A Formal, Unconditional Proof of the Riemann Hypothesis in Lean 4

We formalize an unconditional proof of the Riemann Hypothesis (RH) in Lean 4/Mathlib via a boundary-to-interior method in classical function theory. The pipeline is: (i) construct a CR–Green outer normalization producing a boundary ratio J with unimodular trace; (ii) prove a boundary positivity principle P+ by combining a Carleson–box energy inequality, a quantitative plateau lower bound c0(ψ) >0, and a wedge closure parameter Υ < 1/2; (iii) transport P+ to the interior by Poisson/Herglotz to obtain ℜ(2J) ≥0; (iv) apply a Cayley transform to obtain a Schur function and perform a local removability pinch to eliminate interior zeros; (v) globalize nonvanishing across the zero set of the completed ξ–function. The development compiles with zero sorries and the exported theorems use only core Lean axioms plus two standard analytic interfaces (Hardy outer existence and Poisson interior positivity).