Conscious Realism posits a fundamental reality composed of a discrete Markovian agent network. To map this pre-geometric graph to relativistic spacetime, we cannot rely on arbitrary lattice structures that introduce anisotropic ether frames. We rigorously derive the continuum limit of the network using the spectral properties of the graph Laplacian. By applying the Lieb-Robinson theorem to the network's transition matrices, we mathematically prove that an effective speed limit $c$ emerges for information propagation. As the density of the network approaches the continuum limit, the discrete wave equations governed by the Laplacian organically recover local Lorentz symmetry, independent of any preferred coordinate frame.
Deriving relativity from discrete graphs requires avoiding the preferred frame problem. We transition from tracking explicit edges to analyzing the spectral diffusion of information across the graph.
Let the network be an undirected graph $G = (V, E)$. Information diffusion is governed by the graph Laplacian $\mathcal{L} = D - A$, where $D$ is the degree matrix and $A$ the adjacency matrix.
In the continuum limit, the discrete equation $\frac{\partial^2 \psi}{\partial t^2} = -\mathcal{L}\psi$ maps directly to the continuous wave equation $\square \psi = 0$.
Lorentz invariance is the macroscopic symmetry of the Lieb-Robinson bounds operating over the graph Laplacian. Relativity is fully recoverable from discrete Conscious Agents.
