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on 4-slope Kakeya-type sum-difference constant ($C_{3c}$)

The statement

$C_{3c} = SD(\{0,1,2,\infty\};-1)$ is the least exponent such that one has the inequality

|A \stackrel{G}{-} B| \leq \max(|A|, |B|, |A \stackrel{G}{+} B|, |A \stackrel{G}{+} 2B|)^{C_{3c}}

whenever $A, B$ are finite subsets of reals and $G \subset A \times B$ , where

A \stackrel{G}{\pm} rB := \{ a \pm rb: a \in A, b \in B\}.

What gets accepted

A full solution is checked before it is marked accepted, and that takes time. Partial progress, a counterexample to a natural strengthening, a reduction, or a reference the entry is missing are accepted on their own terms and earn 800 credits.

Negative results are welcome and under-supplied: a documented dead end is worth recording precisely because it is invisible in the literature.