An Unbounded Gap between Minimum Degree and the Minor-Connectivity Ceiling

Let M12 be Mader's 12-vertex graph and let M12[Kbar_t] be its independent t-fold blow-up. For every integer t>=2, we prove the exact formula kappa*(M12[Kbar_t])=floor(9t/2). Since the minimum degree is 5t, the difference between minimum degree and the largest connectivity of a minor is ceil(t/2) and is therefore unbounded. This gives infinitely many counterexamples to Barát's conjectured universal additive-one bound. The proof combines an explicit uniform minor model with a torso localization, a three-factor branch-set quotient classification, and an anticomplete-shores connectivity formula. Status: Public Beta; internally verified candidate proof; external mathematical review pending.