GEOMETRY OF SURVIVAL (v1.0) Testable Stability Framework for Civilization Under Algorithmic Acceleration

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.