combinatorial-geometry

Code to reproduce the numerical results and figures of the paper "Fast Hamiltonian engineering from cut polytope geometry".

Extremal lattice rigidity from the No-Three-In-Line problem: symmetry, fundamental domains, and Sidon structures.

This project features a Manim-based animation of a combinatorial geometry problem, created as a hands-on exercise to learn the MANIM library.

Edge-disjoint non-crossing triangle packings of planar point sets: a convex barrier and a reduction to subcubic trees

Lean 4 formalization of Sierksma's conjecture for nine points in R^3 (d = 3, r = 3)

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.

Erdos problem #1086: how many triangles of one area can n points in the plane span? Open. An explicit constant 6e^gamma/pi^2 = 1.0828 in the square-grid lower bound n^2 log log n (informal proof), g(5)=7, g(6)=12 (computer-assisted), and exact grid counts to 800x800.