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.
