Magnetism as Topological Alignment

Standard quantum mechanics models spin as a continuous vector residing within an infinite-dimensional Hilbert space, frameworking ferromagnetism as the macroscopic alignment of these vectors via the continuous exchange interaction. We propose a radical ontological shift within the paradigm of Computational Finitism: spin is a discrete, geometric orientation of the Fano plane localized within the Planck voxel. Specifically, vehicular spin corresponds to the activation of one of the six peripheral causal channels (mapped to Modulo-9 states 1-6), derived from the Fano-driven 1+2+3 gauge branching that generates emergent 3D spacetime dimensions. Through rigorous 2D cellular automata simulations under varying thermal noise parameters (implemented as perturbations within the Topological Redundancy Buffer), we demonstrate the emergence of spontaneous symmetry breaking without infinite-dimensional manifolds. At low noise scales (T=0.02), localized Fano-Check majority rules dominate, driving the lattice into a globally synchronized computational limit cycle characterized by ~ 95% net macroscopic magnetization. Conversely, high-noise configurations at T=0.35 overwhelm the error-correcting capacity of the substrate, generating a disordered, high-entropy paramagnetic mosaic. Furthermore, we show that magnetic domain walls are not regions of continuous spatial rotation, which is topologically forbidden within a finite alphabet, but are discrete boundaries mediated by the Topological Redundancy Buffer (states 8 and 9) acting as shock absorbers for structural topological friction. By replacing infinite field potentials with finite topological saturation and synchronized modular updates, we offer a parameter-free, falsifiable mechanism for magnetism