },
    {
      "n": 95,
      "j": 5,
      "m": 1
    },
    {
      "n": 96,
      "j": 0,
      "m": 48
    },
    {
      "n": 97,
      "j": 1,
      "m": 24
    },
    {
      "n": 98,
      "j": 0,
      "m": 49
    },
    {
      "n": 99,
      "j": 2,
      "m": 12
    },
    {
      "n": 100,
      "j": 0,
      "m": 50
    },
    {
      "n": 101,
      "j": 1,
      "m": 25
    },
    {
      "n": 102,
      "j": 0,
      "m": 51
    },
    {
      "n": 103,
      "j": 3,
      "m": 6
    },
    {
      "n": 104,
      "j": 0,
      "m": 52
    },
    {
      "n": 105,
      "j": 1,
      "m": 26
    },
    {
      "n": 106,
      "j": 0,
      "m": 53
    },
    {
      "n": 107,
      "j": 2,
      "m": 13
    },
    {
      "n": 108,
      "j": 0,
      "m": 54
    },
    {
      "n": 109,
      "j": 1,
      "m": 27
    },
    {
      "n": 110,
      "j": 0,
      "m": 55
    },
    {
      "n": 111,
      "j": 4,
      "m": 3
    },
    {
      "n": 112,
      "j": 0,
      "m": 56
    },
    {
      "n": 113,
      "j": 1,
      "m": 28
    },
    {
      "n": 114,
      "j": 0,
      "m": 57
    },
    {
      "n": 115,
      "j": 2,
      "m": 14
    },
    {
      "n": 116,
      "j": 0,
      "m": 58
    },
    {
      "n": 117,
      "j": 1,
      "m": 29
    },
    {
      "n": 118,
      "j": 0,
      "m": 59
    },
    {
      "n": 119,
      "j": 3,
      "m": 7
    },
    {
      "n": 120,
      "j": 0,
      "m": 60
    },
    {
      "n": 121,
      "j": 1,
      "m": 30
    },
    {
      "n": 122,
      "j": 0,
      "m": 61
    },
    {
      "n": 123,
      "j": 2,
      "m": 15
    },
    {
      "n": 124,
      "j": 0,
      "m": 62
    },
    {
      "n": 125,
      "j": 1,
      "m": 31
    },
    {
      "n": 126,
      "j": 0,
      "m": 63
    },
    {
      "n": 127,
      "j": 7,
      "m": 0
    }
  ],
  "finite_sample_is_not_proof": "The complete bijection is proved in the caption.",
  "proof_locators": [
    "ca-2",
    "ca-3",
    "ca-4",
    "ca-6"
  ]
}