This comprehensive work presents detailed mathematical formu- lations and technical refinements addressing critical theoretical chal- lenges in the Expanded Quantum String Theory with Gluonic Plasma (EQST-GP) framework. We provide complete derivations for the neg- ative energy density mechanism, Majorana gluon dark matter proper- ties, and rigorous compatibility analysis with Swampland Conjectures. The enhanced model incorporates moduli stabilization with uplifting potentials, refined gravitational wave predictions, and precise numeri- cal verifications using symbolic computation. All derivations maintain mathematical rigor while ensuring phenomenological consistency with cosmological observations and experimental constraints.