This technical supplement (Paper LXVII) provides the formal mathematical derivations for the MSDS cosmological framework. The author presents a point-by-point response to ten critical technical inquiries, covering topics from Z_2 symmetry and Higgs portal couplings to the Majorana ghost mechanism. Notably, this paper corrects previous arithmetic errors in the calculation of the \xi coupling and provides a unit-consistent derivation of the dilaton condensate amplitude. By unifying the cosmological gravitational slip with particle physics observables, this work serves as the primary reference for the theoretical consistency of the MSDS programme.