A FULLY INVERTIBLE GLOBAL ANALYTIC MODEL OF THE RIEMANN ZETA FUNCTION

Abstract. We introduce Sui Theory and present a globally invertible analytic model for functions in the Hardy space H2(C+) [5, 15]. The construction is based on an atomic system {Φn}, where each atom has the intrinsic properties of admissibility, completeness, stability, and modulator regularity [6, 3]. These properties are built into the atomic definition itself, rather than imposed externally as assumptions. The resulting family {Φn}forms a Riesz basis of H2(C+) [2], yielding a unique and stable expansion f(s) = ∞ cnΦn(s), f ∈H2(C+). n=1 This expansion is globally invertible: coefficients can be recovered from analytic data, and conversely the synthesis of coefficients reconstructs the function uniformly on compact subsets of the domain [12]. The model provides a new framework for analyzing analytic functions with growth and symmetry constraints, and suggests applications to L-functions and other areas of analytic number theory [13, 1, 4].