Title:

Large Language Models and the Construction of New Calabi-Yau Manifolds

String theory has been proposed to explain the four fundamental forces: Strong Nuclear Force, Weak Nuclear Force, Electromagnetic Force, and Gravitational Force. According to String Theory, there are ten dimensions, which include the four space-time dimensions, and six additional dimensions. These extra dimensions are curled up in complex shapes that are called Calabi-Yau manifolds (CY Manifolds). A method of finding these CY Manifolds mathematically is through triangulation of four-dimensional reflexive polytopes. There are 473,800,776 possible polytopes that could potentially be triangulated to create these CY Manifolds, and as the polytopes increase in size, the number of possible triangulations grows exponentially. The challenge for future endeavors will be to find how many triangulations are necessary to create a balanced sample of triangulations to use as a training set for a Large Language Models. These Large Language Models would then use this training set to triangulate more polytopes, create Calabi-Yau Manifolds.

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