The Collapse of Thinking: Explaining the Failure of Reasoning Models through Symbolic Motion Theory

This paper presents a symbolic motion-based framework to explain the reasoning collapse observed in frontier language models under compositional complexity. Recent empirical studies have shown that even advanced reasoning models fail abruptly when faced with multi-step logic tasks. This work introduces a set of symbolic constructs, directional motion (Δm), accumulated motion (ΣΔm), recursive compression (Rc), and entropy collapse (Eᴹ = 0)—to formalize the collapse not as a compute limitation, but as a structural failure in symbolic continuity. The framework reinterprets empirical collapse regimes (as observed in the Apple "Illusion of Thinking" paper) as failures in recursive motion survivability. A falsifiability section offers testable conditions for collapse prediction. The paper argues that survivability in reasoning systems depends on maintaining symbolic motion under recursive strain, and introduces entropy as the absence of structural deviation. This work forms part of a broader symbolic framework for cognitive persistence, collapse thresholds, and motion-based modeling of abstract systems. Copyright:© 2025 Michael Aaron Cody. This work is licensed under CC BY 4.0. All symbolic constructs and original models (Δm, ΣΔm, Rc, Eᴹ = 0, Cₜ, Kᵉ) are the intellectual property of the author and are publicly released for citation, study, and independent testing.