but test said it cant be used ...
The average RCT synth would be a few gliders plus one or multiple ridiculously distant glider(s); it could be used for a 35G of anything but it wouldn’t be used for anything in practice...
Might as well get the technicalities right: it's definitely several ridiculously distant gliders, namely the ones building the Sakapuffer. I think
there are any number of possible starting locations for the glider that's bouncing back and forth between the two locations, basically producing a binary representation of the location of the Sakapuffer.
The GPSEs move at the same speed as the Sakapuffer and have to produce gliders to interact with every glider coming in from the Sakapuffer, so they'll have to start from equally far away, in various different directions. So the gliders constructing the GPSEs will also be ridiculously distant. The only gliders that could start near the eventual construction site would be the ones that build the BLSE elbow-block source (unless there turns out to be a way to use only 33 gliders, and skip the BLSE entirely).
Theory Vs. Practice
The issue that's showing up here is a very old problem, a deep division between mathematician-type people and engineer-type people. Engineers want to see real things actually working:
Here's a specific arrangement of Life cells, and when I run this specific search program on it I see that it's going through all the possible predecessors and none of them work, so it's a Garden of Eden -- beautiful!
Mathematicians are just as happy, or maybe happier, with non-constructive existence proofs:
A Garden of Eden must exist in an 1162907980-by-1162907980 square, so let's just make a big square that's 1162907980 * (2 ^ 676177484973840200) on a side. That pattern has to be a Garden of Eden, and we don't have to care which 1162907980-by-1162907980 squares are actually GoEs, or if there are GoEs smaller than that size -- beautiful!
Early Universality Proofs Were Like That
This is pretty much what Conway and Gosper did in their original 1970s-era proofs of the existence of universal constructors in Life. They never had any particular interest in actually building specific examples of self-replicating B3/S23 patterns, since they would have been far too big and complex to ever run through a full replication cycle. Those proofs were non-constructive existence proofs, but that was perfectly fine as far as they were concerned.
Then various unreasonable engineer-type people came along later and figured out how to build specific examples of self-constructing patterns. The engineers were much happier after that, but mathematicians like Conway were just puzzled: "yeah, we knew that was possible forty years ago -- why are you wasting time on this trivial stuff?"
RCT Recipes Are Actually Within Reach
The RCT mechanism is in a somewhat similar state at the moment, and a lot of people are reasonably contented to leave it like that.
However, probably if someone wanted to spend a few years on the problem, it would be possible to construct all the specific mechanisms needed to create an RCT recipe for a pulsar or loafer or spider or whatever.
And then if someone wrote a very customized RCT simulator program, and fed in a description of the locations of the 35 gliders, it would be possible to watch the whole construction process run to completion. The simulator would have to take a lot of special-purpose shortcuts -- e.g., just store start and end locations for debris chains, and don't bother tracking the position of each piece of junk; just fast-forward umpteen bajillion ticks and say "okay, that chain is all cleaned up".
Maybe that seems like cheating, but it's not really so different from what HashLife does today. We can prove that HashLife works, and we could also prove that our custom simulator doesn't take any illegal shortcuts.