Laws of the Φ-Invariant Theory: Decomposition, Conservation, and Carrier-Dependent Manifestation

Invariant identity underlies operational and physical systems. This paper establishesthe fundamental laws governing invariant identity, denoted by Φ, independent of carrierconfiguration. The theory is defined by three structural relations:Φ =nXi=1ϕi(C) dΦdC = 0 M (C) = P (C)ΦThese three laws define identity decomposition, structural conservation, and carrier-dependent manifestation. From these relations, invariant identity is established as theconserved structural quantity underlying observable systems.Keywords: Invariant identity, structural conservation, carrier configuration, Φ-invarianttheory, decomposition.