The area threshold is \(A_* := 232240 / 10^6 = 0.232240\). A Moser set with area strictly less than \(A_*\) would improve the current best lower bound.

Three concrete convex polygons are fixed as benchmark worms:

• the isosceles right triangle with legs of length \(1/2\),

• the unit square with side \(1/3\),

• the right triangle with legs \(1/3\) and \(2/3\).

The initial worm is taken to be the isosceles right triangle; by convention every candidate Moser set in the working set contains an un-shifted copy of it. Its area is exactly \(1/8\).

Let \(\sigma := 4 A_*\). The location range is the square \([-\sigma , \sigma ]^2\), which upper-bounds the positions where a point of a working-set polygon may lie without already exceeding the area threshold (via a triangle formed with the initial worm). The distance cutoff is \(\sigma \cdot \overline{\sqrt{2}}\), where \(\overline{\sqrt{2}} = 1414213562373095/10^{15}\) is a rational upper bound on \(\sqrt2\).