We study equivariant perfect matchings on the Boolean hypercube \B6 under the Klein four-group K4=⟨\comp,\rev⟩ generated by bitwise complement and reversal. Among matchings using only \comp or \rev pairings, there is a unique Hamming-cost minimizer, given by a simple ``reverse-priority rule'': pair each element with its reversal unless it is a palindrome, in which case pair it with its complement. This matching has total Hamming cost 120, compared to 192 for the complement-only matching. The historically significant King Wen sequence of the I Ching realizes precisely this matching. Pure Hamming minimization over the full K4 action is different: allowing \comp∘\rev lowers the cost to 96. The King Wen rule is recovered, however, as the unique Hamming-weight-preserving optimum: it minimizes failures of Hamming-weight preservation before Hamming distance, and it is stable for the weighted energy α∣Δw∣+βdH throughout the open region α>β. The finite orbit counts and case distinctions are checked in Lean~4.
@article{arxiv.2601.07175,
title = {Optimal Equivariant Matchings on the 6-Cube with an Application to the King Wen Sequence},
author = {Alejandro Radisic},
journal= {arXiv preprint arXiv:2601.07175},
year = {2026}
}