A Numerical Conjecture on Spacetime Stiffness: Bridging the Planck and Cosmological Scales

This project proposes a heuristic conjecture: a third energy scale called "spacetime stiffness" (K) geometrically bridges the Planck scale and dark energy scale via the relation: K^3 = ρ_P * ρ_Λ^2. Using gravitational-wave data, we estimate K ≈ 10^32 J/m^3, consistent with the conjecture. From this, unified expressions for G and Λ are derived, offering a new mathematical perspective on fundamental constants. Keywords: spacetime stiffness, cosmological constant, quantum gravity, fundamental constants