Persistence Under Transformation in Finite Cognitive Systems: A Minimal Dynamic Reformulation of Representation Viability

This paper proposes a minimal reformulation of representation viability in finite cognitive and computational systems. Earlier formulations within this research program relied on the notion of stabilization. However, stabilization risks introducing static, reified, or overly global interpretations that obscure the dynamic nature of representational organization. The present work replaces stabilization with the more minimal and operational notion of persistence under transformation in time. Rather than asking whether representations become globally stable, the framework investigates whether representational structures remain sufficiently persistent under transformation, perturbation, and temporal evolution. Three minimal dynamic quantities are introduced: representational accumulation, transformation-relative persistence, and accumulation–persistence coupling. The central claim is that accumulation alone does not imply persistence under transformation. This distinction allows the framework to separate systems that merely accumulate internal structure from systems whose representational organization remains dynamically viable under perturbation. The proposed framework is intentionally minimal and non-ontological. It does not posit a universal principle of stabilization, nor a theory of consciousness or ultimate physical reality. Instead, it provides a compact dynamic framework for studying representational persistence in finite systems under transformation and temporal constraints.