Assertion–Dismantling Cycles in Adaptive Systems: A Constraint-Network Framework

Description:

This paper develops a mathematical framework for understanding cyclic dynamics in adaptive systems—the alternation between phases of structural consolidation (assertion) and structural release (dismantling). We model systems as networks of constraints that regulate accessible configurations and analyze how constraint density affects adaptability and fragility.

Key Results:

• Theorem 1: For systems with linear constraints in generic position, accessible state space contracts exponentially with constraint density
• Theorem 2: For Gaussian random fitness landscapes, adaptive capacity decays with constraint density
• Theorem 3: Under environmental volatility above a computable threshold, cyclic strategies dominate all static strategies

The framework is validated through a complete toy model (n=10 dimensional linear constraint network) with explicit numerical computation of critical thresholds, fragility scaling exponents (β ≈ 1.4), and optimal cycle parameters demonstrating 6% fitness improvement over static strategies.

Applications: The framework generates testable hypotheses for cognitive belief systems, organizational structures, and cultural norms—suggesting that what is commonly labeled "self-destruction" may be a structurally beneficial maintenance mechanism rather than pathology.

Keywords: adaptive systems, constraint networks, structural dynamics, resilience, phase transitions, self-organization, complex systems, dynamical systems