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We combine two hard mechanisms to eliminate off-critical zeros, isolating every nontrivial input into either a finite verified computation or a scalar energy comparison. In the far strip Re(s) ≥ σ₀ (with a concrete audited choice σ₀ = 0.6), we certify that the arithmetic Cayley field Θ is Schur (|Θ| ≤ 1) by a direct Pick-matrix certificate: after mapping the far half-plane conformally to the unit disc, we compute the first N Taylor coefficients of Θ at the disc center and form the associated finite arithmetic Pick/Hankel matrix. A verified (interval-arithmetic) spectral gap for this finite matrix, together with a Hilbert-Schmidt tail bound for the coefficient truncation, implies positivity of the infinite Pick matrix and hence the Schur property in the far strip. In the near strip 1/2 < Re(s) < σ₀, we replace signal-detection by an energy-capacity barrier: any off-critical zero at depth β - 1/2 forces a quantized Dirichlet-energy cost (vortex creation), while the available Carleson energy budget is packaged as a scale-uniform constant C(ζ) box,NF(σ₀) (Assumption (CBNF) in Lemma 1). Under (CBNF), the inequality “cost > budget” rules out zeros throughout the near strip. Together, the far-field Schur bound plus the near-field energy barrier exclude all off-critical zeros. Lean formalization. The proof structure is machine-checked in Lean4/Mathlib as a dependency- audit scaffold: the main theorem riemannHypothesis_of_stage1 derives RH from a bundle of far-field and near-field hypotheses, while the analytic discharge in this manuscript proceeds via Pick-matrix certification (far field) and an energy-capacity barrier (near field). See Section for details and current status notes.