Dyadic Analysis of ζ(s)²

This work develops a dyadic framework associated with the quadratic structure of the Riemann zeta function. Starting from the square of the zeta function, an infinite hierarchy of dyadic families is introduced through successive regroupings at scales 2, 4, 8, .... Explicit analytic representations are obtained in terms of polygamma functions evaluated at rational arguments, yielding effective descriptions of the dyadic structure. The paper establishes the asymptotic behaviour of these families, derives explicit formulas for their leading asymptotic coefficients, and develops a complete hierarchy of higher-order corrections. These coefficients are shown to be governed by a family of shifted Euler sums admitting explicit evaluations. A central result is a global reconstruction identity proving that the asymptotic coefficients recover exactly the off-diagonal contribution to ζ(s)². This provides a direct connection between local asymptotic behaviour and the global quadratic structure of the Riemann zeta function. Keywords: Riemann zeta function, dyadic decomposition, polygamma functions, Euler sums, asymptotic expansions, analytic number theory.