Jain Sequence and Farey Hierarchy Unify Fractional Quantum Hall Topological Orders — E8 Intelligence Research

FINDING: The fractional quantum Hall effect (FQHE) organizes its topological orders via the Jain sequence (ν = n/(2pn±1)) and a Farey-like hierarchy of filling fractions, with composite fermions as the unifying quasiparticle framework. | MATH: Jain sequence: ν = n/(2pn+1) for n=1,2,3,... (p=1 gives 1/3, 2/5, 3/7, ...). General hierarchy: ν = p/(2mp±1) with p integer. Farey mediant structure: between a/b and c/d, the next level is (a+c)/(b+d) — e.g., 1/3 and 2/5 → 3/8 (observed). The Laughlin wavefunction: Ψ_m = ∏_{i Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com