Finite clusters:
+ Prove connected; enumerate combinatorics; prove unique minimum for each combinatorial type with restrictions.
Applies to finite or periodic or on sphere.

"connected" means "each region connected". "restrictions" are necessary because a circular chain of bubbles, enclosing a bubble of negative pressure, is floppy.

"connected" means "each region connected". "restrictions" are necessary because a circular chain of bubbles, enclosing a bubble of negative pressure, is floppy.

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