When Errors Become Irreversible: Closure, Aggregation, and Temporal Dynamics in AI Systems

This paper studies a structural boundary in AI systems that precedes correctness: the loss of revisability.

It distinguishes localized error (correctable) from distributed error (embedded in the trajectory) and defines closure as the transition where a system can no longer meaningfully revise its path under constraint.

A six-lab empirical program shows that identical perturbations behave differently depending on timing: before closure they remain correctable, after closure they become structurally embedded. Across recursive loops, multi-agent systems, and math tasks, raw reinjection leads to early closure and drift, while sanitized reinjection preserves openness and enables correction.

The paper introduces Aggregation-Induced Error (AIE) as a mechanism by which independent constraint violations lose separability and become distributed across a coherent but invalid trajectory.

A minimal reproduction script demonstrating the closure-versus-openness phenomenon is available:
https://github.com/GuardianAI1/closure-repro

The central claim: irreversibility is not a property of error, but of trajectories that can no longer reopen under constraint.