This paper establishes the AMetric Boundary as a necessary division between admissible representational structure and illicit metric reanchoring. The boundary marks the point beyond which quantities, measures, probabilities, or gradients cannot be meaningfully introduced without violating admissibility. The analysis demonstrates that attempts to ground admissibility in metric notions—such as information measures, probabilistic weights, distances, or optimization criteria—implicitly cross the AMetric Boundary and reintroduce structure that admissibility explicitly forbids. When these moves are excluded, admissibility remains strictly non-metric and fail-closed. The result clarifies why admissibility cannot be quantified, tuned, or optimized, and why any metricization of foundational constraints leads to standing failure. The paper introduces no evaluative scales or formal metrics. It records the AMetric Boundary as a structural necessity governing the admissibility constraint map, not as a methodological convention or modeling choice.