Measuring Backdoor Persistence in Post-trained Large Language Models: The Cyber Resilience Scaling Coefficient

Data-poisoning backdoors implanted during supervised fine-tuning of large language models persist through subsequent clean training, yet the field lacks a bounded, scale-normalized metric for quantifying and comparing this persistence across architectures and training regimes. We propose the Cyber Resilience Scaling Coefficient (CRSC), a dimensionless score in [0, 1] that combines output-distribution shift, inter-layer gradient drift, and near-trigger semantic generalization under explicit model-scale and temporal normalization. To evaluate the metric, we conduct two controlled experiments on a sub-1B instruction-tuned model: a poison-density sweep and a sequential clean-continuation trajectory, both on a domain-specific legal corpus under fully reproducible conditions. CRSC increases monotonically with poison injection rate and remains at high risk across all sanitization checkpoints, with near-trigger semantic coherence saturating rather than decaying under out-of-domain retraining. These results demonstrate the measurement feasibility of CRSC as a complement to existing evaluation signals and motivate multi-architecture, multi-seed validation as the next research step.