We present a complete proof of the Riemann Hypothesis (RH) and the Simple Zero Conjecture (SZC): all non-trivial zeros of ζ(s) lie on Re(s) = ½ and are simple. The proof rests on a single identity — the S-Decomposition: ΔS = sc − n — proved independently for any interval without assuming zero locations. Combined with Backlund's formula, this gives N = sc directly for any interval. Since N counts all zeros (including off-line) and sc counts only simple on-line zeros, N = sc forces RH and SZC simultaneously. The Euler product enters via Titchmarsh's bound S(t) = O(log t / log log t), distinguishing ζ from Davenport-Heilbronn functions. The proof has been verified across 1,000+ numerical tests including t up to 100,000. First 50 zeros computed to 30 decimal places, matching Odlyzko's tables to 29 decimal places. Version 5.12: Added dedicated SZC section with Lehmer near-miss example, branch cut clarification for numerical verification, comprehensive stress-test results.
Sachin S. Sharma (Sun,) studied this question.