Infinite tower of trimers with exact 22.7× energy ratio — log-periodic quantum mechanics
Efimov (1970) predicted an infinite geometric series of three-body bound states when the two-body scattering length a → ±∞. Consecutive trimers obey E_{n+1}/E_n = e^{−2π/s₀} ≈ 1/515, and their sizes scale as r_{n+1}/r_n = e^{π/s₀} ≈ 22.7 (s₀ ≈ 1.00624). This discrete scaling symmetry reflects the Efimov Hamiltonian's renormalization group limit cycle — first observed in ultracold cesium (2006).