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The Catastrophic Paradox of Human Cognitive Frameworks in Large Language Model Evaluation: A Comprehensive Empirical Analysis of the CHC-LLM Incompatibility

Mohan Reddy

TL;DR

This study exposes a fundamental mismatch between human psychometric frameworks, exemplified by the Cattell-Horn-Carroll theory, and Large Language Model evaluation. By applying dual scoring (Binary Accuracy and LLM-as-Judge) and psychometric transformations (CTT and IRT) to nine frontier models, it reveals a catastrophic paradox: models with high simulated IQ scores exhibit near-zero performance on crystallized knowledge under exact-match metrics, while judge-based assessments diverge dramatically (r = 0.175, p < 0.001, n = 1800). The Crystallized Knowledge Paradox, where 100% binary accuracy coexists with 25–62% judge scores, together with a Paradox Severity Index PSI = |Judge_acc − Binary_acc| × (IQ_CT T)/100, argues that human-centric evaluation is misaligned with machine cognition. The results motivate abandoning anthropomorphic metrics in favor of native AI evaluation frameworks that focus on capabilities, architecture-aware testing, and information-theoretic measures, acknowledging the epistemic limits of cross-substrate assessment.

Abstract

This investigation presents an empirical analysis of the incompatibility between human psychometric frameworks and Large Language Model evaluation. Through systematic assessment of nine frontier models including GPT-5, Claude Opus 4.1, and Gemini 3 Pro Preview using the Cattell-Horn-Carroll theory of intelligence, we identify a paradox that challenges the foundations of cross-substrate cognitive evaluation. Our results show that models achieving above-average human IQ scores ranging from 85.0 to 121.4 simultaneously exhibit binary accuracy rates approaching zero on crystallized knowledge tasks, with an overall judge-binary correlation of r = 0.175 (p = 0.001, n = 1800). This disconnect appears most strongly in the crystallized intelligence domain, where every evaluated model achieved perfect binary accuracy while judge scores ranged from 25 to 62 percent, which cannot occur under valid measurement conditions. Using statistical analyses including Item Response Theory modeling, cross-vendor judge validation, and paradox severity indexing, we argue that this disconnect reflects a category error in applying biological cognitive architectures to transformer-based systems. The implications extend beyond methodology to challenge assumptions about intelligence, measurement, and anthropomorphic biases in AI evaluation. We propose a framework for developing native machine cognition assessments that recognize the non-human nature of artificial intelligence.

The Catastrophic Paradox of Human Cognitive Frameworks in Large Language Model Evaluation: A Comprehensive Empirical Analysis of the CHC-LLM Incompatibility

TL;DR

This study exposes a fundamental mismatch between human psychometric frameworks, exemplified by the Cattell-Horn-Carroll theory, and Large Language Model evaluation. By applying dual scoring (Binary Accuracy and LLM-as-Judge) and psychometric transformations (CTT and IRT) to nine frontier models, it reveals a catastrophic paradox: models with high simulated IQ scores exhibit near-zero performance on crystallized knowledge under exact-match metrics, while judge-based assessments diverge dramatically (r = 0.175, p < 0.001, n = 1800). The Crystallized Knowledge Paradox, where 100% binary accuracy coexists with 25–62% judge scores, together with a Paradox Severity Index PSI = |Judge_acc − Binary_acc| × (IQ_CT T)/100, argues that human-centric evaluation is misaligned with machine cognition. The results motivate abandoning anthropomorphic metrics in favor of native AI evaluation frameworks that focus on capabilities, architecture-aware testing, and information-theoretic measures, acknowledging the epistemic limits of cross-substrate assessment.

Abstract

This investigation presents an empirical analysis of the incompatibility between human psychometric frameworks and Large Language Model evaluation. Through systematic assessment of nine frontier models including GPT-5, Claude Opus 4.1, and Gemini 3 Pro Preview using the Cattell-Horn-Carroll theory of intelligence, we identify a paradox that challenges the foundations of cross-substrate cognitive evaluation. Our results show that models achieving above-average human IQ scores ranging from 85.0 to 121.4 simultaneously exhibit binary accuracy rates approaching zero on crystallized knowledge tasks, with an overall judge-binary correlation of r = 0.175 (p = 0.001, n = 1800). This disconnect appears most strongly in the crystallized intelligence domain, where every evaluated model achieved perfect binary accuracy while judge scores ranged from 25 to 62 percent, which cannot occur under valid measurement conditions. Using statistical analyses including Item Response Theory modeling, cross-vendor judge validation, and paradox severity indexing, we argue that this disconnect reflects a category error in applying biological cognitive architectures to transformer-based systems. The implications extend beyond methodology to challenge assumptions about intelligence, measurement, and anthropomorphic biases in AI evaluation. We propose a framework for developing native machine cognition assessments that recognize the non-human nature of artificial intelligence.

Paper Structure

This paper contains 32 sections, 2 theorems, 7 equations, 1 figure, 6 tables.

Table of Contents

  1. Introduction
  2. Theoretical Background
  3. Architectural Incompatibilities
  4. The Verbosity Paradox
  5. Methodology
  6. Dual Scoring Methodology
  7. Binary Accuracy Scoring
  8. LLM-as-Judge Evaluation
  9. Psychometric Transformation
  10. Classical Test Theory (CTT) Scoring
  11. Item Response Theory (IRT) Modeling
  12. Models Evaluated
  13. Rate Limiting and Error Handling
  14. Results
  15. Overall Performance Rankings
  16. ...and 17 more sections

Key Result

Theorem 1

Let $g_{\text{LLM}}$ represent the observed general factor in language models. Then: where: This decomposition shares no common factors with human $g$.

Figures (1)

  • Figure 1: The Crystallized Knowledge Paradox: Universal Perfect Binary Accuracy with Variable Judge Scores

Theorems & Definitions (3)

  • Theorem 1: Artificial G-Factor Decomposition
  • Remark 1: The Impossibility Theorem of Cross-Substrate Measurement
  • Proposition 2: The Cognitive Evaluation Paradox