Defines the untangling number for 3-periodic tangles and proves that ground states for infinite open curves are crystallographic rod packings.
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Algorithmic enumeration of genus-one knot and link diagrams up to 8 crossings via cellular 4-regular torus maps encoded by permutation pairs, producing over 33,000 types plus structural facts.
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The untangling number of 3-periodic tangles
Defines the untangling number for 3-periodic tangles and proves that ground states for infinite open curves are crystallographic rod packings.