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I think we should make it so that the lines drawn for differentials indicate the rank of the differential. Basically, we should row reduce the matrix of the differential and then draw a line from source index i to target index j if the matrix has a pivot at (i,j).
I guess what you should do is concatenate all of the differentials from stem n to stem n-1 into one matrix where the columns are ordered descending in filtration. Then row reduce this matrix. Then draw a line for each pivot.
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