多智能体协作快速验证十个数学难题，方法高效且结果可追溯。
A First Proof Sprint
- 用依赖图分解定位证明漏洞，智能体协同生成与修正
- 5个问题有完整证明，3个有条件解决，2个留待后续补全
- 适合关注形式化验证与高效科研协作的研究者
本专著报告了针对十个研究级数学问题的多智能体证明冲刺，结合快速草稿生成、对抗性验证、定向修复与显式溯源。工作流采用命题依赖的线缆图分解来定位缺陷并协调审稿驱动的修订。最终结果多样但明确：数学层面，问题3在限定条件下存在完整验证路径（唯一性/不可约性视为可选），问题5在$F_O$-局部连通谱上以范围受限方式解决，问题10在明确假设下条件求解（假设失效时有显式反例），问题4和6为部分解决，一般情形中提出具体待完成任务（问题6有$K_n$的无条件结果，$c_0 = 1/3$）；问题7通过旋转路径定理链暂定闭合，需独立账本复核。质量控制层面，问题7和9存在节点级验证瑕疵，仍含未解决的验证缺口。主要方法论成果是：结构感知验证与层间切换策略能提升压缩证明冲刺中的可靠性与校准度。
原文摘要 · Abstract (English)
This monograph reports a multi-agent proof sprint on ten research-level problems, combining rapid draft generation with adversarial verification, targeted repair, and explicit provenance. The workflow uses wiring-diagram decompositions of claim dependencies to localize gaps and coordinate reviewer-driven revisions. Final outcomes are heterogeneous but explicit: the manuscript distinguishes mathematical status from QC-validation status. Mathematically, Problem~3 has a validation-complete existence path under the scoped criterion used here (uniqueness/irreducibility treated as optional), Problem 5 is solved in a scope-limited form for $F_O$-local connective spectra, Problem 10 is conditional under clearly stated assumptions (with explicit necessity counterexamples when assumptions are dropped), and Problems 4 and 6 are partial with named remaining obligations in the general case (including an unconditional $K_n$ result for Problem 6 with $c_0 = 1/3$). Problem 7 is treated as provisionally closed via the rotation-route theorem chain, pending independent ledger re-check. At the QC layer, Problems~7 and~9 have node-level validation artifacts but still contain unresolved verifier gaps. The main methodological result is that structure-aware verification and layer-switching strategies improve reliability and calibration in compressed proof sprints.
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