On fundamental obstructions in the Derscariu Programme: Failure of Dixmier trace factorisation and infinite traces on Toeplitz algebras

We document two precise mathematical obstructions that prevent the current formulation of the Derscariu Programme from yielding a complete proof of the Riemann Hypothesis. This version (v2) adds a second obstruction: even on a single Toeplitz algebra, the standard Dixmier trace assigns an infinite value to the projection operators T^m (T*)^m that appear in the expansion of e^{itDp}. Consequently, the individual traces τp(e^{itDp}) are not well-defined in the standard Dixmier framework. Together with the factorisation failure, these results pinpoint exactly why the original construction fails and invite the community to explore alternative traces, von Neumann algebras, or limiting procedures.