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We show some inductive statements for the index conjecture for log canonicalCalabi-Yau pairs. Using it, we show that boundedness of log canonical index forlog canonical Calabi Yau pairs with rational DCC coefficients in dimension 3.We also show boundedness of log canonical index for klt log Calabi-Yau pairs indimension 4 with $B\neq 0$.

Some Results about the Index Conjecture for log Calabi-Yau Pairs