This work proposes a unified mechanism for superconductivity and thermal hyperconductivity in graphene within the framework of Quarkbase Cosmology (CQB), in which physical space is a frictionless etheric plasma described by a scalar pressure field Ψ(x,t). The hexagonal lattice acts as a two-dimensional resonant cavity for Ψ, whose long-range phase coherence produces nondissipative electric currents without Cooper pairing. An effective Ginzburg–Landau formulation is derived, identifying the phase stiffness K and the collective electron–Ψ coupling as the origin of supercurrents. A Berezinskii–Kosterlitz–Thouless analysis yields critical temperatures Tc between 1 and 10 K for realistic parameters, consistent with experimental observations in pristine and twisted-bilayer graphene. The same etheric coherence mechanism explains graphene’s exceptional thermal conductivity (>5000 W/m·K) through pressure-energy transport by the Ψ field at cΨ ~ 10⁶ m/s. Superconductivity and thermal hyperconductivity thus emerge as two measurable manifestations of the same etheric pressure coherence, governed by the frictionless nature of the vacuum and the geometry of the hexagonal lattice.