Fragmented Evolution Theory (FET) is a decision-structural framework for analyzing when and under what conditions a system can be said to “evolve” at a given scale. Rather than assuming that evolution necessarily occurs, the theory treats decidable difference as the sole decision gate. Evolution is defined as the persistence of decidable differences over time intervals; dead loops are characterized as absorbing states in which all future differences collapse to zero; fragmentation is defined as the existence of a positive lower bound on differences, structurally excluding terminal attractors. This Zenodo record contains: Formal theoretical foundationsFragmented Evolution Theory — A Formal Structure Based on Scale-Dependent DifferencesA rigorous, scale-relative decision framework defining evolution, dead loops, fragmentation, complexity, researchability, and irreversibility without assuming optimization, progress, continuity, or monotonic growth. Defensive formalization and threat modelingAttack Surface, Threat Models, and Falsifiability BoundariesA systematic enumeration of valid and invalid attack vectors, clarifying falsifiability conditions, structural boundaries, and why common objections (periodicity, reversibility, non-metric differences, extreme scales, self-reference) do not constitute counterexamples. Reproducible finite-model experimental verificationFinite-Model Experimental Verification of Fragmented Evolution TheoryAn exhaustive parameter-sweep experiment over 828 finite model configurations, testing evolution, dead loops, fragmentation, scale operators, decisional thresholds, and internal transformations.No counterexamples were found to the core implications: DeadLoop ⇒ ¬Evolving Fragmented ⇒ ¬DeadLoop Executable verification codePython scripts used for model enumeration, predicate checking, and counterexample search, enabling independent reproduction and extension of the experiments. Scope and boundaries The theory is intentionally decision-theoretic rather than dynamical. It does not claim: that evolution necessarily occurs, that evolution implies progress, that complexity must increase, or that a unique correct scale exists. Instead, it provides a reusable formal structure for: system classification, boundary annotation, cross-scale comparison, and falsifiable structural reasoning. The framework is applicable to finite, continuous, and stochastic systems under explicit scale and decidability assumptions, while clearly stating where further extensions (e.g. measure-theoretic or categorical formulations) may be required.
xie kaifan (Tue,) studied this question.