A Unification of Coarse-Graining Conditions Across Domains
This paper identifies a single meta-principle governing when structure is preserved under transformation across domains: identity survives transformation if and only if the transformation respects the equivalence relations constituting that identity. We demonstrate that this principle instantiates as (i) lumpability conditions in coarse-graining political and social dynamics, (ii) Nyquist conditions in sampling physical systems, and (iii) structure-preservation conditions in nominalization. The formal parallels are not analogical but structural: category-theoretic naturality conditions provide the common mathematical backbone.
@misc{farzulla2025preservationprinciple,
author = {Farzulla, Murad},
title = {The Preservation Principle: When Identity Survives Scale Transition},
year = {2025},
howpublished = {Farzulla Research Discussion Paper DP-2506},
url = {https://farzulla.org/papers/preservation-principle}
}