Plane and Branch Universe: Definitions, Differences and Structural Rules — A Unified Account from Planetary–Satellite Systems to the Milky Way

Abstract: This paper consolidates prior discussions of the two core concepts of the Taiyin–Deng cosmology—"Plane" (位面) and "Branch Universe" (支系宇宙)—and provides a unified formulation and unified definitions. The Plane corresponds to the cosmological structural model and is defined as "1 central primary body + N discrete orbital shells ∪ the set of bodies on the shells"; it specifies structure and star domain, but not mass. The Branch Universe corresponds to cosmological ontology—it is totality, set, and entity existence—and is defined as "the subordinate Plane governed by a node celestial body as parent star, together with all its contents"; it specifies structure, entities, star domain, mass, and proper motion. Three definitions determine a Branch Universe: the Branch Ancestor Star (Primordial Node Body) sets the origin, the deepest pulse system sets the depth, and the first Plane sets the boundary. A unified convention for mass is given: the Primordial Node Body mass is the mass before reproduction, while the Branch Universe total mass is the current ancestor-star mass plus the sum of child-star masses at all levels; the two are equal when material ejection and surface dust loss are neglected. The paper further distinguishes the Plane-observation perspective—which treats a Branch Universe as equivalent to a Primordial Node Body—from the cosmological-ontology perspective—which treats terminal bodies as equivalent to zero-child Branch Universes; the two perspectives are inverse operations of unfolding and compression. The paper also clarifies key mechanisms: "one orbit, one litter ≠ one orbit, one body"; the child-star parent body is not the parent star; and magnetic tearing determines the number of bodies on an orbit. Using planetary–satellite systems, the Solar System, and the Milky Way as three levels, the paper shows that each is both a Plane and a Branch Universe, and provides a summary table of depth, boundary, and proper-motion attribution.