The Proof of Main Theorem I

The following sections are included:

• The Proof of Main Theorem I for Core Packings with at Least Thirteen Close Neighbors

• The Proof of Main Theorem I for Core Packings with at Most Twelve Close Neighbors

  • Case I: Type I core packing (i.e. with twelve touching neighbors)

  • Case II: Non-type I core packings with twelve close neighbors

  • Case III: Core packings with at most eleven close neighbors