{
 "variant": "triangle",
 "n": 5,
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 "caption": "One 1-parameter slice of the optimal set: point 1 slides along the hypotenuse, (1 \u2212 x, x) for x \u2208 [2 \u2212 \u221a2, 1/\u221a2] (right-frame coordinates; the stored member is the x = 2 \u2212 \u221a2 endpoint). Its motion is parallel to the segment through points 3 and 4, so the tied triangle (1,3,4) keeps its area; the released triangle (1,2,4) grows. Every member achieves exactly A = 3 \u2212 2\u221a2.",
 "verification": "each sample's 30-decimal literals verified in exact arithmetic to within relative 1e-20 of the stored configuration's exact value at build time"
}