Resonance statistics, Fock-space branching, and long-range pair networks in slowly varying interacting chains

In a slowly varying aperiodic potential $h_i=h\cos(2πβi^n+ϕ)$ with random power-law density interactions $V_{ij}/|i-j|^α$, the resonant-object ensemble changes across $α=2n$, wherever Hartree fragmentation is operative, from isolated two-level bonds to a mixture of fragmented multi-site clusters and