ABSTRACTThis paper advances a testable, stability-centered framework for analyzing and governingcomplex adaptive systems under conditions of accelerating algorithmic dynamics. Buildingupon the Lukin Index (Q) and Adaptive Stability Geometry (ASG), we formalize a unifiedcriterion for system survival based on the relationship between nonlinearity, environmentalinstability, and corrective capacity.We demonstrate that collapse is not a linear threshold phenomenon, but a nonlinear phasetransition characterized by cubic divergence near critical boundaries. This behaviorproduces observable precursors that can be measured prior to systemic failure.The framework generates three classes of falsifiable predictions:1. Nonlinear instability acceleration near criticality2. Breakdown of temporal synchronization between decision speed and adaptationcapacity3. Delegitimization as a measurable decline in functional stabilization outputA minimal simulation confirms that systems governed by instability minimization maintainbounded trajectories under noise, while unconstrained systems exhibit rapid divergence.Finally, we introduce a phase-space representation linking Lukin Index (Q) and ASGinvariant (G), providing a geometric classification of stability regimes.
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Roman Lukin (Fri,) studied this question.
www.synapsesocial.com/papers/69d1fceba79560c99a0a296c — DOI: https://doi.org/10.5281/zenodo.19394598
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Roman Lukin
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