{
  "license": "CC0-1.0 to the extent of rights held; font terms separate",
  "group": "Z/2Z",
  "original_Haar_singleton_mass": 1,
  "dual_Haar_singleton_mass": "1/2",
  "coordinate_order_input": [
    "e1",
    "e2"
  ],
  "coordinate_order_crossed_chart": [
    "(+,e1)",
    "(+,e2)",
    "(-,e1)",
    "(-,e2)"
  ],
  "V": [
    [
      "0",
      "1"
    ],
    [
      "1",
      "0"
    ]
  ],
  "input_support_p": [
    [
      "1",
      "0"
    ],
    [
      "0",
      "0"
    ]
  ],
  "moved_support_q": [
    [
      "0",
      "0"
    ],
    [
      "0",
      "1"
    ]
  ],
  "input_weight": "psi(a)=a11",
  "original_action": "alpha_1(a)=V a V",
  "original_support_image": [
    [
      "0",
      "0"
    ],
    [
      "0",
      "1"
    ]
  ],
  "pi_chart": "pi(a)=(a,a)",
  "lambda_chart": "(V,-V)",
  "dual_action": "theta_1(A,B)=(B,A)",
  "dual_weight": "Dpsi(A,B)=(A11+B11)/2",
  "dual_density": [
    [
      "1/2",
      "0",
      "0",
      "0"
    ],
    [
      "0",
      "0",
      "0",
      "0"
    ],
    [
      "0",
      "0",
      "1/2",
      "0"
    ],
    [
      "0",
      "0",
      "0",
      "0"
    ]
  ],
  "dual_support": [
    [
      "1",
      "0",
      "0",
      "0"
    ],
    [
      "0",
      "0",
      "0",
      "0"
    ],
    [
      "0",
      "0",
      "1",
      "0"
    ],
    [
      "0",
      "0",
      "0",
      "0"
    ]
  ],
  "dual_support_image": [
    [
      "1",
      "0",
      "0",
      "0"
    ],
    [
      "0",
      "0",
      "0",
      "0"
    ],
    [
      "0",
      "0",
      "1",
      "0"
    ],
    [
      "0",
      "0",
      "0",
      "0"
    ]
  ],
  "values": {
    "psi(p)": "1",
    "psi(q)": "0",
    "Dpsi(p,0)": "1/2",
    "Dpsi(0,p)": "1/2",
    "Dpsi(1,1)": "1"
  },
  "regular_chart_unitary": [
    [
      "sqrt(2)/2",
      "0",
      "0",
      "sqrt(2)/2"
    ],
    [
      "0",
      "sqrt(2)/2",
      "sqrt(2)/2",
      "0"
    ],
    [
      "sqrt(2)/2",
      "0",
      "0",
      "-sqrt(2)/2"
    ],
    [
      "0",
      "sqrt(2)/2",
      "-sqrt(2)/2",
      "0"
    ]
  ],
  "checks": {
    "unitary": true,
    "pi_conjugation": true,
    "lambda_conjugation": true,
    "moved_original_support": true,
    "fixed_dual_support": true,
    "positive_half_values": true
  },
  "proof_locators": [
    "OA-FLOW-L32.md#l32-5",
    "L32.5.a",
    "L32.5.b",
    "L32.5.c",
    "L32.5.d",
    "L32.5.e"
  ],
  "figure_kind": "Exact two-dimensional matrix-coordinate diagram; no approximation",
  "native_png_pixels": [
    2400,
    1639
  ]
}