Local Symmetry and Residual Decomposition of (s) Near Nontrivial Zeros

The Riemann Hypothesis (RH) conjectures that all nontrivial zeros of the Riemann zeta function ζ(s) lie on the critical line ℜ(s) = 1 2 . We introduce a local analytic framework via the Structural Residual Compensation (SRC) method, employing symmetry-driven Taylor expansions to decompose ζ(s) near simple zeros. Formalized as Structural Local Completeness (SLC) in Section 3, this decomposition reveals parity-aligned structures, validated to 10−6 precision in Section 6. Supporting the Local Structural Residual Regularity (LSRR) conjecture, our approach reframes RH as a condition of local analytic parity, extensible through a recursive computational hierarchy, the Residual Cascade Decomposition (RCD-k), in Section 7.