GPT-5.6 Sol Ultra Proves the Cycle Double Cover Conjecture

GPT-5.6 Sol Ultra produces proof of the Cycle Double Cover Conjecture [pdf]

I present a complete proof of the Cycle Double Cover Conjecture, a decades-old problem in graph theory. This breakthrough was achieved entirely by GPT-5.6 Sol Ultra, with the writeup assisted by Codex. By leveraging the 8-flow theorem and elementary linear algebra, we demonstrate that every finite bridgeless undirected graph possesses a collection of cycles covering each edge exactly twice.

"The proof in this note is entirely due to GPT 5.6 Sol Ultra and the writeup with Codex."