Negative correlation in uniform forests of complete graphs

This repository accompanies Anish Gupta's preprint Edges of the uniform random forest of K_n are pairwise negatively correlated for every n.

The paper proves pairwise negative correlation for every complete graph. It reduces the disjoint-edge inequality to exact component and degree moments, uses effective analytic bounds above a finite threshold, and checks the remaining values by exact integer recurrence.

• Read the paper
• Citable preprint v1 on Zenodo
• See the preferred citation

Verification

The standalone checker uses only Python's standard library.

make check       # fast diagnostic seam; explicitly not proof-complete
make check-proof # proof-complete finite/analytic overlap
make check-full  # wider seam and independent pair-count checks
make paper       # reproducible three-pass PDF build

Status: preprint, 7 August 2026. This repository is a public landing page and reproducibility companion; it is not a claim of peer review.

Repository contents

paper/                    manuscript source, bibliography, and PDF
tests/check.py            standalone exact and analytic verifier
evidence/SHA256SUMS.txt   release-tree integrity manifest
CITATION.cff              citation metadata
LICENSES.md               manuscript/software licence boundary

Citation

The citable preprint v1 is archived at doi:10.5281/zenodo.21833802. Preferred citation metadata are provided in CITATION.cff.

Software and the Makefile are MIT-licensed. The manuscript and public documentation are CC BY 4.0; see LICENSES.md.

Contact: Anish Gupta, independent researcher, ag2269@cantab.ac.uk, ORCID 0009-0008-8137-7729.