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Beneath Gauge

Seeking a relativistic quantum infrastructure for gauge physics, we analyze spacetime into three levels of quantum aggregation analogous to atoms, bonds and crystals. Quantum spacetime points with no extension make up more complex link units with microscopic extension, which make up networks with macroscopic extension. Such a multilevel quantum theory implies parastatistics for the lowest level entities without additional physical assumptions. Any hypercubical vacuum mode with off-diagonal long-range order that is covariant under $\POINCARE$ also has bonus internal symmetries somewhat like those of the standard model. A vacuum made with the dipole link proposed earlier has too much symmetry. A quadrupole link solves this problem.