whatA dry two-dimensional foam: walls under tension, gas leaking across them, the whole structure driven by curvature alone. Cells die their T2 deaths, walls trade neighbours, and the census thins while the survivors swell.

whyThe claim is von Neumann's astonishing law, measured cell by cell: a bubble's fate depends on nothing but its number of sides. Fewer than six and it shrinks; more than six and it grows; exactly six holds its breath. No size, no shape, no position -- just the count. The ledger snapshots every cell's area and side count as the foam coarsens, bins growth by n, and fits the line: dA proportional to (n minus 6), correlation printed beside it. Meanwhile the census halves, and halves again. Click any bubble to pop it by hand and gift its gas to the biggest neighbour.

howCurvature flow via a cool boundary anneal on a fine lattice (T 0.35): boundary sites adopt a neighbouring cell's identity when energy allows, which is exactly how walls drift by curvature; the lattice's own rearrangements play the T1s, vanishing cells are counted as T2 deaths. Snapshots every 30 sweeps; dying cells' final interval is excluded from the fit and declared. The double-struck walls are the film and its shadow.