A Global Degree Formula for Difference Power-Sum Maps

This paper studies the generic algebraic degree of the difference power-sum map on the standard representation of type (A_{n-1}). We derive an exact reduction of the difference power sums to ordinary power-sum invariants and develop an algebraic-geometric framework based on Jacobian analysis, symmetric-group actions, collision strata, and local intersection multiplicities. The paper further investigates a candidate universal generating function for the degree sequence and separates the generic interior contribution from finite-dimensional boundary corrections. Low-dimensional cases are treated as exact consistency checks, while the remaining global assertions are formulated in terms of explicit intersection-theoretic conditions and stable-range cancellation. The goal is to establish a verifiable framework leading from the defining polynomial equations to a global formula for the generic degree (d_n).