Beyond ARC and GSM: Langford Coverage as a Benchmark for ASI

As foundational models approach Artificial Superintelligence (ASI), standard intelligence evaluations like the Massive Multitask Language Understanding (MMLU), Grade School Math 8K (GSM8K), and the Abstraction and Reasoning Corpus (ARC-AGI) fail to adequately differentiate between true algorithmic reasoning and sophisticated statistical correlation. We introduce "Langford Coverage," an infinite, procedurally generated evaluation suite based on the Toroidal Residue-Covering Benchmark (TRCB). By mapping arithmetic intervals to multi-dimensional punctured toroidal grids via the Chinese Remainder Theorem, this benchmark scales the canonical search space beyond physical limits, surpassing $10^{119}$ states by the 17th prime modulus. Furthermore, the benchmark utilizes a Dynamic Entry Protocol, forcing agents to balance computational risk against reward. Langford Coverage provides a mathematically rigorous, physically un-cheatable protocol to verify whether an AI model possesses the fluid intelligence and theorem-discovery capabilities requisite for ASI.