Erdős's conjecture on Sidon bases of order 3

A sequence of positive integers is a Sidon sequence if all sums $a+a'$ with $a,a'$ in the sequence and $a\leq a'$ are distinct; it is an asymptotic basis of order $g$ if every sufficiently large positive integer is a sum of $g$ elements of the sequence. Erdős's conjecture. There exists a sequence of positive integers that is a Sidon basis of order $3$. This is an open problem in additive number theory. The paper proves polynomial-ring analogues over finite fields, but does not resolve the integer conjecture.