Goldman primes and higher cyclic presentations for the small finitistic dimension

Let $R$ be a commutative ring and let $fPD(R)$ be its small finitistic dimension in the sense of Glaz. We study two ways in which Koszul grade can escape a restricted homological test. For a polynomial extension, we prove that if $R$ is Noetherian, the maximal ideals of $R[X]$ detect exactly the Gol