Compression of Calabi–Yau Manifold Solution Space and Fractal Recursive Selection Framework: A Unified Exploration of Mathematical Physics

Calabi–Yau manifolds, serving as crucial geometric structures for the compactificationof higher dimensions in string theory, provide a key bridge between superstring theoryand the four-dimensional physical universe, including the Standard Model. However, theenormous scale of their solution space (approximately 10500) poses a serious ”landscapeproblem”: how to identify the unique solution that meets physical constraints from sucha vast pool of candidates. This study introduces fractal theory and a recursive selectionframework, proposing a multi-layered, dynamic compression mechanism for the solutionspace. By combining physical constraints (such as supersymmetry requirements, par?ticle spectrum consistency, and vacuum stability) with mathematical derivations, andleveraging the capabilities of machine learning and modern optimization algorithms, weachieve significant compression of the solution space while providing novel methods forthe physical validation of solutions. The recursive compression method proposed not onlyoffers efficient tools for studying higher-dimensional compactification but also provides apotential pathway to address the landscape problem in string theory.