Why do shortcuts in Feynman integral calculations give conflicting answers?

Computing Feynman integrals—essential for predicting particle collisions—is expensive. The spanning cuts method cuts corners by discarding terms thought to vanish, but this produces contradictory answers across different calculations. The culprit: certain singularities actually prevent those terms from disappearing, leaving finite errors behind. The authors trace the mechanism and provide an algorithm to detect these hidden traps.