{
  "finite_projection": [
    1,
    1,
    0
  ],
  "finite_operator_eigenvalues": [
    1,
    4
  ],
  "infinite_projection": [
    0,
    0,
    1
  ],
  "cutoff_diagonal": "[1,min(4,n),n] for integers n>=1",
  "vector_path": "cos(theta)e1+sin(theta)e3, 0<=theta<=pi/2",
  "vector_cutoff": "cos(theta)^2+n sin(theta)^2",
  "functional_path": "(1-delta)omega_e2+delta omega_e3",
  "functional_cutoff": "4(1-delta)+n delta for n>=4",
  "complete_proof": "EXTENDED-POSITIVE-FIGURE.md",
  "scope": "All formulas exact; finite set of plotted cutoffs only illustrates the proved increasing limit."
}