Techniques for coordinating many agents to solve hard problems (from OpenAI's prompt for proving the Cycle Double Cover Conjecture)
> Begin with a ... diverse portfolio of approaches. Agents should explore substantially different formulations, invariants, reductions ...
> Maintain an explicit registry of approach families. Group agents by the mathematical idea they are using, not by superficial wording. If many agents converge to one family, redirect some of them toward underexplored formulations.
> Do not tell most agents the currently favored approach. Preserve independence during early rounds so that agents do not all converge to the same attractive but incomplete reduction.
> Keep several incompatible proof routes alive through multiple rounds. Cross-pollinate ideas only after independent agents have developed them far enough to expose their real strengths and gaps.
> When an approach stalls at a theorem-strength missing lemma, mark that route as blocked. Only continue assigning agents to it if someone proposes a materially new mechanism, invariant, or construction.
> Use adversarial agents throughout: every candidate proof must be checked for exact-two multiplicity, repeated-edge closed trails masquerading as cycles, parallel-edge 2-cycles, disconnected graphs, cutvertices, bridges introduced by reductions, and circular use of an equivalent CDC statement.
Ethan Knight (@eknight)
Yesterday, we made GPT-5.6 Sol Ultra generally available. Today, we're sharing that it produced a proof of the 50-year-old Cycle Double Cover Conjecture using 64 subagents in just under one hour. We're sharing the prompt and proof below. We're excited to see what you all do with Ultra!
— https://nitter.net/eknight/status/2075643450196971805#m