ProductGenerator

A non-degenerate n-simplex of X x Y, presented as the pair of SSetElements (each possibly itself degenerate over its own non-degenerate generator) whose word-sets are disjoint -- NOT an Eilenberg-Zilber shuffle triple. The shuffle family indexes the classical chain MAP between C_*(X) tensor C_*(Y) and C_*(X x Y), not the product's own non-degenerate simplices: (e_X, e_Y), both non-degenerate of dimension 1, is a non-degenerate 1-simplex of X x Y that no (p,q)-shuffle with p+q=1 could ever produce, since a shuffle needs p+q=n but here p=q=1=n. See .claude/WORKLOG-simplicial-set-constructions.md.