SqEdges4

A Euclidean 4-simplex has five vertices and therefore $\binom{5}{2}=10$ edges. In the Regge hinge analysis those edges are indexed by Fin 10 via the incidence layer's local edge-pair table, which lists the ten unordered pairs among vertices ${0,1,2,3,4}$ in a fixed slot order.

The ambient module builds the seed-hinge dihedral cosine kernel at the flat Freudenthal point. Configurations of squared edge lengths are the coordinates on which Gram projections, dihedral cosines, and deficit gradients are evaluated. This abbreviation is the shared carrier type for those coordinates; it does not itself encode flatness, positivity, or any geometric constraint.

Downstream pathwise work re-exports the same type and builds affine paths, remappings that pull an arbitrary hinge into the Gram seed slots, and nondegeneracy predicates on top of it.

Definitional abbreviation only: expand to the function type from a ten-element index set into the reals. No lemmas, no tactics.

This is the coordinate type for the entire 4D seed-hinge and pathwise Schläfli stack. Affine paths through the flat seed are maps $t\mapsto \ell^2_{\mathrm{flat}}+t,v$ valued in this type; flat squared edges, remapped squared edges, nondegenerate 4-simplices, and pathwise flat remainders are all stated in terms of it. Without a single named carrier, the ten-slot Gram calculus and the later orbit-sum campaign would not share a common language.

It sits inside the QG full-theory campaign after the flat hinge kernel, still short of the full lattice orbit sum, the flat Hessian of the 4D Regge action, and action recovery toward Einstein–Hilbert. Those remain explicitly open in the module header.