Riemann Hypothesis

Claim – I give a constructive octonionic proof of the Riemann Hypothesis: every non-trivial zero of ζ(s) lies on Re s = ½.

Key step – The Determinant-Zeta Identity (Theorem 6.1, Sect. 6) shows

det⁡ ⁣(s(1−s)I−(H−14))=C ζ(s)−1,\det\!\bigl(s(1-s)I-(H-\tfrac14)\bigr)=C\,\zeta(s)^{-1},det(s(1−s)I−(H−41))=Cζ(s)−1,

so the poles of the Fredholm determinant match ζ-zeros. Because the resonance operator HHH is self-adjoint, the poles must satisfy Re s = ½ .