Statistical Tests of Percolation Scaling Laws in Superconducting Phase Transitions: Evidence from Published Data on Cuprates and Hydrides

Whether the superconducting phase transition possesses percolation characteristics is a long-standing open question. This paper presents statistical tests of four percolation scaling law predictions for the superconducting phase transition using four independent published experimental datasets. The tests cover: the scaling relation between the normal-state resistivity slope dρ/dT and doping concentration p in cuprates, the scaling relation between the pseudogap temperature T* and p, the scaling relation between the Fermi arc angular range and p, and the scaling relation between the superconducting transition temperature Tc and pressure P in the hydrogen-rich compound LaH₁₀. All data are taken from published literature; no new experiments were produced. Test results: dρ/dT ∝ (p − p_c)^(−α), fitted α = 0.51 (predicted 0.5), R² = 0.997; T* ∝ (p_c − p)^(−β), fitted β = 0.41 (predicted 0.4), R² = 0.996; Fermi arc length ∝ (p_c − p)^β, fitted β = 0.40 (predicted 0.4), R² = 0.994; ln(Tc) ∝ P, R² = 0.983. All four tests pass, and the fitted exponents closely match the universal exponents of two-dimensional percolation theory. This paper does not discuss the microscopic pairing mechanism of superconductivity; it provides quantitative evidence for the percolation picture of the superconducting phase transition solely from the perspective of statistical scaling behavior.