From Classical State Geometry to Chiral Quantum State Geometry: A Unified Relational Framework

We present a unified three-layer framework: Classical State Geometry (CSG) as a strictly 3D timeless foundation, Quantum State Geometry (QSG) as its quantization via coarse-graining, and Chiral Quantum State Geometry (CQSG) as the extension to signed gravity. CSG is defined on shape space $\mathcal{S}=\mathcal{C}/\mathcal{G}$ with $\mathcal{G}=\text{Diff}(\Sigma)\ltimes \text{Conf}(\Sigma)$, with entropic time $d\tau_O=dS_O/\sigma_O$, emergent 4D metric $ds_4^2=-N_O^2 dS_O^2+\tilde h_{ij}dx^i dx^j$, speed limit $v^2