The Balance Field Equation as a Recursive World Formula

This preprint specifies the Balance–Field Equation (BFG) as a finite, stratified recursive operator dynamics on unitary equivalence classes. Its declared state is Ξ=(K,ρF,ρW,Y,P). Spectral selection, canonical polar transport, an endogenous positive metric, formation-dependent loads, an ambient reduced singular-value decomposition, R4 realignment, formation inheritance and a rank-one seed rule define a unique successor class or a named terminal outcome. The complete analysis operator acts on the ambient input space, not only on the selected carrier. This choice has restrictive consequences: R4 is isometric on the selected carrier, its witness mass is exactly one, every nonterminal successor satisfies 0<Y_+