Duplicate the apex medial vertex of every singleton up tooth across all
recognised treads -- except each tread's entry tooth, whose apex is left
intact -- in addition to the closing annular-vertex cuts.
For seed59 (source 5) this removes 19 = n-1 source-dual edges and the
remaining dual is a tree (verified for every source/entry choice). The
tree property holds exactly when n-1 distinct edges are cut; some graphs
(e.g. seed7, cutting 17) fall short and retain cycles.
Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
didericis
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