Emergent Reasoning in Large Language Models: Soft Unification, Constraint Mechanisms, and Computational Traversal

This paper proposes a unified formal framework for understanding how Large Language Models (LLMs) produce structured inference through topology-constrained traversal within a learned semantic manifold. The Transformer architecture is reinterpreted as a dynamical system whose core computation is a preferred direction function — an instance of local preorder traversal on a constraint manifold — implicitly implemented by attention. Context induces constraint sets; embeddings give rise to conceptual topology; attention performs soft, graded unification analogous to symbolic unification; and trajectories over the manifold follow structured flows that manifest as reasoning. Embedding clusters form proto-symbolic attractor regions — Markov objects with approximate conditional independence boundaries — enabling symbolic-like behavior to emerge from continuous computations. A multi-causal hallucination taxonomy identifies four structural failure modes: sparse constraint regions, wrong-attractor capture, competing attractor interference, and know-generate gaps. A two-process model of chain-of-thought distinguishes reasoning traversal from verbalization traversal, with variable fidelity between them. Version 3 incorporates backflows from the Constraint-Emergence Ontology, including: local preorder traversal as a universal computational primitive; the Constraint Functor formalizing the LLM-physics structural correspondence via category theory; and an empirical correspondence section mapping 28 citations from 2023–2025 mechanistic interpretability, representation geometry, and reasoning faithfulness research to the framework's core claims.