A formal proof that compiles without errors is not the end of the story. The harder and more consequential challenges lie in what comes next: organizing, integrating, and maintaining formal knowledge at a planetary scale. These are challenges that the world will confront over the coming years as an increasing number of proofs are produced by AI systems. The ability to integrate these proofs into an ever-expanding, intercompatible knowledge base will soon be a basic requirement for scale. We will continue to collaborate with the maintainers of the sphere packing project and other libraries of formal mathematics to ensure the code Gauss has produced remains usable and maintainable for posterity. As a first step in that direction, we used Gauss to automatically refactor, optimize, and improve the style of the formalization it produced, effectively decreasing its size from 500,000 lines at peak to the released version of ~200,000 lines.
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This lawsuit follows the success of a similar class action decided in October. The UK's Competition Appeal Tribunal found that Apple had been abusing its dominant market position and overcharging App Store users. In December, Apple filed an appeal against the £1.5 billion ($2 billion) fine.