Geometry of the Cosmic Web — experiments

Code for the research program scoped in the blog post _posts/2026-07-03-geometry-of-cosmic-web-research-program.md: does lifting the cosmic web to the position–orientation manifold R³×S² ≅ SE(3)/SO(2) improve filament extraction (claim C1), and do the dynamics follow sub-Riemannian geodesics there (claim C2)?

Layout

• src/ — pipeline modules:
  • fields.py — synthetic webs: Voronoi filament model (exact truth, optionally Bézier-curved) and Zel’dovich boxes; CIC deposit; galaxy sampling.
  • lift.py — orientation score on R³×S² (elongated anisotropic ridge filters, Fourier-domain) and hypoelliptic diffusion (splitting scheme).
  • spines.py — ridgeness fields (lifted + Hessian baseline), matched-length skeleton extraction, junction detection. Both methods share identical post-processing so the comparison isolates the lift.
  • metrics.py — M1 spine distance/completeness/purity, M2 junction P/R/F1 (defined in the scoping post, §5).
• scripts/run_e0.py — experiment E0a: calibrate on seed 1, evaluate on held-out seeds, straight (default) or curved (--curved) filaments. --smoke for a fast 64³ sanity run.
• scripts/smoke_test.py — assert-based self-checks.
• docs/ — experiment reports with figures in docs/figures/.
• artifacts/ — result JSONs (gitignored, regenerable).

Reproduce

cd research/cosmic-web
python3.13 -m venv .venv && .venv/bin/pip install numpy scipy matplotlib scikit-image
.venv/bin/python scripts/smoke_test.py
.venv/bin/python scripts/run_e0.py            # straight filaments, ~4 min
.venv/bin/python scripts/run_e0.py --curved   # curved filaments, ~4 min