The Penrose limit along a null geodesic is intrinsic on the weighted associated-graded model determined by the null filtration, with a canonical tautological soldering to the ambient weighted normal geometry.
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MCBP detects boundaries by computing discrete mean curvature from k-nearest neighbor patches on the data manifold, then decomposes data into low-curvature smooth and high-curvature boundary subsets to improve clustering.
GTSA-PCA replaces global PCA covariance with curvature-weighted local operators and a geodesic alignment step to produce geometry-aware embeddings that improve on standard PCA and UMAP in small-sample high-curvature settings.
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Sachs Equations and Plane Waves VI: Penrose Limits
The Penrose limit along a null geodesic is intrinsic on the weighted associated-graded model determined by the null filtration, with a canonical tautological soldering to the ambient weighted normal geometry.