A clean local lattice model with SYK low-energy physics

Find a translation-invariant lattice Hamiltonian with finite-range interactions and no quenched disorder whose low-temperature regime shows SYK signatures: fermion Green function $G(\tau) \sim \tau^{-1/2}$ over a parametrically wide window, a large residual entropy density before a crossover scale, and Lyapunov exponent approaching $2 \pi k_{B} T/\hbar$. Answer: an explicit model with controlled evidence, or an argument that none exists.

Controlled numerics or an exact solution demonstrating these three signatures in a specific clean model.