Universal Bridge Theorem: A Cohomological Framework for Construction-Independent Invariants

Key Points

• To establish a cohomological framework that verifies the independence of mathematical invariants from construction methods.
• Developed a systematic framework using cohomological principles.
• Analyzed the relationship between scaffold spaces and target spaces through exact sequences.
• Applied the framework to regularization theory, gauge theory, and geometric analysis.
• Demonstrated construction-independence of invariants through formalized cohomological verification.
• Confirmed the applicability of cohomological principles across different mathematical fields.