We re-analyze published viscosity data on a series of monodispersed Polystyrene samples covering a wide range of molecular weight across Mc (from M=550 to M=1.2 million g/mole) tested over a broad temperature span in the melt. We show that the classical expected behavior, both below and above Mc, is confirmed at first sight, yet that the separation of M and T is only valid for discrete values of M, all multiples of Mc, but not for all M. Inspired by the Cross-Dual-Phase interpretation of melt entanglement which assumes that a split of the statistical system of interactions into two systems occurs at the critical molecular weight Mc, we introduce new formulas which are tested on the same viscosity data already analyzed by the classical approach. The comparison of the new and the classical formulation of the viscous flow behavior offers a possible explanation to the reptation model historical dilemma: while the original de Gennes’s theory predicted a power exponent of 3 for the molecular weight dependence of Newtonian melt viscosity, several authors successfully tweaked the mathematics of the original reptation model to explain the “reality”, i.e. the 3.4 exponent dependence of viscosity instead of de Gennes’ 3. This presentation questions whether the improvements by Doi, Edwards, Wagner, Marrucci, McLeich and many others were actually necessary. In the Cross-Dual-Phase treatment of viscosity, the viscosity is written as the product of two terms, both M and T dependent. For one range of M,T tested above Mc, we find that at constant T, one of the terms varies with M with an exponent 3, while the other term varies with M with an exponent 0.4. For other T also tested, the exponents 3 and 0.4 take other values. When working at constant free volume instead of constant temperature, the exponent for M> Mc is no longer in the 3.4 range but close to 5.3, which raises the question of truly understanding and quantifying the influence of free volume on the viscosity. In the discussion, we speculate on the thought provoking consequences of this new analysis: is de Gennes’s molecular dynamic calculation correctly addressing the interactions occurring in the core phase of the cross-dual-phase model, only missing the elastic sweeping dissipative component originating from the second-dual phase (above Mc), or is it just a pure coincidence? Are the classical formulations of viscosity simply curve-fitting expressions misleading the comprehension of the physics behind polymer flow deformation and entanglements? This work brings clear answers to these crucial challenging questions.