An Exact Support Certificate for the Finiteness of Cyclic 14-Roots

We give an exact computer-assisted proof that the standard cyclic 14-root equations have finitely many complex solutions. An infinite solution set would produce a balanced support pair for which two Fourier kernel vectors have prescribed complementary supports. We exclude all such pairs by checking 11,745 support orbits. Every exclusion is certified by a full-rank reduction over a finite field or by an exact row-space identity over a cyclotomic field. The same procedure verifies finiteness in the known cases of orders 6 and 10. A standalone checker and the certificates accompany the paper.