Coolout Conjecture
The Coolout Conjecture is a conjecture proposed by Richard Schroeppel before 1992, and disproven by counterexample in 2001.
The conjecture has been stated as
Given a partial Life pattern that's internally consistent with being part of a still life (stable pattern), is there always a way to add a stabilizing boundary?
or alternatively
If a configuration C is locally stable over a rectangle R, then there exists a configuration C* such that (a) C* is locally equal to C over R; and (b) C* is globally stable.
In August 2001, Schroeppel published the following 6x2 pattern as a counterexample to the conjecture:
The row above the top edge must have six consecutive OFF cells; if it does not, the ON cells in the second and fifth columns will turn OFF. However, six consecutive OFF cells prevent the OFF cells in the third and fourth columns from being stabilized: without an ON neighbor above the top row, they will turn ON.