Positive grading is unnecessary for the bimodule 3-Calabi–Yau conclusion

Let (Q,W)(Q,W) be a quiver with potential, and consider the conclusions of the bimodule 33-Calabi–Yau result [?]. In particular, these include the corresponding conclusions for the quiver-with-potential interior construction and for the Frobenius cluster category construction. The no-positive-grading conjecture. The conclusion of the bimodule 33-Calabi–Yau result, and hence those of the quiver-with-potential interior construction and the Frobenius cluster category construction, remains valid without the assumption that (Q,W)(Q,W) admits a positive grading. The conjecture would remove the main technical hypothesis used to obtain these categorical constructions; the source gives no resolution.

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Primary source

Matthew Pressland, “A categorification of acyclic principal coefficient cluster algebras”, arXiv:1702.05352 (2023).

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