The Diversity Threshold – A Threshold Model of Emerent Systems

Timothy Speed (2025)

Abstract

This paper formulates the concept of the diversity threshold as a critical model for emergent systems. Rather than treating diversity simply as a count of elements, it defines diversity as a topology of the possibility space capable of sustaining multiple incommensurable modes simultaneously. Once above this critical folding threshold, systems are able to generate new reality – innovation, resilience, and self-organization – whereas below it, efficiency without future, growth without worldhood, and collapse prevail. ([zenodo.org](https://zenodo.org/records/17847399))

This framework integrates evolutionary, ecological, and complexity theories without replacing them, and shows how diversity is not a passive result of emergence but its necessary cause. Above the threshold, emergent phenomena arise; below it, systems fail to transition into novel modes of organization. ([zenodo.org](https://zenodo.org/records/17847399))

DOI: https://doi.org/10.5281/zenodo.17847399

Keywords: diversity threshold, emergent systems, incommensurability, phase transition, world-formation, modality divergence, self-organization, complexity physics, evolutionary discontinuity

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