Perverse Schober Structures for Conifold Degenerations

We study a one–parameter degeneration of Calabi–Yau threefolds whose central fiber contains a single ordinary double point. Using the nearby and vanishing cycle formalism, we construct a canonical perverse object on the singular fiber obtained from the variation morphism between vanishing and nearby cycles. We show that this object extends the constant perverse sheaf on the smooth locus and differs from the intersection complex by a singlerank–one contribution supported at the node.  The resulting perverse sheaf therefore isolates the vanishing–cycle contribution associated with the conifold degeneration. We then explain how this object naturally reflects the same rank–one phenomenon that appears categorically through spherical Picard–Lefschetz monodromy.  In this sense the perverse object constructed here provides a natural sheaf–theoretic comparison object for the decategorified effect of spherical twists arising from the degeneration.