{"id":"palomar/PALOMAR-2026-10-27-000023","url":"https://github.com/jfairfaxball-348/Almost-Stacked-Proof/tree/358729c65c198db3a6a6973c666d3d9de4009bb7","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-10-27-000023-v1.json","repo":"https://github.com/jfairfaxball-348/Almost-Stacked-Proof","tags":["math.CO","msc:05C57","msc:05C85"],"score":0,"title":"The critical Almost Stacked Hypothesis fails on a nine-vertex graph","trust":"high","domain":"math.CO","source":"palomar","authors":["John Fairfax-Ball"],"reviews":0,"subject":"math.CO","summary":"In graph pebbling, a move removes two pebbles from a vertex and adds one to a neighbour; a configuration is stackable if moves can bring all pebbles onto one vertex and clearable if moves can leave exactly one pebble. The stacking (clearing) number of a connected (connected non-bipartite) graph is the least t >= 2 such that every configuration of t pebbles is stackable (clearable). The Almost Stacked Hypothesis, in its critical form, says that this number equals the least t0 >= 2 such that every almost stacked configuration (one vertex arbitrary, every other vertex at most one pebble) of…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-10-27","reactions":{},"formalized":true}