The Inevitable Limits of Adaptive Systems: A Structural Theory of Drift, Entropy, and Survival Horizons

This work develops a structural theory of the inevitable limits governing long-horizon adaptive systems. It demonstrates that drift, entropy growth, irreversibility, loss of causal trace, structural asymmetry, latent residual accumulation, and internal time depletion are not implementation defects, but unavoidable consequences of sustained directed interaction under finite resources. The theory establishes a fundamental decoupling between action-level optimization and identity preservation. It shows that admissible behavior, bounded error, stability, and reward maximization are insufficient to guarantee long-horizon viability. Survival is constrained by structural limits orthogonal to control accuracy and short-horizon performance. The work is formulated as a compact axiomatic and theorem-based framework, independent of any specific algorithm, controller, or learning mechanism. It provides a conceptual foundation for analyzing long-horizon failure modes, regime transitions, and coherence collapse in adaptive systems, and serves as prior art for coherence-preserving architectures without disclosing implementation details.