Computational laboratory for the Erdős–Straus conjecture studying residue-class identities, structural coverage, and empirical hardness of representations 4 / 𝑛 = 1 / 𝑥 + 1 / 𝑦 + 1 / 𝑧 4/n=1/x+1/y+1/z.

A finite algebraic covering system for the Erdos-Straus conjecture, verified to 10^11. Gateway decompositions via divisors of N^2.