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Jun 3, 2022 at 15:55 comment added Ian Agol The $v$ and $w$ don’t actually generate H. Take $(K,L,M)= (3,2,2)$. Then $(0,1,-1)$ is in H but not in the sub lattice generated by v, w. This was pointed out by my student Larsen Linov. So at least you need to divide by the gcd of the entries. What is your proof that these generate?
Jun 3, 2022 at 15:26 history edited Daniel Asimov CC BY-SA 4.0
added 1 character in body
Jun 3, 2022 at 1:42 history edited Daniel Asimov CC BY-SA 4.0
Mentioned case I had overlooked.
Jun 3, 2022 at 0:17 history answered Daniel Asimov CC BY-SA 4.0