Formal Description of Cross-Dimensional Proposition Transfer with Fractal Model Theory Framework

With the increasing demand for multi-scale system analysis and high-dimensionaldata processing, cross-dimensional logical transfer has become a frontier area informal methods research. Traditional methods, such as topological embedding andquantum logic, face challenges in dimensionality limitations and measure preserva?tion when dealing with high-dimensional data. This paper proposes a novel theo?retical framework based on fractal model theory, which achieves semantic conserva?tion between dimensions through fractal self-similarity, overcoming the limitationsof traditional methods. We provide a detailed introduction to the constructionof fractal signatures, cross-dimensional transfer mechanisms, and measure invari?ance theorems, and validate the framework’s effectiveness through case studies ofthe Sierpinski triangle and Menger sponge. Experimental results demonstrate thatthe framework achieves high-precision measure-preserving transfer in polynomialtime, with good scalability. Future work will focus on extending the framework tonon-integer dimensional transfers and online transfers of dynamic fractal systems