Work

The Mathematics of Hyperbolic Grading

Year: 2025

Type: article

Abstract: This document serves as the theoretical manual for the Hyperbolic Grading Simulator. We propose a rigorous unification of Item Response Theory (Psychometrics) and Special Relativity. By reinterpreting a grade not as a linear score but as a normalized expected payoff (velocity), we demonstrate an exact isomorphism between the Elo rating system and the geometry of Minkowski spacetime. We prove that while Elo competence $\theta$ behaves like an additive rapidity on a hyperbola, the observable grade $v$ is its stereographic projection onto a bounded segment.

Source: Zenodo (CERN European Organization for Nuclear Research)

DOI: 10.5281/zenodo.18394833

Author: PFAFF, Fabrice

Language: English

Topic: Psychometric Methodologies and Testing

Subfield: Management Science and Operations Research

Field: Decision Sciences

Domain: Social Sciences

Open Access status: green

OpenAlex ID: W7125775741

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