CoreLumen Stage IX : Information Geometry of Cosmological Constraints

This document constitutes Stage IX of the CoreLumen Stage Series (v2.0). Stage IX performs an information-geometry analysis of the lockedStage VIII likelihood interface. Using exclusively the exportedderivative matrix (D) and covariance matrix (C), the effectiveFisher operator F_eff = D^T C^{-1} D is constructed and spectrallyanalyzed. No observable definitions, derivative protocols, covariance policies,or parameter bases are modified at this stage. The eigen-spectrum, condition number, effective rank (r_eff),and null-subspace structure are evaluated, together withthreshold-sweep robustness tests. Under the conservative single-bin linear weak-lensing baseline,the 12-dimensional response basis collapses to an effectiveinformation dimension r_eff ≈ 1.001,indicating intrinsic degeneracy of the adopted configuration. Stage IX records the information geometry of the lockedcomputation-layer interface and introduces no new theoreticalstructures or observational channels.