Robin's Inequality for 74-Free Integers

We give an explicit conditional proof of Robin’s inequality for integers (n>5040) with (v_2(n)≤ 73), a class containing all 74-free integers. The argument combines an exact decomposition on primorial intervals, a cancellation in a normalized Mertens product, an integrated formula for the Chebyshev function, a weighted prime-block estimate, and explicit zero-density bounds. Its analytic input includes the proposed zero-free half-plane ( s>7/8) for the Riemann zeta function. The required finite interval comparisons are certified by exact rational arithmetic in the executable appendix.