A Kastler-Kalau-Walze Type Theorem for 5-Dimensional Manifolds with Boundary for Statistical de Rham Hodge Operator

Key Points

• The aim is to provide a proof for the Kastler-Kalau-Walze type theorem specifically for 5-dimensional manifolds with boundaries.
• Utilized a brute-force approach to develop the proof
• Focused on the specific context of the 5-dimensional manifold and its boundary
• Analyzed the statistical de Rham Hodge operator within this framework
• Successfully established the Kastler-Kalau-Walze type theorem for the defined conditions
• Provided foundational insights into the behavior of the statistical de Rham Hodge operator in the context of the manifold
• Demonstrated implications for the study of geometric structures with boundary