ARQUITETURA FORMAL E DINÂMICA DE DECISÃO DO SISTEMA MPHD: Uma Abordagem Topológica para Monitorização da Estabilidade Inferencial em Modelos de Linguagem

This work presents the Propedeutic-Hermeneutic Displacement Method (MPHD), a theoretical and experimental framework designed to analyze and monitor inferential stability in large language models (LLMs). The central hypothesis of the MPHD is that hallucinations in autoregressive models are not purely stochastic artifacts, but rather topological transitions between regimes of structural stability and instability in a nonlinear decision landscape. The inferential process is formalized as the evolution of a state variable governed by a potential function V(x), inspired by catastrophe theory and nonlinear dynamical systems. The framework introduces a monitoring architecture referred to as the Hermeneutic Satellite, an out-of-band system that tracks latent signals derived from logits during text generation. From these signals, operational metrics are defined, including the Decision Health Score (DHS) and the instability index (Δ*), which enable early detection of structural degradation prior to the manifestation of hallucinated outputs. Experimental validation demonstrates the existence of early-warning signals, consistent with the phenomenon of critical slowing down, including increased variance, reduced logit gap, and rising entropy. These indicators reveal a temporal anticipation window—typically between 3 and 8 tokens—within which preventive intervention becomes feasible. The MPHD reframes AI safety as a problem of topological metrology rather than purely probabilistic estimation, emphasizing the importance of structural stability over instantaneous likelihood. This shift suggests a new paradigm for the development of resilient AI systems, where reliability emerges from continuous monitoring of the inferential geometry rather than from the elimination of uncertainty. This work contributes to the intersection of artificial intelligence safety, nonlinear dynamics, and applied topology, and proposes a scalable approach for enhancing robustness in future generations of intelligent systems, including those approaching Artificial General Intelligence (AGI).