Establish convergence and numerical stability of the regulated 3D Ising construction

Establish convergence of the regulated full double-twist family sums and stability of the thermal coefficients extracted from the thermal Polyakov bootstrap for the three-dimensional Ising CFT, while controlling omitted operators and the associated regulator dependence.

Background

The proposed numerical treatment divides the Polyakov matrix into light operators and modeled double-twist trajectories. The matched rows determine the modeled thermal coefficients as functions of the stress-tensor and energy-operator one-point coefficients, which are then constrained by effective low-row equations.

This reduction is algebraic, but a controlled Ising computation additionally requires common regulation of the full family sums, control over omitted low-lying and heavy operators, convergence of the regulated inverse matrix, and numerical conditioning. The paper explicitly identifies convergence and stability as unresolved issues rather than established consequences of the matrix reduction.