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I'm wondering if it is possible to prove that the following link as described is impossible to construct, or, if not, to construct it. Consider 6 rings, labeled A through F. I want the system to decouple into 6 disconnected rings if any two are cut; furthermore (so that this isn't just any generalized Brunnian link) I would like for it to be possible to make a single cut that partitions the AB rings from the other four, and similarly for CD from the other four and EF from the other four.

I am also OK with introducing additional "internal" rings (with the external rings being A through F still) so long as the properties above hold, generalized to any two cuts completely separate A through F from each other, and the single cuts separate AB from the other four external rings, etc.

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