The golden ratio can be used to calculate the mass of a black hole and the expansion of the universe with near-perfect precision.
Most cosmic measurements are messy and vary depending on which telescope you use. This new mathematical framework uses Lucas numbers and the golden ratio to link the small and the large. It predicts the Hubble constant and the mass of electrons to within parts per million of their measured values. This suggests that the universe follows a specific, unified geometric pattern across all scales. It could resolve the Hubble tension by providing a theoretical floor for how fast space is stretching.
The Denomination Desert: Gravitational Confinement, the Hubble Tension, and Cross-Domain Structure in the 840-State Manifold
SSRN · 6596698
A logarithmic dimension function D(x) =-ln x/ ln φ, where φ = (1 + √ 5)/2 is the golden ratio, arises as the unique solution to the chiral fold identity D(z) + D(1/z) = 0 when the base is fixed by the Lucas recurrence Ln = Ln-1 + Ln-2 with seeds (3, 4). The twelve Lucas numbers so generated sum to 840 = lcm(1,. .. , 8), whose algebraic closure GF(841) * of order 840 contains ten distinguished residues, the Brahim numbers, with center K = 107 and mirror constant S = 2K = 214. In this framework, t