GLOBAL CHEEGER-GORESKY-MACPHERSON FOR FUBINI-STUDY METRICS ON PROJECTIVE SIMPLE-EDGE SPACES

Let X ⊂ CP N be a complex projective variety whose singular locus is a smooth connected stratum Y , with simple-edge transverse type, and let g FS be the metric induced on Xreg by the ambient Fubini-Study metric. We show that (Xreg, g FS ) has wedge structure near Y with a canonical radial function and a smooth link fibration L → Y . Moreover, the argument is entirely domain-level: from the Fubini-Study wedge expansion we deduce the constantmultiplicity stability in the critical strip and hence a fully checkable Calderón boundary package. This geometric input implies, without any additional spectral stability hypothesis, that the wedge Hodge-de Rham operator admits a Dirac normal form and a constant-multiplicity indicial (critical weight) strip, yielding the trace/Poisson/Calderón package and a Lagrangian Cauchy data bundle Wcan = ran(C) ⊂ H = ker(A). The resulting canonical closed de Rham complex (Dom(dcan), d) (equivalently the associated self-adjoint Fredholm realization Dcan = dcan + δcan) satisfies H * (Dom(dcan), d) ∼ = IH * Wcan (X), and in the Witt case this reduces to middle-perversity intersection cohomology. We give nontrivial projective families of examples, including cones, joins, and fibered homogeneous singularities.