{
  "schema": "compact-frame-quotient-figure/v1",
  "license": "CC0",
  "toy": {
    "K": "S1",
    "P": "S1",
    "T": "point",
    "Y_H": "P",
    "E_H": "P times C (complexification)",
    "Theta_H": 2,
    "quotient_E": "C",
    "quotient_inverse_rank": 1,
    "averaged_E": "L2(S1) times C",
    "averaged_inverse": "one-half identity, noncompact"
  },
  "exact_checks": {
    "quotient_inverse_rank_one": true,
    "fourier_image_squared_norm": true,
    "theta_positive": true
  },
  "circle_samples": 513,
  "circle_exact_formula": "u(theta)=(cos(theta),sin(theta)); theta marker pi/3",
  "text_canvas_overflows": [],
  "font_sha256": "3fdf69cabf06049ea70a00b5919340e2ce1e6d02b0cc3c4b44fb6801bd1e0d22",
  "font_source": "Shared unchanged DejaVuSans.ttf; full font and notice embedded in the SVG",
  "proof_locators": [
    "IJ.1-IJ.7",
    "FD.7"
  ],
  "human_source_context": "Connes, A survey of foliations and operator algebras (1982), the graph-operator problem; the intrinsic field and quotient proofs are IJ.1\u2013IJ.7",
  "normal_weight_derivative_proved": false,
  "physical_graph_operator_constructed": false
}