From Probabilistic Generation to Physical Reasoning: Semantic Field Dynamics and Geometric Stabilization for Trustworthy AI

Title: From Probabilistic Generation to Physical Reasoning: Semantic Field Dynamics and Geometric Stabilization for Trustworthy AI Abstract: This paper proposes a paradigm shift in artificial intelligence from probabilistic token generation toward physically constrained reasoning to address systemic risks such as hallucinations and semantic inconsistencies in Large Language Models (LLMs). While existing LLMs achieve linguistic fluency, their reliance on stochastic prediction lacks the structural integrity required for trustworthy social infrastructure in fields like law, medicine, and governance. We introduce "Narrative Physics," a formal framework that treats meaning as a dynamical field governed by energy minimization, causal continuity, and geometric stability. Within this framework, narratives are modeled as structured state trajectories inside an informational potential field rather than memoryless Markov processes. To operationalize this, we present NOMOS (Neural Operative Meaning Optimization System), an architecture that detects semantic contradictions as localized energy spikes—termed Contradiction Field Intensity (CFI)—and repairs them through consistency-driven projection dynamics. Key Highlights: NOMOS Architecture: A next-generation reasoning system that prioritizes physically admissible semantic transitions over statistical plausibility. Honest Infrastructural Brake: A principled refusal mechanism that allows AI to autonomously suspend generation when semantic uncertainty exceeds coherence thresholds. Empirical Validation: Evaluations using 1,733 real-world semantic states demonstrate that NOMOS maintains orders-of-magnitude greater geometric stability (mean improvement: ~1.8x; peak ratio: 460x under extreme noise) compared to conventional LLMs. Human Alignment: Experiments achieved perfect inter-rater agreement ($\kappa = 1.000$) for causal and structural consistency constraints. Information Crystallization: Discovery of a phase transition phenomenon in social information space where informational entropy collapses into consensus structures at a critical threshold ($T_c \approx 0.227$). This work argues that the transition to "Gravitational Intelligence"—AI capable of preserving causal memory and structural honesty—is the foundational step toward deploying trustworthy autonomous intelligence within human society.