Shevelev's bound for the normalized maximal minor increment

Write

$$\rho^{(i)}=\lambda_i n_{i-1},\qquad \lambda_i\geq1.$$

A normalized-increment bound conjecture asserts that, for every $i\geq6$,

$$\lambda_i\leq\frac54.$$

The paper uses this proposed bound to derive the stated sufficient condition for infinitely many twin primes; the supplied source does not establish the bound.