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  "universal_bound": 1.2840254166877414,
  "closed_formula_vs_svd_max_error": 3.3306690738754696e-16,
  "exact_formula": "(sqrt(4+(b-c)^2)+b+c)/4, b=exp(-s^2/4-s/2), c=exp(-s^2/4+s/2)",
  "proof": "GRAPH-FRAME-FIGURE.md; numerical checks validate the renderer only"
}