discrete-geometry

Discrete Kakeya cover for LLM KV cache: D4/E8 nested-lattice quantisation realising a Kakeya-style tube-cover over the direction sphere. 2.4x-2.8x compression at <1% perplexity loss on Qwen3, Llama-3, DeepSeek, GLM-4, Gemma. Drop-in transformers.DynamicCache. pip install kakeyalattice.

This repository is associated with the paper: “A Poset-Based Approach to Curvature of Hypergraphs”

Disk covering problem (disc covering): global optimality proof claims for n = 11-20, exact certificates, Chinese proofs, and reproducible verification code. External review pending.

A Codex research workbench for discrete geometry and geometric analysis

An SAT encoding of Erdős-Szekeres conjecture, including counterexamples of its variants

Independent Python reproduction of the 2026 OpenAI/Sawin disproof of the Erdős unit-distance conjecture. mpmath-200-bit verbatim match (0.01% rel.err) to equation (2.2) of the remarks PDF. MIT, NumPy + mpmath only.

Новые верхние оценки хроматических чисел евклидовых пространств: χ(ℝ⁴)≤43, χ(ℝ⁵)≤132, χ(ℝ⁷)≤1029, χ(ℝ⁹)≤7203, χ(ℝ¹⁰)≤45619 — код, точные сертификаты и статьи

Collaborative research on Erdős Problem 99 using autonomous agents, reproducible mathematical evidence, and independent review.

Rigorous bounds and reproducible certificates for covering the unit disk with 100 equal disks, with constructions, local results and failed routes; the global optimum remains open.

Two chiral 36-point witnesses for C(13) >= 36 (no 5 points on a sphere or plane in the 13x13x13 grid). Exact integer certificates, two independent verifiers.

Certificate-backed lower bounds for AlphaEvolve Problem 6.60, through C(20) >= 50

Explicit 4,096-cylinder cover of the regular tetrahedron with normalized area 0.4996138 (saving 3.86e-4 below 1/2), openai/math problem 100, with two independent exact checkers

Computational-geometry research on the minimum central circle problem: certified finite optima and global asymptotic theory.

Exactly certified work on Heilbronn's triangle problem: one improved lower bound in the unit disk (n=14), plus a rigidity audit of the unit-square landscape. Every number re-derived from integers in exact arithmetic.

Numerical attack on the Erdos unit-distance problem: a complete graph of unit-rest-length springs, annealed then projected onto exact unit distances. Matches every proven optimum for n <= 14, with audited counts and a live 2D view.

Exact results on cone-order intervals: the Ball-Lens Lemma, closed-form interval and boundary counts on lattices, dimension recovery, and an identifiability boundary for winding on diluted causal cylinders. Every claim machine-verified; reviewers welcome.

Edge-disjoint triangulations of convex polygons: packing number floor(n/2), resolutions of P_2m, and their classification (2^(m-2) of them)

Packings of equal circles, spheres and hyperspheres (Packomania, 21 tables). 6,071 records released; 4,063 still best-known on 2026-10-18 (2,008 since beaten or tied by others, listed in SUPERSEDED.csv). Each verified by two independent exact checkers. By Moki&Julio.

No symmetric 12-face Szilassi polyhedron: a computer-assisted proof with DRAT certificates (36 SAT instances, independent encodings, one-command reproduction).

Proof package for a certified pointwise lower bound in the Erdős unit-distance problem