no-way-labs/residue
Hamiltonian decomposition of Z_m^3 Cayley digraphs for all m 2 — a complete solution to Knuth's "Claude's Cycles," found by LLM agents under a structured exploration prompt. Constructions, proofs, Lean formalization, and a verification suite.
Why it is useful
residue is a recent open-source project in Formal Methods. It is included because it has recent repository activity and can support mathematical learning, research, modelling, software development, or AI workflows.
Repository at a glance
- Owner: no-way-labs
- Primary language: TeX
- Latest update: 2026-07-31
- Stars / forks: 26 / 3
- License: MIT
- Links: Official project site
Good starting points
- Read the project README and installation instructions.
- Try the smallest example before changing parameters or datasets.
- Check tests, issues, and release notes before relying on results in teaching or research.
- Cite the repository and its license when reusing code or figures.
README snapshot
Hamiltonian decomposition of Z_m^3 Cayley digraphs for all m 2. This repository contains constructions, proofs, exploration logs, and a verification suite for the Hamiltonian decomposition problem posed by Knuth in "Claude's Cycles" (2026). Consider the digraph with m^3 vertices ijk for 0 ≤ i, j, k m, and three arcs from each vertex: to i⁺jk, ij⁺k, and ijk⁺, where i⁺ = (i+1) mod m. Decompose the arcs into three directed Hamiltonian cycles, for all m 2. Knuth's Claude solved the odd case in 31 explorations with significant human guidan