The Prime-Zeta Reconstruction: An Exact Analytical Basis using Two Fixed Primes

This paper presents a comprehensive analytical framework for the Riemann Zeta function, ζ(s), derivedf romarecursivereductionmethodoriginallyappliedtolinearprimeprediction.Byextendingtheconceptof the reduction" into the continuous complex domain, we establish a strict closed-form identity that expresses ζ(s) as a linear superposition of any two distinct prime numbers, P a and P b .The derivation proves that the spectral properties of the Zeta function can be completely reconstructed using a Two-Prime Basis" and a specific set of functional coefficients.These coefficients are shown to possess barycentric symmetry governed by the Reflection Formula, effectively mapping the distribution of prime numbers to a torque-balance system in the complex plane.This document details the exact algebraic steps, the integral bootstrapping method, and the residue calculus required to prove this identity.