{
  "title": "Tensor weights: exact blocks, Haar normalization and graph domains",
  "license": "CC0-1.0 to the extent of rights held; DejaVu font terms retained separately",
  "coefficient_density": [
    2,
    5
  ],
  "outer_inner_basis_order": [
    "(1,1)",
    "(1,2)",
    "(2,1)",
    "(2,2)",
    "(3,1)",
    "(3,2)"
  ],
  "operator_matrix_X": [
    [
      1,
      0,
      0,
      1,
      0,
      0
    ],
    [
      0,
      0,
      0,
      0,
      0,
      0
    ],
    [
      0,
      0,
      0,
      0,
      0,
      0
    ],
    [
      2,
      0,
      0,
      0,
      0,
      0
    ],
    [
      0,
      0,
      0,
      0,
      1,
      0
    ],
    [
      0,
      0,
      0,
      0,
      0,
      1
    ]
  ],
  "six_dimensional_density": [
    2,
    5,
    2,
    5,
    2,
    5
  ],
  "block_squared_gns_norms_row_major": [
    2,
    5,
    0,
    8,
    0,
    0,
    0,
    0,
    7
  ],
  "block_adjoint_squared_gns_norms_row_major": [
    2,
    2,
    0,
    20,
    0,
    0,
    0,
    0,
    7
  ],
  "Omega_XstarX": 22,
  "Omega_XXstar": 31,
  "old_diagonal_weight_contributions": [
    "10",
    "5",
    "7"
  ],
  "new_diagonal_weight_contributions": [
    "15/2",
    "15/2",
    "7"
  ],
  "haar_singleton_mass": "2",
  "kernel_K": [
    [
      "1/2",
      "0",
      "0",
      "1/2",
      "0",
      "0"
    ],
    [
      "0",
      "0",
      "0",
      "0",
      "0",
      "0"
    ],
    [
      "0",
      "0",
      "0",
      "0",
      "0",
      "0"
    ],
    [
      "1",
      "0",
      "0",
      "0",
      "0",
      "0"
    ],
    [
      "0",
      "0",
      "0",
      "0",
      "1/2",
      "0"
    ],
    [
      "0",
      "0",
      "0",
      "0",
      "0",
      "1/2"
    ]
  ],
  "normalized_kernel_operator_rule": "X_rs = c K(r,s)",
  "weighted_kernel_squared_norm": "22",
  "rank_one_projection_kernel_nonzero_entry": "1/2",
  "rank_one_projection_usual_trace": 1,
  "graph_example": {
    "weight": "phi(a)=sum_{n>=0}4^n <a e_n,e_n>",
    "orthonormal_GNS_basis": "f_mn=2^(-n) Lambda(e_mn)",
    "half_power_on_basis": "Delta^(1/2) f_mn = 2^(m-n) f_mn",
    "vector": "xi=sum_{n>=1}2^(-n) f_n0",
    "partial_indices": [
      1,
      2,
      3,
      4,
      5,
      6
    ],
    "partial_squared_norms": [
      "1/4",
      "5/16",
      "21/64",
      "85/256",
      "341/1024",
      "1365/4096"
    ],
    "partial_squared_half_power_norms": [
      "1",
      "2",
      "3",
      "4",
      "5",
      "6"
    ],
    "limit_squared_norm": "1/3",
    "limit_in_half_power_domain": false
  },
  "nonseparable_scope": {
    "E": "ell^2(I), I arbitrary uncountable",
    "Omega_1_tensor_pF": "7 |F|",
    "indexing": "all finite subsets F of I ordered by inclusion",
    "no_sequence_exhaustion_claim": true
  },
  "proof_locators": [
    "OA-FLOW-TW.html#tw-matrix-model",
    "OA-FLOW-TW.html#tw-basis-diagnostic",
    "OA-FLOW-TW.html#tw-haar-diagnostic",
    "OA-FLOW-TW.html#tw-domain-diagnostic"
  ],
  "human_antecedent": {
    "work": "Takesaki, Theory of Operator Algebras II",
    "locator": "VIII.4, Lemma4.1, Definition4.2, Proposition4.3, printed133-134",
    "url": "https://doi.org/10.1007/978-3-662-10451-4",
    "relationship": "Tensor-weight theorem context; example and artwork are original"
  }
}