Split-Zero Divisor-Pair Reconstruction of Residual Erdős–Straus Shells

The normalized residual shell calculus for the Erdős–Straus equation converts the fixed-shell divisor congruence d ≡ −N (mod R), N = pa, into the invariant target dN⁻¹ ≡ −1 in a finite unit torus. The preceding residual pre-Niemeier note used this normalization to construct a static modulo-840 support fibration and its rank-24 closure of type A₅⁴D₄. The present note applies the split-zero support formalism to the remaining shell obstruction. The main result is a divisor-pair reconstruction theorem: after reducing by g = gcd(R, N), a shell works if and only if N₀ = XYZ, gcd(X, Y) = 1, R₀ | X + Y, where R₀ = R/g and N₀ = N/g. This reconstructs the missing additive relation hidden behind the multiplicative condition X/Y ≡ −1. The corresponding denominators are b = XZ(X + Y)/R₀ and c = YZ(X + Y)/R₀. In the coprime shell case gcd(R, pa) = 1, the reconstruction separates into a central branch (a = XYZ, R | X + Y) and an edge branch (a = XYZ, R | 4X²Z + 1). These two additive reconstruction laws replace the three raw p-origin divisor tests. We derive explicit identity generators, edge-ramification identities, a new necessary condition for primes surviving all ramified edge shells, and a split-zero orbit-support invariant distinguishing unsupported absence from supported parity-zero certificate sectors. The remaining constructive target is formulated as a finite supported divisor-pair covering problem over the six residual classes modulo 840.