An unconstructable still life in Conway's Game of Life: https://cp4space.hatsya.com/2022/01/14/conway-conjecture-settled/
The configuration shown in the link is stable (if its boundary is stabilized appropriately) but, if it appears in any pattern, it must always have been that way, in all predecessors of the pattern. As such, it answers the question "can every still life be constructed by gliders?" negatively.
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