This paper introduces Informational Set Theory (IST), a foundational mathematical framework that treats set-theoretic identity through the lens of informational conservation. While standard Zermelo-Fraenkel Set Theory (ZFC) treats mathematical operations as costless mappings, IST establishes the Law of Kept Data (AKD), an axiom requiring that the net change in information (Delta I) remains zero for any valid transformation.
Asa Smith (Tue,) studied this question.