starSlotClass

The module treats the type-(1,2) triangle hinge ${0,e_0,e_0+e_1+e_2}$ (masks $0,1,7$) inside the 4D integer lattice under the Freudenthal–Kuhn triangulation. Exactly four (cube translate, Kuhn simplex) pairs contain that hinge; those four 4-simplices form the full periodic star.

Each 4-simplex has ten edges. The global geometry is tracked by a fixed 15-class edge stencil (imported from the edge-stencil and dihedral-kernel layers). Local edge indices on a star member must be rewritten into those global classes before any deficit sum can be assembled.

Parallel tables exist for the seed orbit (type (1,1)) and for other orbits ((1,3), (2,2)); each orbit needs its own hinge-ordered slot-to-class map after vertices are reordered so the hinge sits at a standard triple.

Pure definition by exhaustive pattern match on the pair $(m,e)\in\mathrm{Fin},4\times\mathrm{Fin},10$. No lemmas, no tactics, no computation: forty concrete assignments into $\mathrm{Fin},15$. Downstream code treats the table as the committed incidence data for this orbit.

This table is the incidence bridge used by assembleStarMember in the same module: that assembler sums local deficit-kernel values over edges whose class equals a given stencil index $d$. The member-evaluation lemmas (member0_eval and siblings) then simplify those sums to sparse closed forms with coefficients in ${\pm\sqrt{2}/2,\pm 1/2,\pm 1/4}$.

Those closed forms feed the full-star deficit class kernel on all 15 stencil classes, the flatness gate (star angle sum $=2\pi$), and the nonvacuity / swap / scaling / homothety gates listed in the module deliverable. The work sits in the QG full-theory campaign after the type-(1,1) seed orbit; it does not yet close the flat Hessian over all hinges, nor $S_{\mathrm{RS}}\to\mathrm{EH}_{4d}$, nor gap-action recovery. Complement type (2,1) and the remaining hinge orbits stay open.