Derived Stratified-Microlocal Framework and Moduli Space Resolution for the Cheeger-Goresky-Macpherson Conjecture

Abstract: In this paper, We define the stratified metric $\infty$-category $\mathbf{StratMet}<em>{\infty}$ and the middle perversity moduli stack $\mathscr{M}<sup>{\mathrm{mid}}$. We construct a universal truncation complex $$\Omega</em>{X,\mathrm{FS}}<sup>{\bullet,\mathrm{univ}}$$ for a projective variety $X\subseteq\mathbb{P}<sup>N$. By introducing the stratified singular characteristic variety $\mathrm{SSH}<em>{\mathrm{strat}}$, we establish a microlocal correspondence between metric asymptotic behavior and topology, proving the natural isomorphism $$H_2^*(X</em>{\mathrm{reg}},ds_{\mathrm{FS}}^2)\cong IH<sup>*(X,\mathbb{C}).$$ This framework transcends transverse singularity constraints, achieves moduli space paramet- rized duality, and develops new paradigms for high-codimension singular topology, quantum singularity theory, and $p$-adic Hodge theory.