A proof of the "Axis of Evil Theorem" for distinct points

In this work we provide a complete and constructive proof of Marinari-Mora’s “Axis of Evil Theorem”. Given a finite set X ⊆ A^n(k) of distinct points and fixed on P := k[x1 , ..., xn ] the lexicographical order, the theorem states that one can produce a “linear” factorization for a minimal Groebner basis of the ideal I(X) of P, via interpolation and a combinatorial algorithm. We display here the related algorithm showing its termination and correctness.