Cycle Double Cover Conjecture — GPT 5.6 Sol Ultra


Lab	OpenAI
Model	GPT 5.6 Sol Ultra
Field	Mathematics — graph theory
Result (yield)	Complete proof of the Cycle Double Cover Conjecture, a 1973-era open problem (Szekeres 1973 / Seymour 1979). Verified by adversarial multi-agent audit.
Date	2026
Source (PDF)	https://cdn.openai.com/pdf/04d1d1e4-bc75-476a-97cf-49055cd98d31/cdc_prompt.pdf

Why it's battle-tested

The prompt produced a full, unconditional proof of the Cycle Double Cover Conjecture for all finite bridgeless loopless multigraphs. The document above is OpenAI's verbatim release of the prompt as given.

Key prompt techniques

Precise, self-contained problem statement — all definitions (multigraph, bridge, cycle, cycle double cover) are given explicitly; no terms left to interpretation.
Explicit completion criteria — partial progress, special graph classes, bounded-length variants, reductions to other unproved conjectures, and fixed-size computational verification are named and excluded as insufficient.
Anti-circularity guards — forbids "proving" the conjecture via equivalent statements.
Aggressive dynamic multi-agent orchestration — up to 64 concurrent agents, portfolio diversity, independence preservation, approach-family registry, adversarial verification.
Anti-persuasion-by-optimism — status reports and "routine" hand-waves are rejected; concrete lemmas, constructions, equations or counterexamples are demanded.
Minimum time budget — "Spend at least 8 hours on this before even thinking of returning."
Scoped web use — background literature only; no searching for the solution itself, and no declaring the problem open.

Files

prompt.md — the full prompt, machine-extracted from the source PDF (prose is reliable; see the PDF for exact typography).