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

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

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Published July 23, 2026

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

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Jonathan Michael Langford

Mlangford75@protonmail.com

Description

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.

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Publication:

10.5281/zenodo.21502824

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Keywords and subjects

Keywords

ASI

AGI

Artificial Superintelligence

ASI Benchmark

LLM Evaluation

Fluid Intelligence

Langford Coverage

Chinese Remainder Theorem

Singleton-Class Theorem

EuroSciVoc

Combinatorics

MeSH

Benchmarking/methods

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DOI

10.5281/zenodo.21502973

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Resource type<br>Working paper

Publisher<br>Zenodo

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English

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Creative Commons Attribution 4.0 International

The Creative Commons Attribution license allows re-distribution and re-use of a licensed work on the condition that the creator is appropriately credited.

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Copyright (c) 2026 Jonathan Michael Langford

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Created

July 23, 2026

Modified

July 23, 2026

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