{
  "title": "Countable orbit algebras: exact S3 and weighted integer examples",
  "license": "CC0-1.0 to the extent of rights held; font terms separate",
  "finite": {
    "X": [
      1,
      2,
      3
    ],
    "group": "S3",
    "action": "g.x = g(x)",
    "masses": [
      1,
      2,
      4
    ],
    "stabilizer_at_1": [
      "identity",
      "(23)"
    ],
    "cosets_reaching_1": [
      "identity",
      "(23)"
    ],
    "cosets_reaching_2": [
      "(12)",
      "(123)"
    ],
    "cosets_reaching_3": [
      "(13)",
      "(132)"
    ],
    "fiber_dimension": 3,
    "relation_pairs": 9,
    "right_counting": [
      [
        1,
        2,
        4
      ],
      [
        1,
        2,
        4
      ],
      [
        1,
        2,
        4
      ]
    ],
    "left_counting": [
      [
        1,
        1,
        1
      ],
      [
        2,
        2,
        2
      ],
      [
        4,
        4,
        4
      ]
    ],
    "delta": [
      [
        "1",
        "1/2",
        "1/4"
      ],
      [
        "2",
        "1",
        "1/2"
      ],
      [
        "4",
        "2",
        "1"
      ]
    ],
    "right_total": 21,
    "left_total": 21,
    "wrong_group_counting_total": 42,
    "matrix_algebra": "M3(C), acting on the left",
    "expectation": "diag(A11,A22,A33)",
    "weight": "Tr(diag(1,2,4) A)",
    "weight_identity": 7,
    "norm_Lambda_e12_squared": 2,
    "norm_S_Lambda_e12_squared": 1,
    "delta_e12": "1/2",
    "t_star": "pi/(2*log(2))",
    "sigma_tstar_e12": "-i e12",
    "coordinates": "row y; column x"
  },
  "infinite": {
    "X": "Z",
    "group": "Z",
    "action": "m.x=x+m",
    "mass": "mu_x=2^x",
    "delta": "2^(y-x)",
    "vector": "xi(n,0)=2^-n for n>=1, zero elsewhere",
    "sampled_indices": [
      1,
      2,
      3,
      4,
      5,
      6,
      7,
      8
    ],
    "sampled_H_norm_terms": [
      "1/4",
      "1/16",
      "1/64",
      "1/256",
      "1/1024",
      "1/4096",
      "1/16384",
      "1/65536"
    ],
    "sampled_S_norm_terms": [
      "1/2",
      "1/4",
      "1/8",
      "1/16",
      "1/32",
      "1/64",
      "1/128",
      "1/256"
    ],
    "sampled_Delta_norm_terms": [
      1,
      1,
      1,
      1,
      1,
      1,
      1,
      1
    ],
    "full_sums": [
      "1/3",
      "1",
      "infinity"
    ],
    "graph_norm_tail_squared": "4^-N/3+2^-N",
    "Delta_truncation_norm_squared": "N",
    "sampling_notice": "Only n=1,...,8 is plotted. Full convergence and divergence follow from the exact infinite series proved in REL7.i-j."
  },
  "proof_locators": [
    "REL6.a-j",
    "REL6.k-t",
    "REL7.a-c",
    "REL7.h-j"
  ]
}