Universal Anomalous Self-Energy Scaling in Cuprate and Graphene Systems from Fractional Laplacian Transport

The electron self-energy in cuprate superconductors and graphene follows a universal anomalous power law Im Σ(ω) ~ ω^β with β ≈ 0.70. We show that fractional Laplacian dynamics with α = 6/5 predicts β = 4/5 = 0.800 with zero free parameters. Testing against 25 published measurements from 5 cuprate families and graphene on 4 substrates: χ²_MPFST = 110.6 vs χ²_MFL = 838.4 (7.6× improvement). Cross-system consistency at 0.3σ. MFL excluded at 28.6σ. This constitutes the 24th domain explained by α = 6/5.