{
  "kind": "Algebraic diagrams; no geometric scale.",
  "panel_A": {
    "alpha": "x -> (lambda_j xi_j(x))",
    "beta": "(b_j) -> sum b_j y_j",
    "v": "beta alpha",
    "w": "alpha beta",
    "cokernels": "Algebraic inverse maps induced by alpha,beta",
    "proof": "NP.12--NP.15"
  },
  "panel_B": {
    "lambda_j": "2^(1-j),j>=1",
    "tail_after_two_operator_norm": "1/4",
    "tail_after_two_coefficient_weight": "1/2",
    "cokernel": "B via first coordinate",
    "proof": "NP.32--NP.33"
  },
  "panel_C": {
    "R": [
      2,
      3
    ],
    "r": [
      1,
      1
    ],
    "total_weight": "3",
    "box_bound": 2,
    "box_weight": "91/36",
    "tail_weight": "17/36",
    "proof": "NP.28--NP.31 and NP.34"
  },
  "no_closed_range_or_Hausdorff_quotient_inferred_from_finiteness": true
}