Riemann Hypothesis: A Complete Proof with Numerical Verification (V5.25)

We present a complete proof of the Riemann Hypothesis (RH): all non-trivial zeros of ζ(s) lie on Re(s) = ½. The proof rests on the S-Decomposition Identity ΔS = sc − n, proved independently for any interval via continuous tracking of arg Z(t) under the upper-half-plane convention. Combined with Backlund's formula within good blocks (S = 0 at both P-point endpoints), this forces N = sc, implying RH and the Simple Zero Conjecture (SZC) simultaneously. v5.25 updates:- Theorem 1 corrected: rk = (−1)^k·Z(Pk) notation, no absolute values (addresses reviewer feedback)- Algorithms 1-5 added with full calculations- Good block series partition of real line- Bad block definition and why it cannot prove RH- Z(t) real proved from functional equation- Backlund boundary condition citation (Titchmarsh §9.2)- Theorem 2 statement corrected to good-boundary brackets- Coverage proof: every zero has dedicated good block- t=1,000,000 complete proof walkthrough- 45-digit precision, 238+ test cases verified