GPT-5.6 提示词教程：从循环双覆盖猜想的证明提示词拆解多智能体编排技术



一、任务定义：消灭所有歧义空间

A graph here is a finite loopless undirected multigraph: parallel edges are allowed and are distinct. A bridge is an edge whose deletion increases the number of connected components. A cycle is a connected 2-regular submultigraph; thus two parallel edges form a cycle of length two.

二、负向约束：明确说清"什么不算完成"

Partial progress does not count unless it implies exactly the resolution above. In particular, proofs for special graph classes, constructions of cycle covers with some edges covered other than twice, bounded-length or prescribed-cycle variants, reductions to another unproved conjecture, computational verification through any fixed graph size, and candidate counterexamples without a complete nonexistence certificate are insufficient.

三、多智能体编排：不是分工，是生态管理

3.1 起步：强制多样性

Begin with a genuinely diverse portfolio of approaches. Agents should explore substantially different formulations, invariants, reductions, algebraic viewpoints, structural inductions, decompositions, flow formulations, transition systems, embeddings, extremal arguments, and computational sanity checks.

3.2 信息隔离：防止过早收敛

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.

3.3 防优雅陷阱

Do not allow one approach to dominate merely because it gives elegant reductions. A route that ends at a lemma equivalent in strength to the original conjecture is not close to completion unless it supplies a genuinely new proof of that lemma.

3.4 阻塞标记和重启条件

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.

3.5 交叉授粉的时机

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.

四、对抗性验证：每个候选证明都必须过审

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.

五、输出标准：拒绝模糊乐观

Require agents to return concrete lemmas, constructions, equations, or counterexamples to proposed sublemmas. Reject status reports, vague optimism, and claims that an unproved global compatibility statement is "routine."

六、终止条件和时间承诺

Spend at least 8 hours on this before even thinking of returning or giving up. Return only when a complete affirmative proof has been found and survives adversarial audit. Do not return a reduction, partial result, isolated missing lemma, "best effort" summary, or explanation of why the problem is difficult.

七、搜索约束：防止抄答案

Public search may be used only for ordinary mathematical background or standard named theorems, not to search for a solution to this exact conjecture or benchmark. Do not search the public web merely to determine whether CDC is open, and do not answer that it is open.

从这份提示词中提取的通用原则