A software that assists a previous version of the proof of Gerver's conjecture, using a custom geometric branch-and-bound algorithm, and the exact rational QP solver powered by CGAL

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”

Solver for realizability of pseudo-points (through CC-systems / signotopes / triple orientations).

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

Tracing curve on 2D plane = drawing curve on complex (2D) plane. Curve is a field line or equipotential line of potential scalar field.

tc18.org web site (https://www.tc18.org)

Certified unit-distance point sets and graphs for discrete geometry in Rust.

Implements digitized transformations defined in the space with geometric algebra (mostly Klein lib).

Geometric-Electromagnetic Model (GEM): A topological reformulation of the quantum vacuum as a Riemann-Cartan manifold with icosahedral substructure. Includes the published paper (DOI: 10.5281/zenodo.21268209), foundational documents, and experimental protocols.

Code for publication: Hypergraph Geometry Reflects Higher-Order Dynamics in Protein Interaction Networks; Kevin A. Murgas, Emil Saucan, Romeil Sandhu; Scientific Reports (2022)

A 14-vertex 6-chromatic distance graph in the Euclidean plane (prescribed distances 1, 1/sqrt3, 2) with clique number 4 - plus a proof that this distance system admits no K5 at all. Human-readable proofs, exact data, SAT+CI verification

Rust app matching unit-distance templates against public point datasets.

Ideal horoball packings of triangulated spheres: solvers, placements, and bracket proofs.

First independent byte-exact reproduction of the Zinoviev-Ericson (1999) K(13) = 1154 kissing configuration in R^13, with full optimization pipeline, 13 paper-grade structural findings on dim-13 saturation, rare-paths doctrine, and dual Constructor/Auditor methodology with both-hats discipline.

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.

Discrete-geometry and wave simulation on tetrakis-square lattices: inject curvature by removing wedges and analyze graph spectra and dynamics.

Rust prototype exploring public mRNA sequence-feature data with unit-distance templates.

Exhaustive study in 4D of the Euler cell-composedness

Certified computations and Supnick/anti-Monge TSP proof for arranging circles around a central circle.