Abstract: The Standard Model of particle physics describes the interactions of elementary particles with remarkable precision, yet the spectrum of particles itself—why are there three generations of fermions? Why do quarks have fractional charges? Why do right-handed particles not participate in weak interactions? —has remained a mystery. Based on the first principles of Space Ontology, we provide a purely geometric answer: all fermions of the Standard Model arise from the irreducible representations of the discrete spatial symmetry group 2T × C₃ at the Planck scale. Starting from the basic symmetries of the spatial orientation field equation, we independently derive the mathematical structures of the binary tetrahedral group 2T and the cyclic group C₃, and establish an exact mapping between the 21 irreducible representations and the 21 fermion types of the Standard Model (including chirality and color). This "Particle Periodic Table" naturally gives rise to new physical laws such as the charge-topology correspondence law, the confinement threshold law, and the coherence cascade law. The table also predicts 10 "void" particles/states, among which the mass prediction for the doubly charmed baryon Ξcc⁺ has been confirmed by the experimental results published by the LHCb collaboration in 2026. We further reveal four deep unifying laws that run through the Particle Periodic Table (the law of coherence depth, the topological-charge–charge correspondence law, the confinement threshold law, and the coherence cascade law), and extend the table toward high-energy completion—extracting 3 additional high-energy voids from the representation theory of 2I × C₃, which belong to the Grand Unification energy scale. This paper is the fourth in the first series (17 papers total) of Space Ontology, demonstrating that the Standard Model spectrum is not arbitrary input but the necessary projection of deeper space geometry and algebra.
Yunjie Qiu (Fri,) studied this question.