ITERATED CALDER ÓN PACKAGES AND CANONICAL MEZZOPERVERSITIES FOR FUBINI-STUDY METRICS ON PROJECTIVE VARIETIES OF ARBITRARY STRATIFICATION DEPTH

Let X ⊂ CP N be a complex projective variety equipped with a Thom-Mather stratification of arbitrary depth, and let gFS be the induced Fubini-Study metric on X reg . By iterating a parameter-dependent Calderón package on the stratified link fibrations, we construct canonically defined Cauchy-data bundles {Wi,can}-equivalently, a canonical mezzoperversity Wcan in the sense of ideal boundary conditions-and a canonical self-adjoint Fredholm realization Dcan of the de Rham (Gauss-Bonnet) operator ∂ dR = d + δ on (X reg , gFS). The resulting canonical de Rham Hilbert complex (Dom(dcan), dcan) computes intersection cohomology in the form H • (Dom(dcan), dcan) ∼ = IH • Wcan (X), canonically; in the iterated Witt case this specializes to the middle-perversity theory IH • m(X ). The main new analytic input is an iterated stability theorem for domain-dependent tangential families: at each stratum, the tangential operator acts on a stratified link and its self-adjoint realization depends on the canonical boundary conditions already selected on deeper strata. We prove constant-rank kernel bundles and uniform spectral gaps for these families, yielding a constant-multiplicity critical strip and enabling the recursive Calderón construction.