The Theory of Persistence -- Articles M1-M5: Mathematical Foundations

May 18, 2026Open Access

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Key Points

This series aims to solidify the mathematical underpinnings of the Theory of Persistence by providing rigorous definitions and frameworks.
Published five articles presenting mathematical theories and principles related to Persistence Theory.
Included companion scripts for verifying mathematical concepts and findings.
Emphasized the relationship between topological data analysis and Persistence Theory.
Clarified the mathematical definitions relevant to Persistence Theory and its applications.
Provided tools for verifying the theoretical aspects of Persistence Theory through scripts.
Set the stage for future applications and research grounded in solid mathematical foundations.

Series establishes the mathematical principles of Persistence Theory, emphasizing verification methods.

Five-article series establishing the mathematical foundations of the Theory of Persistence (PT). Includes companion verification scripts.

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Yan Senez (2026) studied this question.

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