Goe

Some others goe further and alledging or rather indeede abusing some peece of the Scripture[…].

And God ſpake vnto Noah, ſaying, / Goe foorth of the Arke, thou, and thy wife, and thy ſonnes, and thy ſonnes wiues with thee:[…]

With divers kinds of Riddance The smoaking Earth is wet, And all aflowe to seaward goe The Torrents wide of Sweat!

About a year and a half ago, Schroeppel and Hickerson found a bunch of patterns with very small predecessor counts. These are used as modules in existence proofs for GOE's within various rectangles, some quite cozy.

This describes briefly the discovery of the first GOL GOE by Roger Banks, saying: "[he] used sophisticated mathematical techniques to prove that a certain 9-by-33 rectangular pattern is itself a Garden-of-Eden pattern."

As far as I know, even a definite result for the 6x6 case would be progress. The most recent investigation of GoEs that I know about was some interesting work that Donald Knuth recently did in passing for his upcoming Volume 4 of _The Art of Computer Programming_, using binary decision diagrams.