The evaluation of Large Language Models (LLMs) over extended context windows requires mathematically rigorous frameworks to assess distributed information retention and anomaly detection. This paper formalizes the "Context Length -- Benchmarking" algorithm, a highly scalable synthetic data generator engineered by Sapiens Technology. We propose a strict topological mapping of lexical tokens to an arbitrarily defined dimensional space N, utilizing a modulo-periodic continuation operator to ensure precise context boundaries. We subsequently introduce a stochastic noise injection mechanism, conceptualized as a discrete structural anomaly drawn from a uniform distribution, embedded completely uniformly across the text vector space. The evaluation task is mathematically formulated as an adversarial multiple-choice classification problem, compelling the model's self-attention mechanism to isolate the non-manifold perturbation. This methodology provides a quantifiable, unbiased environment to evaluate attention degradation, effectively addressing constraints inherent to contemporary long-context computational benchmarks.
Ben-Hur et al. (Sat,) studied this question.