We present an exact identity connecting four quantities drawn from otherwise separate domains of physics: the cosmological constant (large-scale cosmology), the de Sitter horizon entropy SdS Λ (holography and black-hole thermodynamics), the unified coupling GUT (high-energy particle α physics), and the dimension of the fundamental representation of the exceptional Lie algebra G2. Within the G2 framework established in prior work, two independently derived results — GUT = 1/ (6×7) = α 1/42 and = 6/SdS — combine to give × SdS × GUT × 7 = 1 exactly. The identity is a theorem, not a Λ Λ α numerical coincidence: it follows algebraically from 6×7 = 42. We interpret it as a holographic constraint in which the G2 symmetry of the vacuum locks together dark energy, information capacity, coupling strength, and compact dimensionality so that they cannot vary independently. A corollary is that if SdS grows as the universe expands, GUT must decrease at a rate of order the Hubble rate — a falsifiable, if α currently unmeasurable, prediction of a slowly time-varying unified coupling. Keywords: cosmological constant, de Sitter entropy, holographic principle, grand unification, unified coupling, G2 algebra, varying constants, dark energy
Vali Ilyas (Fri,) studied this question.