What question did this study set out to answer?

To establish a cohomological framework that verifies the independence of mathematical invariants from construction methods.

March 27, 2026Open Access

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.

Abstract

A systematic cohomological framework for analyzing when mathematical invariants extracted from analytical constructions are independent of implementation choices. Formalizes the relationship between scaffold spaces (spaces of constructions) and target spaces (spaces of invariants) through exact sequences. The primary contribution is the systematic application of well-established cohomological principles as a general-purpose verification tool for construction-independence. Applications in regularization theory, gauge theory, and geometric analysis.

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

Key Points

Abstract

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