can tear near the cone, and its topology can change. These singular target spaces, i.e. conifolds, correspond to certain mild degenerations of algebraic varieties which appear in a large class of supersymmetric theories, including superstring theory (E. Witten, 1982). Essentially, different cohomology theories on singular target spaces yield different results thereby making it difficult to determine which theory physics may favor. Several important characteristics of the cohomology, which correspond to the massless fields, are based on general properties of field theories, specifically, the (2,2)-supersymmetric 2-dimensional world-sheet field theories. These properties, known as the Kähler package (T. Hubsch, 1992), should hold for singular and smooth target spaces. Paul Green and Tristan Hubsch (P. Green & T. Hubsch, 1988) determined that the manner in which you move between singular CY target spaces require moving through either a small resolution or deformation of the singularity (T. Hubsch, 1992) and called it the 'conifold transition'. Tristan Hubsch (T. Hubsch, 1997) conjectured what this cohomology theory should be for singular target spaces. Tristan Hubsch and Abdul Rahman (T. Hubsch and A. Rahman, 2005) worked to solve the Hubsch conjecture by analyzing the non-transversal case of Witten's gauged linear sigma model (E. Witten, 1993) which induces a stratification of these algebraic varieties (termed the ground state variety) in the case of isolated conical singularities. Under certain conditions it was determined that this ground state variety was a conifold (P. Green & T.Hubsch, 1988; T. Hubsch, 1992) with isolated conic singularities over a certain base with a 1-dimensional exocurve (termed exo-strata) attached at each singular point. T. Hubsch and A. Rahman determined the (co)-homology of this ground state variety in all dimensions, found it compatible with Mirror symmetry and String Theory but found an obstruction in the middle dimension (T. Hubsch and A. Rahman, 2005). This obstruction required revisiting Hubsch's conjecture of a Stringy Singular Cohomology (T. Hubsch, 1997). In the winter of 2002, T. Hubsch and A. Rahman met with R.M. Goresky to discuss this obstruction and in discussions between R.M. Goresky and R. MacPherson, R. MacPherson made the observation that there was such a perverse sheaf that could have the cohomology that satisfied Hubsch's conjecture and resolved the obstruction. R.M. Goresky and T. Hubsch advised A. Rahman's Ph.D. dissertation on the construction of a self-dual perverse sheaf (A. Rahman, 2009) using the zig-zag construction of MacPherson-Vilonen (R. MacPherson & K. Vilonen, 1986). This perverse sheaf