Chain-Space Theory: A Discrete Network Model of Space with Chain Tension

We propose Chain-Space Theory (CST), a model in which space is a discrete network of nodes and links below the Planck scale, with geometry defined entirely by link lengths. Curvature is the Regge deficit angle, and the dynamics follow from the Regge action supplemented by an elastic chain-tension term that fixes a preferred link length. The new elements are this tension term, its weighting by an invariant four-volume so that it selects no preferred frame, and two numerical tests. On geodesic spheres of up to 10,242 nodes, the deficit-angle curvature converges in the mean in inverse proportion to the number of nodes, but the five-valent nodes keep a pointwise error of 14.6%. For the three-dimensional wave operator, a periodic random network of 8000 nodes has a directional anisotropy 37 times smaller than a cubic lattice of equal density, falling as N^(-1.08) against N^(-0.66) for N nodes, while the isotropic quadratic correction to the dispersion relation persists with a coefficient about 1.7 times larger. A uniform stretch of the network has the sign of the observed cosmological constant but relaxes to zero, so its value is not predicted. Open problems are the time-evolution rule, the Bianchi identities on the lattice, fermion doubling, leakage of Lorentz violation to low energy, and the value of the cosmological constant.