Philosophers have proposed several competing treatments of the paradox: denying that any fixed grain count marks a heap, fixing a stipulated boundary, epistemicism (a real but unknowable boundary, held by Timothy Williamson and Roy Sorensen), supervaluationism, many-valued logics, fuzzy logic, and Diana Raffman's hysteresis account. The sourced Wikipedia article lists all of these as live, competing proposals with no stated resolution among them.
What would resolve this A decisive argument, or a real convergence of expert opinion, establishing that one treatment of vague predicates (a bivalent account with a real or stipulated boundary, a many-valued or fuzzy-logic account, or a context-dependent account such as hysteresis) is correct and the competing accounts mistaken.
Openphilosophy of logic and language (vagueness)Sorites Paradox (Wikipedia)