The Case for Identity-Preserving Arithmetic in Scientific Computation

This document examines the idea of identity-preserving arithmetic as a potential foundation for reproducible scientific computation. Rather than proposing an implementation or claiming a completed method, it analyzes the consequences of numerical identity loss in floating-point arithmetic and explores how computation might change if representation were treated as a conserved quantity. The paper outlines why current arithmetic undermines reproducibility, how reversible and lossless operations could serve as a conceptual benchmark, and what research questions might follow from treating identity as a structural requirement rather than a practical compromise. The work is presented as a theoretical perspective for researchers in numerical methods, computational physics, reproducibility studies, and the philosophy of computation. It invites scientific inquiry into whether identity-preserving computation is feasible, how its constraints would operate, and what standards of validation might emerge if computation were required to conserve representational identity.