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We give an alternate proof of the integrality conjecture of genus zeroGopakumar-Vafa type invariants on semi-positive varieties using algebraicgeometry. The main technique is to relate Gopakumar-Vafa type invariants toquantum $K$-invariants and to utilize the integrality of the latter.

Integrality of genus zero Gopakumar-Vafa type invariants of semi-positive varieties