Let $ A $ be an additive set of non-zero integers. Then A contains a sum free-free subset of size $ |B|> \frac{|A|}{3} $ ( a result of erdos). It is conjectured that RHS can be improved to $\frac{|A|}{3} +10$  .Is there any evidence/heuristic justification for this conjectured bound.

Let $ A $ be a set of non-zero integers. Then $A$ contains a sum-free subset $B$ of size $ |B|> \frac{|A|}{3} $ (a result of Erdős). It is conjectured that RHS can be improved to $\frac{|A|}{3} +10$. Is there any evidence/heuristic justification for this conjectured bound?

(A set $B$ is sum-free if it contains no solution to $x+y=z$.)

Let $ A $ be an additive set of non-zero integers. Then A contains a sum free-free subset of size $ |B|> |A|/3 $ ( a result of erdos). It is conjectured that RHS can be improved to $|A|/3 +10$ .Is there any evidence/heuristic justification for this conjectured bound.

Let $ A $ be an additive set of non-zero integers. Then A contains a sum free-free subset of size $ |B|> \frac{|A|}{3} $ ( a result of erdos). It is conjectured that RHS can be improved to $\frac{|A|}{3} +10$ .Is there any evidence/heuristic justification for this conjectured bound.