Set-Theoretic Structure and Combinatorial Properties of the 6-Dimensional Hypercube — Spin Classification, Set Enumeration, and Sign Product

v7: Q-axis restructured from 3-bit (8-valued) to 2-bit (4-valued: Q=2c₂+c₃). Q=0 orthogonal to Q-axis (colorless/lepton), Q∈{1,2,3} = 3 colors (quark). Anti-quarks carry same color (spatial sign flip only). Total states reduced from 21 to 13. This paper defines a 6-dimensional structure obtained by appending a 4-valued discrete label axis Q to a 5-dimensional hypercube, and derives the combinatorial properties of its set-theoretic structure through pure combinatorial enumeration without physical terminology.