The Preservation Principle: When Identity Survives Scale Transition

Abstract

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, where violation produces memory terms and apparent non-Markovianity; (ii) Nyquist conditions in sampling physical systems, where violation produces aliasing phenomena misidentified as 'superposition'; and (iii) structure-preservation conditions in nominalization, where violation produces pseudo-entities like 'consciousness' generating intractable philosophical problems. The formal parallels are not analogical but structural: category-theoretic naturality conditions provide the common mathematical backbone. We present proofs for each domain-specific instantiation and demonstrate that apparent domain-specific complexities—the measurement problem in quantum mechanics, emergence in social systems, the hard problem in philosophy of mind—are artifacts of transformation failure rather than ontological depth.