The structure of the particulate realm is infused with the same themes as the behavioral realm: economy and symmetry. The fundamental structure of the physical realm is the wave, which is infused with the symmetry of balanced displacements about an equilibrium surface. Quantum mechanical waves, which model elementary particles, are indirectly physical as they are waves in complex-numbers space (e.g., Hilbert space). Although quantum mechanical waves exist in an indirectly physical space they are "real" nonetheless. 

Economy manifests itself in nature’s use of structural duality when duality will suffice and triality when it will not. After the Big Bang, the universe’s particulate realm began evolving towards complexity. The diffusion of energy coupled with field splitting phase transitions unfurled the universe’s stable particulate building blocks. As best as can be understood this process occurred in the simplest way, which was also the most economical way. The degree of structural and behavioral complexity required of the particulate building blocks is the minimum required for physical reality to self-assemble into life. This complexity in its entirety is embedded into the supraintelligent design.

Electromagnetic waves, which comprise coupled oscillating electric and magnetic waves, exist as a result of nature’s promotion of the magnetic field into perfect symmetry with the electric field in electromagnetic radiation.

Nature’s set of structural primitives arise about existential neutrality, which is reflective of the primordial symmetry that lies at the foundation of form-wise reality. Elementary particles arise from (both vacuum and non-vacuum) energy as reciprocally symmetric excitations of unstructured-energy into particle and antiparticle pairs. All particles are excitations of their field substrate and possess the reciprocal bipolar symmetry of the wave-packet. Charges are arrayed in a reciprocally symmetric way about neutrality: electric charge is exactly balanced (across the universe) into positive and negative, weak-isospin charge is arrayed about neutrality usually taking the values +½ or -½ in structure particles and +1, 0, or -1 in weak force particles, and color charge is arrayed about neutrality taking the values of red, green, and blue in a way that averagely adds to white ó charge neutrality. All charge polarizations sum to zero over the universe, which preserves the balance that preceded the charge’s form-wise existence. The preservation of the potential to return to the absence of charge—if all charges were overlaid and combined—is the meaning of the preservation of existential neutrality.

The foundation of matter's structure, which are the atomic orbitals are structures whose spatial extent and distribution is determined by symmetry constraints.