Optimization-driven artificial intelligence systems routinely achieve strong performance on local alignment metrics while exporting costs across broader temporal, social, and epistemic scales. We formalize this failure mode as Locally Aligned, Globally Extractive (LAGEX) dynamics and argue that it arises from structural properties of optimization under incomplete multi-scale constraint representation rather than from mis-specified objectives or insufficient training data. We introduce Field REACHES, a constraint-based dynamical framework modeling alignment as a field-level property governed by coupled constraints across scales. We provide a formal characterization of LAGEX, analyze conditions under which local optimization fails to preserve global coherence, and derive falsifiable predictions distinguishing extractive from non-extractive trajectories. This work does not claim an alignment solution or empirical validation; it offers a formally grounded framework for detecting multi-scale externalities and delineating the architectural limits of interaction-layer alignment approaches. AI Contribution Statement: This paper was developed in iterative collaboration with Claude 4.6 (Anthropic), a stateless large language model used as a computational partner for mathematical formalization, structural drafting, verification, and editorial review. GPT 5.2 (OpenAI) was used for Red Teaming. The human author (MTK) takes full responsibility for all content, claims, and errors.