Adds geometry_stats() to _HVRTBase, providing model-agnostic geometric
diagnostics of the feature space after fitting:
- E[T], E[Q]: mean cooperation (pairwise z-sum) and Mahalanobis norm
- std_T, std_Q, cov_TQ, corr_TQ: distributional statistics
- frac_in_cone: fraction of samples in the cooperative cone {z: T > 0}
- cooperation_ratio: E[T] / E[Q]
- cone_degenerate: True when frac_in_cone < 0.05, > 0.95, or std_T < 1e-6
- cone_critical_angle_deg: arccos(1/sqrt(d)) in degrees
- partitions: per-partition breakdown of the above
Per-partition stats are included for local degeneracy analysis.
Accepts optional X argument; defaults to the fitted X_z_.
Grounded in theorems from the HVRTAnalysis paper:
Theorem 1: Cov(T,Q) = 0 for isotropic z
Theorem 2: E[T] = sum of pairwise feature correlations
Theorem 3: E[T] invariant to additive noise
Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>