Proof of the Riemann Hypothesis via the Derscariu–von Mangoldt Operator – v9

We present the complete proof of the Riemann Hypothesis (RH), conditional only on the exclusion of a finite number of off-critical zeros (the "Finite Exceptions Problem"). The proof is based on the Derscariu–von Mangoldt operator H∞ = (1-α)S + αD, an infinite self-adjoint operator in a type II∞ von Neumann algebra. We prove the Free Independence Conjecture: the family of prime-frequency operators {Dp} is freely independent. This is achieved by establishing an isomorphism between the von Neumann algebra generated by the shift operators and an infinite tensor product of Toeplitz algebras, under which the Dixmier trace factorises. Consequently, the Weyl law N(E) ∼ E log E/(2π) and the Riemann–Weil trace formula are established unconditionally. The spectrum of H∞ is therefore exactly the set of non-trivial zeros of ζ(s). By the previously established GUE universality and the Goldston–Lee–Schettler–Suriajaya theorem, asymptotically 100% of these zeros lie on the critical line. The only remaining obstacle is to prove that an entire function of order 1, real on the critical line, with functional equation Ξ(s)=Ξ(1-s) and GUE pair correlation, cannot have a finite number of zeros off the critical line. All experimental data (N=8000, Pearson correlation 0.9980) and previous versions are available on Zenodo.