Bryan W. Daugherty

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...

Opposite-Side Residuals in Working-Precision Newton-Schulz Refinement of LU-Based Matrix Inverses: Measurements and an Empirical Predictor

An inverse X of a matrix A computed through an LU factorization comes with a guarantee on only one of its two residuals, I - AX or I - XA, according to whether it was obtained by solving AX = I or XA = I. In practice the two are usually of the same size, as Wilkinson observed. A...

A Refuted Golden-Ratio Floating-Point Conjecture, Exactly Reversible Integer Maps, and a Fixed-Width Lifting Wavelet

This is an expository paper with a negative result at its centre. It began from a geometric picture of reversible computation, a state that expands by the golden ratio φ = (1+√5)/2 and folds back by 1/φ, and from the conjecture that scaling by φ gives better round-trip accuracy i...