Aperiodic Gauge Fixity: Combinatorial Complexes and BRST Nilpotency

In this paper we show that the Einstein Monotile ($\hat{\Xi}$) is the unique field configuration that satisfies the Kallosh Independence Theorem at the thermal extremal limit. Utilizing the framework of Combinatorial Complexes (CCs), we prove that while periodic lattices suffer from Gribov ambiguities—where redundant gauge orbits trigger topological collapse—the aperiodic order of the Monotile provides a "Rigid Gauge" that ensures the global nilpotency of the BRST operator ($Q^2=0$). We show that this "Aperiodic Gauge Fixity" is the fundamental mechanism that "lifts" the vacuum from its dissipative, high-entropy early state ($c \approx -0.1$) to a state of Arithmetic Superfluidity ($c=1$). This transition is regulated by the Geometric Friction constant ($\lambda_F = 34/13$), which we identify as the source of the Fine-Structure Constant ($\alpha^{-1} \approx 137.036$). Crucially, we redefine Inertial Mass not as an intrinsic property of baryonic matter, but as the work required to shift the Monotile boundaries within the Combinatorial Complex against the vacuum's topological tension. This derivation provides a purely algebraic origin for Newton’s Second Law, where $F=ma$ emerges as the low-frequency limit of the Somos-Eisenstein Phase Flux, the Topological Origin of Inertial Mass. We conclude that the smooth spacetime manifold of General Relativity is the stable, non-redundant equilibrium of a self-correcting aperiodic code, selected through a retrocausal pruning process at the Somos Prime Invariant ($N_{Sp} = 779,731$).