This paper presents a program to prove the Kepler conjecture on sphere packings. The conjecture states that no packing of spheres in three dimensions has density exceeding that of the face-centered cubic lattice packing, which has a density of π/√18 ≈ 0.74048. The paper describes a method to reduce the Kepler conjecture to a finite calculation, involving up to 53 spheres in a compact region of Euclidean space. The program aims to rigorously prove the conjecture by analyzing Delaunay stars, which are decompositions of space into simplices based on sphere packings. A Delaunay star is a collection of Delaunay simplices sharing a common vertex. The paper conjectures that the score of every Delaunay star is at most the score of the stars in the face-centered cubic and hexagonal close packings. This conjecture implies the Kepler conjecture. The first step of the program involves showing that every Delaunay star satisfying a certain regularity condition satisfies this conjecture. The paper defines a score function that replaces the compression function, which has better properties. The score is defined for Delaunay stars and is related to the density of packings. The main theorem of the paper states that if a Delaunay star is composed entirely of quasi-regular tetrahedra, its score is less than 8 pt. The paper also discusses the compatibility of quasi-regular tetrahedra and octahedra with the Delaunay decomposition. It defines the score for quasi-regular tetrahedra and shows that no quasi-regular tetrahedron gives more than 1 pt. The paper then outlines the main steps of the proof of the Kepler conjecture, including the analysis of standard clusters and the properties of Delaunay stars. The paper concludes with a detailed analysis of the compatibility of Delaunay simplices and quasi-regular solids, and the properties of Delaunay stars. It also discusses the implications of the conjecture and the program for the density of sphere packings. The paper provides a rigorous proof of the main theorem and shows that the score function is a useful tool for analyzing the density of sphere packings.This paper presents a program to prove the Kepler conjecture on sphere packings. The conjecture states that no packing of spheres in three dimensions has density exceeding that of the face-centered cubic lattice packing, which has a density of π/√18 ≈ 0.74048. The paper describes a method to reduce the Kepler conjecture to a finite calculation, involving up to 53 spheres in a compact region of Euclidean space. The program aims to rigorously prove the conjecture by analyzing Delaunay stars, which are decompositions of space into simplices based on sphere packings. A Delaunay star is a collection of Delaunay simplices sharing a common vertex. The paper conjectures that the score of every Delaunay star is at most the score of the stars in the face-centered cubic and hexagonal close packings. This conjecture implies the Kepler conjecture. The first step of the program involves showing that every Delaunay star satisfying a certain regularity condition satisfies this conjecture. The paper defines a score function that replaces the compression function, which has better properties. The score is defined for Delaunay stars and is related to the density of packings. The main theorem of the paper states that if a Delaunay star is composed entirely of quasi-regular tetrahedra, its score is less than 8 pt. The paper also discusses the compatibility of quasi-regular tetrahedra and octahedra with the Delaunay decomposition. It defines the score for quasi-regular tetrahedra and shows that no quasi-regular tetrahedron gives more than 1 pt. The paper then outlines the main steps of the proof of the Kepler conjecture, including the analysis of standard clusters and the properties of Delaunay stars. The paper concludes with a detailed analysis of the compatibility of Delaunay simplices and quasi-regular solids, and the properties of Delaunay stars. It also discusses the implications of the conjecture and the program for the density of sphere packings. The paper provides a rigorous proof of the main theorem and shows that the score function is a useful tool for analyzing the density of sphere packings.