whatA silo draining through a hole in its floor, grains recirculating to the top so the experiment never ends. Some grains, poised over a void with both shoulders supported, freeze into bridges -- drawn as open rings. Chains of bridges anchored on the lips of the hole are arches.

whyThe claim is the grain-elevator engineer's nightmare, measured: arch formation is stochastic, but whether an arch can SPAN the hole depends on the mouth. Below about five grain-diameters the jam rate explodes -- watch the flow trace flatline as rings lock across the orifice -- while a wide mouth almost never jams. The jam ledger counts jams per thousand steps at every width you try and prints the map; the knee in that map is the claim. When it jams, tap (click): the arch shatters and the flow resumes as if nothing happened.

howGrains fall straight or topple diagonally; a grain over a void whose two diagonal neighbours are full freezes with probability 0.35 and unfreezes when a support vanishes (plus a whisper of creep). Over the hole itself, freezing is lip-nucleated: only the lip or an already-frozen neighbour anchors a new arch cell, so arches must grow inward from the lips, their exposed tip racing erosion -- and a standing arch fractures at a rate that grows steeply with its span, leaking grains through the cracks -- narrow arches seal, wide ones cannot hold. A tap shatters every bridge near the mouth and briefly fluidizes it. Jam means nothing has exited for 150 steps while grain waits above the mouth -- a declared threshold. Exits respawn at the top.