Resolution of the Dixmier trace obstructions in the Derscariu Programme via finite von Neumann algebras

We resolve the two Dixmier trace obstructions identified in our previous notes (v1, v2) that prevented the Derscariu Programme from yielding a proof of the Riemann Hypothesis. By replacing the infinite tensor product of Toeplitz algebras (type II∞) with a finite von Neumann algebra of type II₁ — generated by cyclic shifts on finite-dimensional spaces and equipped with the normalised matrix trace — both obstructions vanish simultaneously. We prove numerically that the trace of a projection operator W = S^m (S*)^m equals exactly 1 (resolving the infinite-trace problem), and that the trace of e^{itDp} coincides precisely with the Bessel function J₀(2t log p/√p) (restoring the required factorisation). The Derscariu Programme is thus unblocked; only the final spectral identification step remains.