{
  "title": "Hilbert graded core: exact coordinate models",
  "license": "CC0-1.0 to the extent of rights held; font terms separate",
  "scalar": {
    "transform": "Fhat(q)=integral exp(-i*q*s) F(s) ds",
    "domain_measure": "ds",
    "target_measure": "dq/(2*pi)",
    "translation": "lambda_t F(s)=F(s-t)",
    "generator_image": "exp(-i*t*q)",
    "density": "exp(-q)",
    "dual": "theta_r f(q)=f(q+r)",
    "trace_density": "exp(q)/(2*pi)",
    "projection_support": [
      0,
      1
    ],
    "r": "log(2)",
    "translated_support": [
      "-log(2)",
      "1-log(2)"
    ],
    "trace": "(e-1)/(2*pi)",
    "trace_ratio": "1/2"
  },
  "matrix": {
    "h": [
      [
        3,
        0
      ],
      [
        0,
        1
      ]
    ],
    "k": [
      [
        2,
        1
      ],
      [
        1,
        2
      ]
    ],
    "t_star": "pi/(2*log(3))",
    "spatial": "D^it xi=h^it xi k^-it",
    "2p_plus": [
      [
        "1",
        "-i"
      ],
      [
        "i",
        "1"
      ]
    ],
    "2p_minus": [
      [
        "1",
        "i"
      ],
      [
        "-i",
        "1"
      ]
    ],
    "2z": [
      [
        "1+i",
        "1-i"
      ],
      [
        "0",
        "0"
      ]
    ],
    "identities": [
      "z*p_plus=z",
      "z*p_minus=0",
      "norm_HS(z)=1"
    ]
  },
  "square": {
    "source_degrees": [
      "0",
      "r"
    ],
    "target_degrees": [
      "t",
      "r+t"
    ],
    "r": "t_star",
    "A0": "R_e11",
    "B0": "R_p_plus",
    "horizontal": "L_x D^ir",
    "identity": "B0 L_x D^ir = L_x D^ir A0 for every x in M2"
  },
  "phase": {
    "S": [
      [
        0,
        1
      ],
      [
        1,
        0
      ]
    ],
    "U": "xi -> S xi S",
    "inputs": "e11",
    "outputs": [
      "e22",
      "i e22"
    ],
    "distance": "sqrt(2)",
    "plane": "exact complex line C e22",
    "second_iterates": [
      "I",
      "-I"
    ]
  },
  "proof_locators": [
    "HLB9.b-d",
    "HLB9.j-k",
    "HLB9.n",
    "HLB10.b-e"
  ],
  "sampling": "None. The displayed objects and labels are exact; only page positions are drawing coordinates."
}