Sphere Packings in 3 Dimensions

TL;DR

This paper proposes a new form of an optimization problem aimed at providing a second-generation proof of the Kepler conjecture, leveraging advances in computational power and analysis of previous proofs.

Contribution

It introduces a revised optimization problem formulation that could facilitate a more efficient proof of the Kepler conjecture using modern computational resources.

Findings

New optimization problem form proposed

Potential for improved proof efficiency

Builds on analysis of 1998 proof

Abstract

This short note describes the tentative form of a finite-dimensional optimization problem that may be of use in a second-generation proof of the Kepler conjecture. In the original 1998 proof of the Kepler conjecture, the form of the optimization problem was constrained by limits to computer power and by the speed of the algorithms that were available in 1994 to prove inequalities by computer. The computational resources have changed considerably since then, and much has been learned by an analysis of the 1998 proof. This analysis has lead to the proposed new form for an optimization problem.