Threshold-Affine Normal Form

Primitive recursive functions, recurrent ReLU computations, and threshold-affine normal forms are equivalent according to Theorem 14. Threshold-affine normal form uses affine maps and integer-coefficient tests controlled by a threshold function. LOOP programs are compiled into finite-dimensional integer states whose updates and control can be expressed using affine assignments and threshold gates. Threshold-affine normal form is described as the central mediator between LOOP-style recursion and bounded dynamical iteration.