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ZENODO
Preprint . 2026
License: CC BY
Data sources: ZENODO
ZENODO
Preprint . 2026
License: CC BY
Data sources: Datacite
ZENODO
Preprint . 2026
License: CC BY
Data sources: Datacite
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State-Expanding Systems: A Constraint-Limited Theory of Novelty Growth

Authors: Costolo, Michael;

State-Expanding Systems: A Constraint-Limited Theory of Novelty Growth

Abstract

This paper introduces a constraint-limited model of combinatorial growth that examines how feasibility scales with increasing system dimensionality. The framework analyzes the balance between expanding possibility spaces and constraint structures that prune feasible configurations. The model shows that when feasible configurations grow as c^n within a combinatorial space of size 2^n, the feasible fraction collapses for constant c < 2. Sustained novelty generation therefore requires c(n) to approach the combinatorial base, producing a narrow “complexity corridor” between regimes of trivial repetition and combinatorial sparsity. The paper derives the analytic structure of this corridor and explores it through numerical simulations and visualizations. The results suggest a possible structural explanation for why complex systems may emerge only within a narrow range where combinatorial expansion and constraint relaxation operate at comparable scales. The manuscript includes the full mathematical derivation, simulation results, and discussion of implications for complex systems.

Keywords

novelty generation, combinatorial innovation, constraint dynamics, adjacent possible, emergence, state space expansion, state space growth, complexity

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
Average
Average