This manuscript develops a mathematically disciplined version of the electromagnetic motherboard hypothesis. It does not assert that all gravitational curvature is electromagnetic in origin. Instead, it advances a focused and testable claim: in a wide class of physically important systems—plasmas, jets, accretion flows, magnetospheres, radiation fields, and atomic structure—electromagnetic fields act as primary organizers of morphology, transport, stability, and stress-energy. The paper reviews the exact role of electromagnetism in general relativity, quantum electrodynamics, magnetohydrodynamics, and black-hole electrodynamics, emphasizing the regimes in which electromagnetic stress-energy measurably influences curvature and dynamics. It then develops a cross-scale pattern taxonomy—orbit, rotation, resonance, spiral, vortex, and jet—and shows how these motifs arise naturally in electromagnetic and MHD systems and can be inherited by gravitationally bound systems through shared differential equations and stability conditions. The manuscript concludes with falsifiable, quantitative research questions concerning electromagnetic influence on jet power, near-horizon polarization, spiral-galaxy morphology, motif statistics in GRMHD simulations, and curvature sourced by electromagnetic energy density in EM-dominated regimes. The result is a constrained, mathematically grounded research program that identifies where electromagnetic structure plays a decisive architectural role in nature, without claiming a universal unification.