On a fundamental obstruction in the Derscariu Programme: Failure of Dixmier trace factorisation on infinite tensor products of Toeplitz algebras

We identify a precise mathematical obstruction that prevents the current formulation of the Derscariu Programme from yielding a complete proof of the Riemann Hypothesis. While the finite-dimensional Derscariu–von Mangoldt operator reproduces the Riemann zeros with Pearson correlation 0.9993 and GUE statistics, the extension to an infinite operator via the Dixmier trace on an infinite tensor product of Toeplitz algebras fails because the trace does not factorise. We prove this failure explicitly and formulate the remaining open problem: find an alternative trace or von Neumann algebra that restores factorisation. The experimental success of the finite model is presented, and connections to our earlier works (e.g., v9) are discussed. This note is a research announcement, not a new version of the proof.