http://arxiv.org/abs/0710.1548 Propagation and interaction of chiral states in quantum gravity Lee Smolin, Yidun Wan 34 pages, 30 figures (Submitted on 5 Oct 2007) "We study the stability, propagation and interactions of braid states in models of quantum gravity in which the states are four-valent spin networks embedded in a topological three manifold and the evolution moves are given by the dual Pachner moves. There are results for both the framed and unframed case. We study simple braids made up of two nodes which share three edges, which are possibly braided and twisted. We find three classes of such braids, those which both interact and propagate, those that only propagate, and the majority that do neither." http://arxiv.org/abs/0710.1312 On Braid Excitations in Quantum Gravity Yidun Wan 24 pages, 16 figures, 5 tables (Submitted on 5 Oct 2007) "We propose a new notation for the states in some models of quantum gravity, namely 4-valent spin networks embedded in a topological three manifold. With the help of this notation, equivalence moves, namely translations and rotations, can be defined, which relate the projections of diffeomorphic embeddings of a spin network. Certain types of topological structures, viz 3-strand braids as local excitations of embedded spin networks, are defined and classified by means of the equivalence moves. This paper formulates a mathematical approach to the further research of particle-like excitations in quantum gravity."