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Quotient (m, k, path, chords, cycle) by the order-2(m+k) dihedral action on the rung sequence; exhaustive sweep over outer 3..7, inner 7..9 yields 19 distinct supports with a unique floor at 252/732 realised by m=3, k=7, single-chord 6-face. Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>