“At least one of you is red”
They will all assume that they are the red one because they see no other red ones, but since that assumption is wrong, they will not shut down. They will discover that this is a lie and just assume that the intruder is a liar.
Oh good you united the sentient dots in a campaign to rid the universe of lies.
yes, some lie might work, to undo the original message. But to say that one is red poses the risk of all of them shutting down in a second. How can they know that they are not red?
Offer to take several random synths as ambassadors. The collective does not know how many, or of which color, but understands that not only will their common knowledge of other beings grow, their own will be saved.
The death spiral presumes that every synth knows that every other synth correctly heard the external statement about color. It would not be logical for a synth to make such an assumptIon, and they cannot query each other about the content of the statement or propogate that knowledge, because they cannot talk about color.
