A recovering pair is a pair 
of nonempty families of subsets
of the same finite set such that 
implies 
and 
implies 
for every 
and 
. Each member of either family can therefore be recovered
from its set difference with a member of the other
family.
For an 
-element
ground set, Costa (2026) proved
 |
The sandglass conjecture predicts the stronger bound 
.
Costa (2026) states that ChatGPT generated initial versions of the retained proofs
and computational code under his research strategy, and that he independently verified
all retained claims.
