What question did this study set out to answer?

The aim is to present a unified measurement theory for machine cognition that is both invariant and adaptable.

April 17, 2026Open Access

NCAP-10: A Unified, Invariant, Geometry-Based Measurement Theory for Machine Cognition

Puntos clave

The aim is to present a unified measurement theory for machine cognition that is both invariant and adaptable.
Defines a manifold-valued object encompassing cognitive scores and difficulty coordinates.
Utilizes principles from information geometry and scaling law research.
Develops invariance axioms to support the framework.
Establishes the final mathematical form of NCAP-10.
Demonstrates the framework's commercial utility for evaluating diverse AI systems.

Resumen

NCAP-10 is a closed-form, architecture-invariant measurement theory for machine cognition. It defines a single manifold-valued object N = (X,p(m | d),gI,T ) from which all cognitive scores, difficulty coordinates, and invariants are derived. The framework draws on modern information geometry, scaling-law research, alignment and safety literature, and neuromorphic computation. This paper presents the final closed mathematical form of NCAP-10, its invariance axioms, and its commercial utility for evaluating heterogeneous AI systems.

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