Shawn Ryan

Kernel-checked Hermite–Biehler theorems for shifted Riemann ξ, with disk localization

Let Ξ(z)=ξ(1/2+iz) and, for h>0, E_h(z)=Ξ(z+ih), E_h^#(z)=Ξ(z-ih). We give a Lean 4 formalization of Hermite–Biehler modulus inequalities, phase monotonicity, and simple interlacing zeros for the combinations S_θ=A_h cos θ+B_h sin θ of these imaginary translates, where A_h=(E_h+E...

Twenty-Three Certified Decimals: Rigorous Ground-State Energies, Correlations and a Coupling Curve for the Half-Filled 4×4 Hubbard Model: certificate bundle v1.0.0

We prove the ground-state energy of the periodic, half-filled 4×4 repulsive Hubbard model with t = 1 to at least 23 decimal places at U = 1, 2, 3, 4, 5, 6, 7, 8, 10, 12 and 16: every enclosure has width below 10⁻²⁴. The double occupancy, the spin correlations and the staggered st...