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README.md

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+---
+license: mit
+task_categories:
+  - other
+tags:
+  - point-cloud
+  - geometry
+  - topology
+  - benchmark
+  - higher-dimensions
+  - synthetic
+pretty_name: HyperShadow
+size_categories:
+  - 10K<n<100K
+---
+
+# HyperShadow
+
+A benchmark for one question: given a 3D point cloud, can you tell whether
+it is an ordinary 3D object or the 3D projection (the "shadow") of an
+object from a higher spatial dimension?
+
+Most datasets that say "4D" mean 3D plus time. Here the extra dimensions
+are spatial: label 1 clouds are projections of objects living in R^4, R^5
+or R^6 (hyperspheres, tesseracts, Clifford tori, duocylinders, hypertori,
+random smooth manifolds), rotated randomly in their ambient space before
+projection. Label 0 clouds are native 3D shapes given the same rotation
+and corruption treatment, so nothing in the preprocessing separates the
+classes.
+
+## Why this is an interesting task
+
+A shadow is still at most 3-dimensional data, so intrinsic-dimension
+estimation cannot solve this. On this benchmark, TwoNN and the
+Levina-Bickel MLE reach about 71-73% accuracy. What actually separates
+the classes are the traces the projection map leaves behind: density
+folds, volumes filled with a particular radial profile, changed topology.
+A small PointNet (190k parameters) picks these up at 96.6%, and still
+detects shape families it was never trained on (79-91%).
+
+The temporal track has the strongest result, and it needs no learning at
+all. A rigid 3D object in rigid motion can be aligned frame to frame by a
+rigid 3D transform with near-zero residual. The shadow of a rigidly
+rotating 4D object cannot: no rigid 3D motion explains it. The mean
+Kabsch alignment residual, one number per sequence, separates the classes
+at AUROC 0.982.
+
+## Files
+
+| file | contents |
+|---|---|
+| `static.npz` | `points`: float32 (10800, 1024, 3); `labels`: int64 (10800,) |
+| `static_meta.json` | per-sample shape name, ambient dimension, corruption tier, projection type |
+| `temporal.npz` | `points`: float32 (1800, 16, 512, 3), rigid-rotation sequences; `labels` |
+| `temporal_meta.json` | per-sequence metadata |
+
+Labels: 0 = native 3D, 1 = projection of a higher-dimensional object.
+Classes are balanced across corruption tiers. All clouds are centred,
+scaled to unit mean radius, and resampled to a fixed point count.
+
+Corruption tiers (cumulative): 0 clean; 1 Gaussian jitter (2% of scale);
+2 plus random half-space occlusion; 3 plus heavier jitter and
+distance-dependent dropout.
+
+## Loading
+
+```python
+import numpy as np
+
+d = np.load("static.npz")
+x, y = d["points"], d["labels"]     # (10800, 1024, 3), (10800,)
+
+t = np.load("temporal.npz")
+seq = t["points"]                    # (1800, 16, 512, 3)
+```
+
+## Baseline numbers to beat
+
+| Method | Accuracy (static) |
+|---|---|
+| intrinsic dimension, best threshold | 0.732 |
+| persistent homology + GBT | 0.904 |
+| geometric features + GBT | 0.956 |
+| PointNet-lite, 190k params | 0.966 |
+
+Temporal track: Kabsch rigidity residual threshold, AUROC 0.982.
+
+## Reproducing or extending
+
+The generator is plain seeded NumPy, no GPU needed. Code, tests, and all
+baseline implementations are in the GitHub repository (link in the
+citation section once the paper is up). Regenerating with the published
+seeds reproduces these exact files. New shape families can be added with
+a single sampler function.
+
+## Limitations
+
+Everything here is simulated, under specific choices of sampling measure,
+projection model and noise. Results on this data say nothing about
+physical reality. The intended uses are: benchmarking point-cloud models
+on a task where the ground truth is known and the shortcut routes have
+been closed off, studying out-of-distribution detection with a
+mathematically defined "out", and comparing machine performance against
+the human 4D-rigidity perception results reported by He, Bi and Zaidi
+(2023).
+
+## Citation
+
+```bibtex
+@misc{hypershadow2026,
+  title  = {HyperShadow: A Benchmark for Detecting 3D Projections of
+            Higher-Dimensional Spatial Objects},
+  author = {Sasi, Akshay},
+  year   = {2026},
+}
+```