Relationship between the 3SUM Hypothesis and SETH

Determine whether the 3SUM Hypothesis implies SETH or whether SETH implies the 3SUM Hypothesis, thereby clarifying the implication relationship between these two central fine-grained hypotheses.

Background

The paper emphasizes long-standing questions about how the prominent hypotheses in fine-grained complexity relate to one another and specifically discusses the challenge of connecting 3SUM-based and SAT-based hypotheses.

Although the paper shows a novel implication from k-SUM/k-XOR hardness to a treewidth-parameterized SAT hypothesis, the broader pairwise relationship between classic 3SUM and SETH remains unresolved.